LOFAR, a new low frequency radio telescope

LOFAR, the Low Frequency Array, is a large radio telescope consisting of approximately 100 soccer-field sized antenna stations spread over a region of 400 km in diameter. It will operate at frequencies from ~10 to 240 MHz, with a resolution at 240 MHz of better than an arcsecond. Its superb sensitivity will allow for studies of a broad range of astrophysical topics, including reionisation, transient radio sources and cosmic rays, distant galaxies and AGNs. In this contribution a status rapport of the LOFAR project and an overview of the science case is presented.Comment: 6 Pages, including 1 postScript figure. To appear in the proceedings of the conference "Radio Galaxies: Past, present and future", Leiden, 11-15 Nov 200

Constructing Cubature Formulas of Degree 5 with Few Points

This paper will devote to construct a family of fifth degree cubature formulae for $n$-cube with symmetric measure and $n$-dimensional spherically symmetrical region. The formula for $n$-cube contains at most $n^2+5n+3$ points and for $n$-dimensional spherically symmetrical region contains only $n^2+3n+3$ points. Moreover, the numbers can be reduced to $n^2+3n+1$ and $n^2+n+1$ if $n=7$ respectively, the later of which is minimal.Comment: 13 page

Strategic programming on graph rewriting systems

We describe a strategy language to control the application of graph rewriting rules, and show how this language can be used to write high-level declarative programs in several application areas. This language is part of a graph-based programming tool built within the port-graph transformation and visualisation environment PORGY.Comment: In Proceedings IWS 2010, arXiv:1012.533

Sparse Pseudospectral Approximation Method

Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses a numerical integration rule to approximate the Fourier-type coefficients of a truncated expansion in orthogonal polynomials. For problems in more than two or three dimensions, a sparse grid numerical integration rule offers accuracy with a smaller node set compared to tensor product approximation. However, when using a sparse rule to approximately integrate these coefficients, one often finds unacceptable errors in the coefficients associated with higher degree polynomials. By reexamining Smolyak's algorithm and exploiting the connections between interpolation and projection in tensor product spaces, we construct a sparse pseudospectral approximation method that accurately reproduces the coefficients of basis functions that naturally correspond to the sparse grid integration rule. The compelling numerical results show that this is the proper way to use sparse grid integration rules for pseudospectral approximation

Fuzzy Modeling for Uncertain Nonlinear Systems Using Fuzzy Equations and Z-Numbers

In this paper, the uncertainty property is represented by Z-number as the coefficients and variables of the fuzzy equation. This modification for the fuzzy equation is suitable for nonlinear system modeling with uncertain parameters. Here, we use fuzzy equations as the models for the uncertain nonlinear systems. The modeling of the uncertain nonlinear systems is to find the coefficients of the fuzzy equation. However, it is very difficult to obtain Z-number coefficients of the fuzzy equations. Taking into consideration the modeling case at par with uncertain nonlinear systems, the implementation of neural network technique is contributed in the complex way of dealing the appropriate coefficients of the fuzzy equations. We use the neural network method to approximate Z-number coefficients of the fuzzy equations

Uncertainty quantification of inflow boundary condition and proximal arterial stiffness coupled effect on pulse wave propagation in a vascular network

International audienceSUMMARY This work aims at quantifying the effect of inherent uncertainties from cardiac output on the sensitivity of a human compliant arterial network response based on stochastic simulations of a reduced-order pulse wave propagation model. A simple pulsatile output form is utilized to reproduce the most relevant cardiac features with a minimum number of parameters associated with left ventricle dynamics. Another source of critical uncertainty is the spatial heterogeneity of the aortic compliance which plays a key role in the propagation and damping of pulse waves generated at each cardiac cycle. A continuous representation of the aortic stiffness in the form of a generic random field of prescribed spatial correlation is then considered. Resorting to a stochastic sparse pseudospectral method, we investigate the spatial sensitivity of the pulse pressure and waves reflection magnitude with respect to the different model uncertainties. Results indicate that uncertainties related to the shape and magnitude of the prescribed inlet flow in the proximal aorta can lead to potent variation of both the mean value and standard deviation of blood flow velocity and pressure dynamics due to the interaction of different wave propagation and reflection features. These results have potential physiological and pathological implications. They will provide some guidance in clinical data acquisition and future coupling of arterial pulse wave propagation reduced-order model with more complex beating heart models

Simulation-based optimal Bayesian experimental design for nonlinear systems

The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general mathematical framework and an algorithmic approach for optimal experimental design with nonlinear simulation-based models; in particular, we focus on finding sets of experiments that provide the most information about targeted sets of parameters. Our framework employs a Bayesian statistical setting, which provides a foundation for inference from noisy, indirect, and incomplete data, and a natural mechanism for incorporating heterogeneous sources of information. An objective function is constructed from information theoretic measures, reflecting expected information gain from proposed combinations of experiments. Polynomial chaos approximations and a two-stage Monte Carlo sampling method are used to evaluate the expected information gain. Stochastic approximation algorithms are then used to make optimization feasible in computationally intensive and high-dimensional settings. These algorithms are demonstrated on model problems and on nonlinear parameter estimation problems arising in detailed combustion kinetics.Comment: Preprint 53 pages, 17 figures (54 small figures). v1 submitted to the Journal of Computational Physics on August 4, 2011; v2 submitted on August 12, 2012. v2 changes: (a) addition of Appendix B and Figure 17 to address the bias in the expected utility estimator; (b) minor language edits; v3 submitted on November 30, 2012. v3 changes: minor edit