12,725 research outputs found

    Distribution of Gaussian Process Arc Lengths

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    We present the first treatment of the arc length of the Gaussian Process (GP) with more than a single output dimension. GPs are commonly used for tasks such as trajectory modelling, where path length is a crucial quantity of interest. Previously, only paths in one dimension have been considered, with no theoretical consideration of higher dimensional problems. We fill the gap in the existing literature by deriving the moments of the arc length for a stationary GP with multiple output dimensions. A new method is used to derive the mean of a one-dimensional GP over a finite interval, by considering the distribution of the arc length integrand. This technique is used to derive an approximate distribution over the arc length of a vector valued GP in Rn\mathbb{R}^n by moment matching the distribution. Numerical simulations confirm our theoretical derivations.Comment: 10 pages, 4 figures, Accepted to The 20th International Conference on Artificial Intelligence and Statistics (AISTATS

    Perspectives on subnational carbon and climate footprints: A case study of Southampton, UK

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    Sub-national governments are increasingly interested in local-level climate change management. Carbon- (CO2 and CH4) and climate-footprints—(Kyoto Basket GHGs) (effectively single impact category LCA metrics, for global warming potential) provide an opportunity to develop models to facilitate effective mitigation. Three approaches are available for the footprinting of sub-national communities. Territorial-based approaches, which focus on production emissions within the geo-political boundaries, are useful for highlighting local emission sources but do not reflect the transboundary nature of sub-national community infrastructures. Transboundary approaches, which extend territorial footprints through the inclusion of key cross boundary flows of materials and energy, are more representative of community structures and processes but there are concerns regarding comparability between studies. The third option, consumption-based, considers global GHG emissions that result from final consumption (households, governments, and investment). Using a case study of Southampton, UK, this chapter develops the data and methods required for a sub-national territorial, transboundary, and consumption-based carbon and climate footprints. The results and implication of each footprinting perspective are discussed in the context of emerging international standards. The study clearly shows that the carbon footprint (CO2 and CH4 only) offers a low-cost, low-data, universal metric of anthropogenic GHG emission and subsequent management

    Implementing vertex dynamics models of cell populations in biology within a consistent computational framework

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    The dynamic behaviour of epithelial cell sheets plays a central role during development, growth, disease and wound healing. These processes occur as a result of cell adhesion, migration, division, differentiation and death, and involve multiple processes acting at the cellular and molecular level. Computational models offer a useful means by which to investigate and test hypotheses about these processes, and have played a key role in the study of cell–cell interactions. However, the necessarily complex nature of such models means that it is difficult to make accurate comparison between different models, since it is often impossible to distinguish between differences in behaviour that are due to the underlying model assumptions, and those due to differences in the in silico implementation of the model. In this work, an approach is described for the implementation of vertex dynamics models, a discrete approach that represents each cell by a polygon (or polyhedron) whose vertices may move in response to forces. The implementation is undertaken in a consistent manner within a single open source computational framework, Chaste, which comprises fully tested, industrial-grade software that has been developed using an agile approach. This framework allows one to easily change assumptions regarding force generation and cell rearrangement processes within these models. The versatility and generality of this framework is illustrated using a number of biological examples. In each case we provide full details of all technical aspects of our model implementations, and in some cases provide extensions to make the models more generally applicable

    A temperate river estuary is a sink for methanotrophs adapted to extremes of pH, temperature and salinity

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    River Tyne (UK) estuarine sediments harbour a genetically and functionally diverse community of methane-oxidizing bacteria (methanotrophs), the composition and activity of which were directly influenced by imposed environmental conditions (pH, salinity, temperature) that extended far beyond those found in situ. In aerobic sediment slurries methane oxidation rates were monitored together with the diversity of a functional gene marker for methanotrophs (pmoA). Under near in situ conditions (4-30°C, pH 6-8, 1-15gl-1 NaCl), communities were enriched by sequences affiliated with Methylobacter and Methylomonas spp. and specifically a Methylobacter psychrophilus-related species at 4-21°C. More extreme conditions, namely high temperatures ≥40°C, high ≥9 and low ≤5 pH, and high salinities ≥35gl-1 selected for putative thermophiles (Methylocaldum), acidophiles (Methylosoma) and haloalkaliphiles (Methylomicrobium). The presence of these extreme methanotrophs (unlikely to be part of the active community in situ) indicates passive dispersal from surrounding environments into the estuary

    Head and Flow Observations on a High- Efficiency Free Centrifugal-Pump Impeller

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    A series of studies of the flow through the various components of hydrodynamic machinery is in progress in the Hydraulic Machinery Laboratory of the California Institute of Technology. Observations have been made on an impeller patterned after the Grand Coulee design. The impeller was operated as an isolated unit hydraulically free of the casing. The flow pattern at the discharge has been determined quantitatively for one flow rate, and a head-capacity curve for the impeller has been obtained. This paper constitutes a report on the findings up to the present

    The Complexity of Admissibility in Omega-Regular Games

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    Iterated admissibility is a well-known and important concept in classical game theory, e.g. to determine rational behaviors in multi-player matrix games. As recently shown by Berwanger, this concept can be soundly extended to infinite games played on graphs with omega-regular objectives. In this paper, we study the algorithmic properties of this concept for such games. We settle the exact complexity of natural decision problems on the set of strategies that survive iterated elimination of dominated strategies. As a byproduct of our construction, we obtain automata which recognize all the possible outcomes of such strategies

    The interplay between tissue growth and scaffold degradation in engineered tissue constructs

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    In vitro tissue engineering is emerging as a potential tool to meet the high demand for replacement tissue, caused by the increased incidence of tissue degeneration and damage. A key challenge in this field is ensuring that the mechanical properties of the engineered tissue are appropriate for the in vivo environment. Achieving this goal will require detailed understanding of the interplay between cell proliferation, extracellular matrix (ECM) deposition and scaffold degradation.\ud \ud In this paper, we use a mathematical model (based upon a multiphase continuum framework) to investigate the interplay between tissue growth and scaffold degradation during tissue construct evolution in vitro. Our model accommodates a cell population and culture medium, modelled as viscous fluids, together with a porous scaffold and ECM deposited by the cells, represented as rigid porous materials. We focus on tissue growth within a perfusion bioreactor system, and investigate how the predicted tissue composition is altered under the influence of (i) differential interactions between cells and the supporting scaffold and their associated ECM, (ii) scaffold degradation, and (iii) mechanotransduction-regulated cell proliferation and ECM deposition.\ud \ud Numerical simulation of the model equations reveals that scaffold heterogeneity typical of that obtained from μCT scans of tissue engineering scaffolds can lead to significant variation in the flow-induced mechanical stimuli experienced by cells seeded in the scaffold. This leads to strong heterogeneity in the deposition of ECM. Furthermore, preferential adherence of cells to the ECM in favour of the artificial scaffold appears to have no significant influence on the eventual construct composition; adherence of cells to these supporting structures does, however, lead to cell and ECM distributions which mimic and exaggerate the heterogeneity of the underlying scaffold. Such phenomena have important ramifications for the mechanical integrity of engineered tissue constructs and their suitability for implantation in vivo
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