Fast ray-tracing algorithm for circumstellar structures (FRACS) II. Disc parameters of the B[e] supergiant CPD-57 degrees 2874 from VLTI/MIDI data

Context. B[e] supergiants are luminous, massive post-main sequence stars exhibiting non-spherical winds, forbidden lines, and hot dust in a disc-like structure. The physical properties of their rich and complex circumstellar environment (CSE) are not well understood, partly because these CSE cannot be easily resolved at the large distances found for B[e] supergiants (typically greater than or similar to 1 kpc). Aims. From mid-IR spectro-interferometric observations obtained with VLTI/MIDI we seek to resolve and study the CSE of the Galactic B[e] supergiant CPD-57 degrees 2874. Methods. For a physical interpretation of the observables (visibilities and spectrum) we use our ray-tracing radiative transfer code (FRACS), which is optimised for thermal spectro-interferometric observations. Results. Thanks to the short computing time required by FRACS (<10 s per monochromatic model), best-fit parameters and uncertainties for several physical quantities of CPD-57 degrees 2874 were obtained, such as inner dust radius, relative flux contribution of the central source and of the dusty CSE, dust temperature profile, and disc inclination. Conclusions. The analysis of VLTI/MIDI data with FRACS allowed one of the first direct determinations of physical parameters of the dusty CSE of a B[e] supergiant based on interferometric data and using a full model-fitting approach. In a larger context, the study of B[e] supergiants is important for a deeper understanding of the complex structure and evolution of hot, massive stars.

A new algorithm and refined bounds for extended gcd computation

Extended gcd computation is interesting itself. It also plays a fundamental role in other calculations. We present a new algorithm for solving the extended gcd problem. This algorithm has a particularly simple description and is practical. It also provides refined bounds on the size of the multipliers obtained.

An augmented Lanczos algorithm for the efficient computation of a dot-product of a function of a large sparse symmetric matrix

The Lanczos algorithm is appreciated in many situations due to its speed. and economy of storage. However, the advantage that the Lanczos basis vectors need not be kept is lost when the algorithm is used to compute the action of a matrix function on a vector. Either the basis vectors need to be kept, or the Lanczos process needs to be applied twice. In this study we describe an augmented Lanczos algorithm to compute a dot product relative to a function of a large sparse symmetric matrix, without keeping the basis vectors.

Multi-centre validation of an automatic algorithm for fast 4D myocardial segmentation in cine CMR datasets

Quantitative analysis of cine cardiac magnetic resonance (CMR) images for the assessment of global left ventricular morphology and function remains a routine task in clinical cardiology practice. To date, this process requires user interaction and therefore prolongs the examination (i.e. cost) and introduces observer variability. In this study, we sought to validate the feasibility, accuracy, and time efficiency of a novel framework for automatic quantification of left ventricular global function in a clinical setting.

Vertex component analysis: a fast algorithm to extract endmembers spectra from hyperspectral data

Chapter in Book Proceedings with Peer Review First Iberian Conference, IbPRIA 2003, Puerto de Andratx, Mallorca, Spain, JUne 4-6, 2003. Proceedings

Vertex component analysis: a fast algorithm to unmix hyperspectral data

Given a set of mixed spectral (multispectral or hyperspectral) vectors, linear spectral mixture analysis, or linear unmixing, aims at estimating the number of reference substances, also called endmembers, their spectral signatures, and their abundance fractions. This paper presents a new method for unsupervised endmember extraction from hyperspectral data, termed vertex component analysis (VCA). The algorithm exploits two facts: (1) the endmembers are the vertices of a simplex and (2) the affine transformation of a simplex is also a simplex. In a series of experiments using simulated and real data, the VCA algorithm competes with state-of-the-art methods, with a computational complexity between one and two orders of magnitude lower than the best available method.

Fast numerical algorithms for the computation of invariant tori in Hamiltonian systems

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of invariant tori in Hamiltonian systems (exact symplectic maps and Hamiltonian vector fields). The algorithms are based on the parameterization method and follow closely the proof of the KAM theorem given in [LGJV05] and [FLS07]. They essentially consist in solving a functional equation satisfied by the invariant tori by using a Newton method. Using some geometric identities, it is possible to perform a Newton step using little storage and few operations. In this paper we focus on the numerical issues of the algorithms (speed, storage and stability) and we refer to the mentioned papers for the rigorous results. We show how to compute efficiently both maximal invariant tori and whiskered tori, together with the associated invariant stable and unstable manifolds of whiskered tori. Moreover, we present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori. Since quasi-periodic cocycles appear in other contexts, this section may be of independent interest. The numerical methods presented here allow to compute in a unified way primary and secondary invariant KAM tori. Secondary tori are invariant tori which can be contracted to a periodic orbit. We present some preliminary results that ensure that the methods are indeed implementable and fast. We postpone to a future paper optimized implementations and results on the breakdown of invariant tori.

A fast Bayesian reconstruction algorithm for emission tomography with entropy prior converging to feasible images

The development and tests of an iterative reconstruction algorithm for emission tomography based on Bayesian statistical concepts are described. The algorithm uses the entropy of the generated image as a prior distribution, can be accelerated by the choice of an exponent, and converges uniformly to feasible images by the choice of one adjustable parameter. A feasible image has been defined as one that is consistent with the initial data (i.e. it is an image that, if truly a source of radiation in a patient, could have generated the initial data by the Poisson process that governs radioactive disintegration). The fundamental ideas of Bayesian reconstruction are discussed, along with the use of an entropy prior with an adjustable contrast parameter, the use of likelihood with data increment parameters as conditional probability, and the development of the new fast maximum a posteriori with entropy (FMAPE) Algorithm by the successive substitution method. It is shown that in the maximum likelihood estimator (MLE) and FMAPE algorithms, the only correct choice of initial image for the iterative procedure in the absence of a priori knowledge about the image configuration is a uniform field.

An O(N) Algorithm for Three-Dimensional N-Body Simulations

We develop an algorithm that computes the gravitational potentials and forces on N point-masses interacting in three-dimensional space. The algorithm, based on analytical techniques developed by Rokhlin and Greengard, runs in order N time. In contrast to other fast N-body methods such as tree codes, which only approximate the interaction potentials and forces, this method is exact ?? computes the potentials and forces to within any prespecified tolerance up to machine precision. We present an implementation of the algorithm for a sequential machine. We numerically verify the algorithm, and compare its speed with that of an O(N2) direct force computation. We also describe a parallel version of the algorithm that runs on the Connection Machine in order 0(logN) time. We compare experimental results with those of the sequential implementation and discuss how to minimize communication overhead on the parallel machine.

Fast Sorting on a Distributed-Memory Architecture

We consider the often-studied problem of sorting, for a parallel computer. Given an input array distributed evenly over p processors, the task is to compute the sorted output array, also distributed over the p processors. Many existing algorithms take the approach of approximately load-balancing the output, leaving each processor with Θ(n/p) elements. However, in many cases, approximate load-balancing leads to inefficiencies in both the sorting itself and in further uses of the data after sorting. We provide a deterministic parallel sorting algorithm that uses parallel selection to produce any output distribution exactly, particularly one that is perfectly load-balanced. Furthermore, when using a comparison sort, this algorithm is 1-optimal in both computation and communication. We provide an empirical study that illustrates the efficiency of exact data splitting, and shows an improvement over two sample sort algorithms.

Fast kernel classifier construction using orthogonal forward selection to minimise leave-one-out misclassification rate

We propose a simple yet computationally efficient construction algorithm for two-class kernel classifiers. In order to optimise classifier's generalisation capability, an orthogonal forward selection procedure is used to select kernels one by one by minimising the leave-one-out (LOO) misclassification rate directly. It is shown that the computation of the LOO misclassification rate is very efficient owing to orthogonalisation. Examples are used to demonstrate that the proposed algorithm is a viable alternative to construct sparse two-class kernel classifiers in terms of performance and computational efficiency.

A fast linear-in-the-parameters classifier construction algorithm using orthogonal forward selection to minimize leave-one-out misclassification rate

We propose a simple and computationally efficient construction algorithm for two class linear-in-the-parameters classifiers. In order to optimize model generalization, a forward orthogonal selection (OFS) procedure is used for minimizing the leave-one-out (LOO) misclassification rate directly. An analytic formula and a set of forward recursive updating formula of the LOO misclassification rate are developed and applied in the proposed algorithm. Numerical examples are used to demonstrate that the proposed algorithm is an excellent alternative approach to construct sparse two class classifiers in terms of performance and computational efficiency.

Givens rotation based fast backward elimination algorithm for RBF neural network pruning

A fast backward elimination algorithm is introduced based on a QR decomposition and Givens transformations to prune radial-basis-function networks. Nodes are sequentially removed using an increment of error variance criterion. The procedure is terminated by using a prediction risk criterion so as to obtain a model structure with good generalisation properties. The algorithm can be used to postprocess radial basis centres selected using a k-means routine and, in this mode, it provides a hybrid supervised centre selection approach.