Abstract
In this paper we introduce an identification algorithm for MIMO bilinear systems subject to deterministic inputs. The new algorithm is based on an expanding dimensions concept, leading to a rectangular, dimension varying, linear system. In this framework the observability, controllability, and Markov parameters are similar to those of a time-varying system. The fact that the system is time invariant, leads to an equaivaleet linear deterministic subspace algorithm. Provided a rank condition is satisfied, the algorithm will produce unbiased parameter estimates. This rank condition can be guaranteed to hold if the ratio of the number of outputs to the number of inputs is larger than the system order. This is due to the typical exponential blow-out in the dimensions of the Hankel data matrices of bilinear systems, in particular for deterministic inputs since part of the input subspace cannot be projected out. Other algorithms in the literature, based on Walsh functions, require that the number of outputs is at least equal to the system order. For ease of notation and clarification, the algorithm is presented as an intersection based subspace algorithm. Numerical results show that the algorithm reproduces the system parameters very well, provided the rank condition is satisfied. When the rank condition is not satisfied, the algorithm will return biased parameter estimates, which is a typical bottleneck of bilinear system identification algorithms for deterministic inputs. © 2005 IEEE.

Abstract
Computational methods have been used with great application to biomedical optics. The events created by the interaction of radiation with biological materials can easily be translated to computer languages with the objective of producing simulation techniques to be used prior to physical intervention. The addition of biocompatible and hyper osmotic agents to several types of biological tissues has proven the enhancement of transparency to radiation flux by reduction of material's optical properties. The evolutionary behavior of the agent's action in the tissue samples before saturation has been observed by numerous researchers but has never been described mathematically. In the present work we will describe the application of Monte Carlo simulation to estimate the evolutionary states of optical transparency of biological tissues when immersed in an osmotic solution. We begin our study with typical values for the optical properties of rabbit muscle and proceed by reducing the absorption and scattering coefficients independently and simultaneously. The results show the number of transmitted, absorbed, scattered and reflected photons in different stages of the action of a generic osmotic agent over a small and well defined tissue sample.

Abstract
Port Wine ageing process is very important to produce the most appreciated and expensive wines from the class. The process takes decades to accomplish and involves particular techniques which are taken inside refrigerated cellars. Different wines pass through such process to produce 10 year, 20 year, 30 year and 40 year Ports. There are no documented data about color or turbidity evolution during the ageing process. We decided to verify the states of color and spectral turbidity of different aged Gold white port wine. The acquired results show a spectral evolution on transmition and scattered radiation along with color modification which are a close and direct consequence of adopted corrective measures. In measuring the four samples, we have used our spectronephelometer with optical fiber tips to illuminate sample and to acquire transmitted or scattered radiation. Transmition results were calibrated with a standard spectrophotometer at our laboratory, and scattered spectra were measured considering a system calibration with ISO12103 standard dust. We are aware that the four samples were harvested in different years, but the wine type is the same and the ageing process does not differ from one sample to another.

Abstract
In this paper we provide a different way to estimate matrices B and D, in subspace identification algorithms. The starting point was the method proposed by Van Overschee and De Moor [10] - the only one applying subspace ideas to the estimation of those matrices. We have derived new (and simpler) expressions and we found that the method proposed by Van Overschee and De Moor [10] can be rewritten as a weighted least squares problem, involving the future outputs and inputs.

Abstract
In this paper, two approaches, for the estimation of matrices A and C in CV A-type subspace identification algorithms are compared and the differences between the two obtained estimates are analysed. One of the methods, "least squares" based, was proposed in the original CVA algorithm. The other method, inspired in the techniques of the classical Realization Theory and proposed by Verhaegen, is far more efficient. Therefore, although the two methods produce two different estimates, a replacement is proposed and an expression for correction of the estimates is obtained, in order to reduce the loss of accuracy.

Abstract
In this paper, a recursive algorithm is presented, based on the CVA subspace identification algorithm. The main idea was to explore the relations between the orthogonal and oblique projections involved and to provide simpler expressions that allowed a recursive version of the algorithm - guaranteeing most of the advantages of this kind of methods, and still improving the numerical efficiency.