Rossella Cancelliere

Gaia Data Release 2 - The astrometric solution

Context. Gaia Data Release 2 (Gaia DR2) contains results for 1693 million sources in the magnitude range 3 to 21 based on observations collected by the European Space Agency Gaia satellite during the first 22 months of its operational phase. Aims. We describe the input data, models, and processing used for the astrometric content of Gaia DR2, and the validation of these resultsperformed within the astrometry task. Methods. Some 320 billion centroid positions from the pre-processed astrometric CCD observations were used to estimate the five astrometric parameters (positions, parallaxes, and proper motions) for 1332 million sources, and approximate positions at the reference epoch J2015.5 for an additional 361 million mostly faint sources. These data were calculated in two steps. First, the satellite attitude and the astrometric calibration parameters of the CCDs were obtained in an astrometric global iterative solution for 16 million selected sources, using about 1% of the input data. This primary solution was tied to the extragalactic International Celestial Reference System (ICRS) by means of quasars. The resulting attitude and calibration were then used to calculate the astrometric parameters of all the sources. Special validation solutions were used to characterise the random and systematic errors in parallax and proper motion. Results. For the sources with five-parameter astrometric solutions, the median uncertainty in parallax and position at the reference epoch J2015.5 is about 0.04 mas for bright (G < 14 mag) sources, 0.1 mas at G = 17 mag, and 0.7 masat G = 20 mag. In the proper motion components the corresponding uncertainties are 0.05, 0.2, and 1.2 mas yr−1, respectively.The optical reference frame defined by Gaia DR2 is aligned with ICRS and is non-rotating with respect to the quasars to within 0.15 mas yr−1. From the quasars and validation solutions we estimate that systematics in the parallaxes depending on position, magnitude, and colour are generally below 0.1 mas, but the parallaxes are on the whole too small by about 0.03 mas. Significant spatial correlations of up to 0.04 mas in parallax and 0.07 mas yr−1 in proper motion are seen on small (< 1 deg) and intermediate (20 deg) angular scales. Important statistics and information for the users of the Gaia DR2 astrometry are given in the appendices.

A comparative analysis of neural network performances in astronomical imaging

Neural networks are widely used as recognisers and classifiers since the second half of the 80s; this is related to their capability of solving a nonlinear approximation problem. A neural network achieves this result by training; this iterative procedure has very useful features like parallelism, robustness and easy implementation.The choice of the best neural network is often problem dependent; in literature, the most used are the radial and sigmoidal networks. In this paper we compare performances and properties of both when applied to a problem of aberration detection in astronomical imaging.Images are encoded using an innovative technique that associates each of them with its most convenient moments, evaluated along the {x, y} axes; in this way we obtain a parsimonious but effective method with respect to the usual pixel by pixel description.

Efficient training of Time Delay Neural Networks for sequential patterns

Abstract Time Delay Neural Networks are an extension of the classical multi-layer perceptron with time-delayed links. They are used to deal with sequence recognition problems in which a finite memory of past events is sufficient. Usually Time Delay Neural Networks are trained by performing a complete spatial expansion of delayed links through time to reconduct the training to that of a feedforward network. But this complete expansion is unnecessary. In fact it is sufficient to combine a partial spatial expansion with a sliding input window to obtain the same result. In this way we exploit the computational efficiency of standard backpropagation while increasing the flexibility of the method to deal with variable length sequences and reducing the storage occupation. In this paper a general training algorithm for Time Delay Neural Networks is presented, showing in detail the formal differences with respects to error backpropagation for feedforward networks. Furthermore, an efficient implementation is described, which exploits a partial spatial expansion of delayed links, showing formally its equivalence with the general algorithm.

An efficient point spread function construction method

Image computation is a fundamental tool for performance assessment of astronomical instrumentation, usually implemented by Fourier transform techniques. We review the numerical implementation, evaluating a direct implementation of the discrete Fourier transform (DFT) algorithm, compared with fast Fourier transform (FFT) tools. Simulations show that the precision is quite comparable, but in the case investigated the computing performance is considerably higher for DFT than FFT. The application to image simulation for the mission Gaia and for Extremely Large Telescopes is discussed.

Neural network correction of astrometric chromaticity

In this paper, we deal with the problem of chromaticity, i.e. apparent position variation of stellar images with their spectral distribution, using neural networks (NNs) to analyse and process astronomical. images. The goal is to remove this relevant source of systematic error in the data reduction of high-precision astrometric experiments, like Gaia. This task can be accomplished thanks to the capability of NNs to solve a non-linear approximation problem, i.e. to construct a hypersurface that approximates a given set of scattered data couples. Images are encoded associating each of them with conveniently chosen moments, evaluated along the y-axis. The technique proposed, in the current framework, reduces the initial chromaticity of a few milliarcseconds to values of few microarcseconds.

Recurrent network automata for speech recognition: a summary of recent work

The integration of hidden Markov models (HMMs) and neural networks is an important research line to obtain new speech recognition systems that combine a good time-alignment capability and a powerful discrimination-based training. The recurrent network automata (RNA) model is a hybrid of a recurrent neural network, which estimates the state emission probability of a HMM, and a dynamic programming, which finds the best state sequence. This paper reports the results obtained with the RNA model, after three years of research and application in speaker independent digit recognition over the public telephone network.<<ETX>>

A High Parallel Procedure to Initialize the Output Weights of a Radial Basis Function or BP Neural Network

The training of a neural network can be made using many different procedures; they allow to find the weights that minimize the discrepancies between targets and actual outputs of the network. The optimal weights can be found either in a direct way or using iterative techniques; in both cases its sometimes necessary (or simply useful) to evaluate the pseudo-inverse matrix of the projections of input examples into the function space created by the network. Every operation we have to perform to do this can however become difficult (and sometimes impossible) when the dimension of this matrix is very large, so we deal with a way to subdivide it and to obtain our aim by a high parallel algorithm.

Statistically optimal fitting of astrometric signals

A general purpose fitting model for one-dimensional astrometric signals is developed, building on a maximum likelihood framework, and its performance is evaluated by simulation over a set of realistic image instances. The fit quality is analysed as a function of the number of terms used for signal expansion, and of astrometric error, rather than rms discrepancy with respect to the input signal. The tuning of the function basis to the statistical characteristics of the signal ensemble is discussed. The fit sensitivity to a priori knowledge of the source spectra is addressed. Some implications of the current results on calibration and data reduction aspects are discussed, in particular with respect to Gaia.

Matrix pseudoinversion for image neural processing

Recently some novel strategies have been proposed for training of Single Hidden Layer Feedforward Networks, that set randomly the weights from input to hidden layer, while weights from hidden to output layer are analytically determined by Moore-Penrose generalised inverse. Such non-iterative strategies are appealing since they allow fast learning, but some care may be required to achieve good results, mainly concerning the procedure used for matrix pseudoinversion. This paper proposes a novel approach based on original determination of the initialization interval for input weights, a careful choice of hidden layer activation functions and on critical use of generalised inverse to determine output weights. We show that this key step suffers from numerical problems related to matrix invertibility, and we propose a heuristic procedure for bringing more robustness to the method. We report results on a difficult astronomical image analysis problem of chromaticity diagnosis to illustrate the various points under study.

Dynamics and stability of generalized cellular nonlinear network model

The aim of this paper is the definition of a new model of neural network, called generalized cellular nonlinear network, that covers architectures and dynamics of the well known and widely used classes of feedforward neural networks and cellular neural networks. We show how cellular neural networks and feedforward neural networks can be derived from the general model: moreover we prove a theorem of existence and uniqueness for the solution of the system that describes the generalized cellular nonlinear network dynamics. These results are obtained using the method of Lyapunovs finite majorizing equations that also represents a new approach in studying the stability of cellular neural networks.