Absfraci-Recently, attention has been focused on the class of bilinear systems, both for its applicative interest and intrinsic simplicity.In fact, it appears that many important processes, not only in engineering, but also in biology, socio-economics, and ecology, may be modeled by bilinear systems. Moreover, since their nonlinearity is due to products between input and state variables, this class frequently may be studied by techniques similar to those employed for linear systems. This work is intended to motivate the interest of bilinear systemsand to present the current state of research in its various aspects.After an introductory section, in which theoretical and applicative aspects of bilinear systems are enlightened, four other sections follow, respectively, devoted to structural properties, mathematical models, identification and optimization. In a final section, some concluding remarks are made on still open problems and possible trends for future research.

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Optical coherence tomography (OCT) has recently become one of the primary methods for noninvasive probing of the human retina. The pseudoimage formed by OCT (the so-called B-scan) varies probabilistically across pixels due to complexities in the measurement technique. Hence, sensitive automatic procedures of diagnosis using OCT may exploit statistical analysis of the spatial distribution of reflectance. In this paper, we perform a statistical study of retinal OCT data. We find that the stretched exponential probability density function can model well the distribution of intensities in OCT pseudoimages. Moreover, we show a small, but significant correlation between neighbor pixels when measuring OCT intensities with pixels of about 5 µm. We then develop a simple joint probability model for the OCT data consistent with known retinal features. This model fits well the stretched exponential distribution of intensities and their spatial correlation. In normal retinas, fit parameters of this model are relatively constant along retinal layers, but varies across layers. However, in retinas with diabetic retinopathy, large spikes of parameter modulation interrupt the constancy within layers, exactly where pathologies are visible. We argue that these results give hope for improvement in statistical pathology-detection methods even when the disease is in its early stages.

We present here a procedure for automatic determination of the aminoacid sequence of peptides by processing data obtained from mass spectrometry analysis. This is a basic and relevant problem in the field of proteomics. It furthermore carries an even higher conceptual and applicative interest in peptide research, as well as in other connected fields. The analysis does not rely on known protein data bases, but on computation of all aminoacid sequences compatible with the given spectral data. By formulating a mathematical model for such combinatorial problem, structural limitations of known methods are overcome, and efficient solution algorithms can be developed. Results are very encouraging both from the accuracy and from the computational points of view.