Abstract
In this paper we analyse the estimates of the matrices produced by the non-biased deterministic-stochastic subspace identification algorithms (NBDSSI) proposed by Van Overschee and De Moor ( 1996). First, an alternate expression is derived for the A and C estimates. It is shown that the Chiuso and Picci result ( Chiuso and Picci 2004) stating that the A and C estimates delivered by this algorithm robust version and by the Verhaegen's MOESP (Verhaegen and Dewilde 1992a, Verhaegen and Dewilde 1992b, Verhaegen 1993, Verhaegen 1994) are equal, can be obtained from this expression. An alternative approach for the estimation of matrices B and D in subspace identification is also described. It is shown that the least squares approach for the estimation of these matrices estimation can be just expressed as an orthogonal projection of the future outputs on a lower dimension subspace in the orthogonal complement of the column space of the extended observability matrix. Since this subspace has a dimension equal to the number of outputs, a simpler and numerically more efficient ( but equally accurate) new subspace algorithm is provided.

Abstract
We tackle the problem of sequence classification using relevant subsequences found in a dataset of protein labelled sequences. A subsequence is relevant if it is frequent and has a minimal length. For each query sequence a vector of features is obtained. The features consist in the number and average length of the relevant subsequences shared with each of the protein families. Classification is performed by combining these features in a Bayes Classifier. The combination of these characteristics results in a multi-class and multi-domain method that is exempt of data transformation and background knowledge. We illustrate the performance of our method using three collections of protein datasets. The performed tests showed that the method has an equivalent performance to state of the art methods in protein classification.

Abstract
Considering the characteristics of biological sequence databases, which typically have a small alphabet, a very long length and a relative small size (several hundreds of sequences), we propose a new sequence mining algorithm (gIL). gIL was developed for linear sequence pattern mining and results from the combination of some of the most efficient techniques used in sequence and itemset mining. The algorithm exhibits a high adaptability, yielding a smooth and direct introduction of various types of features into the mining process, namely the extraction of rigid and arbitrary gap patterns. Both breadth or a depth first traversal are possible. The experimental evaluation, in synthetic and real life protein databases, has shown that our algorithm has superior performance to state-of-the art algorithms. The use of constraints has also proved to be a very useful tool to specify user interesting patterns.

Abstract
In this paper we introduce a new identification algorithm for MIMO bilinear systems driven by white noise inputs. The new algorithm is based on a convergent sequence of linear deterministic-stochastic state space approximations, thus considered a Picard based method. The key to the algorithm is the fact that the bilinear terms behave like white noise processes. Using a linear Kalman filter, the bilinear terms can be estimated and combined with the system inputs at each iteration, leading to a linear system which can be identified with a linear-deterministic subspace algorithm such as MOESP, N4SID, or CVA. Furthermore, the model parameters obtained with the new algorithm converge to those of a bilinear model. Finally, the dimensions of the data matrices are comparable to those of a linear subspace algorithm, thus avoiding the curse of dimensionality.

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.