18,050 research outputs found
Parallel computation of optimized arrays for 2-D electrical imaging surveys
Modern automatic multi-electrode survey instruments have made it possible to use non-traditional arrays to maximize the subsurface resolution from electrical imaging surveys. Previous studies have shown that one of the best methods for generating optimized arrays is to select the set of array configurations that maximizes the model resolution for a homogeneous earth model. The ShermanâMorrison Rank-1 update is used to calculate the change in the model resolution when a new array is added to a selected set of array configurations. This method had the disadvantage that it required several hours of computer time even for short 2-D survey lines. The algorithm was modified to calculate the change in the model resolution rather than the entire resolution matrix. This reduces the computer time and memory required as well as the computational round-off errors. The matrixâvector multiplications for a single add-on array were replaced with matrixâmatrix multiplications for 28 add-on arrays to further reduce the computer time. The temporary variables were stored in the double-precision Single Instruction Multiple Data (SIMD) registers within the CPU to minimize computer memory access. A further reduction in the computer time is achieved by using the computer graphics card Graphics Processor Unit (GPU) as a highly parallel mathematical coprocessor. This makes it possible to carry out the calculations for 512 add-on arrays in parallel using the GPU. The changes reduce the computer time by more than two orders of magnitude. The algorithm used to generate an optimized data set adds a specified number of new array configurations after each iteration to the existing set. The resolution of the optimized data set can be increased by adding a smaller number of new array configurations after each iteration. Although this increases the computer time required to generate an optimized data set with the same number of data points, the new fast numerical routines has made this practical on commonly available microcomputers
A General Framework for the Construction and the Smoothing of Forward Rate Curves
This paper establishes a general theoretical and numerical framework for the construction and the smoothing of instantaneous forward rate curves. It is shown that if the smoothness of a curve is defined as an integral of a function in the derivatives of the curve, then the optimal curves are splines that satisfy certain ordinary differential equations. For such curves, and efficient numerical method is given for the determination of the spline parameters subject to mild assumptions. The resulting forward rate curves do not generally possess the desired degree of smoothness due mainly to the constraints imposed on the curves by the various market observed prices. A Partial solution to this problem is then introduced which achieves additional smoothing by taking into account the bid-ask ranges of each market rate. This eliminates much of the oscillatory patterns and the points of high curvature, and produces curves that are ideal for applications such as the estimation of interest rate models, and the pricing and risk management of interest rate derivatives, which are sensitive to forward rate curves.
Distribution functions of Poisson random integrals: Analysis and computation
We want to compute the cumulative distribution function of a one-dimensional
Poisson stochastic integral I(\krnl) = \displaystyle \int_0^T \krnl(s) N(ds),
where is a Poisson random measure with control measure and \krnl is a
suitable kernel function. We do so by combining a Kolmogorov-Feller equation
with a finite-difference scheme. We provide the rate of convergence of our
numerical scheme and illustrate our method on a number of examples. The
software used to implement the procedure is available on demand and we
demonstrate its use in the paper.Comment: 28 pages, 8 figure
Direct estimation of kinetic parametric images for dynamic PET.
Dynamic positron emission tomography (PET) can monitor spatiotemporal distribution of radiotracer in vivo. The spatiotemporal information can be used to estimate parametric images of radiotracer kinetics that are of physiological and biochemical interests. Direct estimation of parametric images from raw projection data allows accurate noise modeling and has been shown to offer better image quality than conventional indirect methods, which reconstruct a sequence of PET images first and then perform tracer kinetic modeling pixel-by-pixel. Direct reconstruction of parametric images has gained increasing interests with the advances in computing hardware. Many direct reconstruction algorithms have been developed for different kinetic models. In this paper we review the recent progress in the development of direct reconstruction algorithms for parametric image estimation. Algorithms for linear and nonlinear kinetic models are described and their properties are discussed
Detection of exomoons in simulated light curves with a regularized convolutional neural network
Many moons have been detected around planets in our Solar System, but none
has been detected unambiguously around any of the confirmed extrasolar planets.
We test the feasibility of a supervised convolutional neural network to
classify photometric transit light curves of planet-host stars and identify
exomoon transits, while avoiding false positives caused by stellar variability
or instrumental noise. Convolutional neural networks are known to have
contributed to improving the accuracy of classification tasks. The network
optimization is typically performed without studying the effect of noise on the
training process. Here we design and optimize a 1D convolutional neural network
to classify photometric transit light curves. We regularize the network by the
total variation loss in order to remove unwanted variations in the data
features. Using numerical experiments, we demonstrate the benefits of our
network, which produces results comparable to or better than the standard
network solutions. Most importantly, our network clearly outperforms a
classical method used in exoplanet science to identify moon-like signals. Thus
the proposed network is a promising approach for analyzing real transit light
curves in the future
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