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
Design and control of mixer-settler batteries is very important for the technical and economical viability of the industrial processes of liquid-liquid extraction. Direct experimentation with these equipments is not always feasible, due to their complexity and cost. Computer simulation allows predicting the behaviour and optimizing the design of this type of equipments thus reducing costs. In previous works, we have already proposed a model to simulate the behaviour of a dispersion band in a gravitational settler unit of a mixer-settler system. Although the algorithm developed was able to simulate the band thickness for the transient state and the results obtained were in agreement with previously published results, some possible physical as well as conceptual limitations of this algorithm were detected. To overcome these problems, a new dynamic model using a kinetic formulation was proposed. This paper describes a new model for the shallow-layer settler unit which is able to describe the transient state of a liquid-liquid system, the hydrodynamic phenomena of drop-drop and drop-interface coalescence as well as the transport processes being explicitly taken into account. © 2006 Civil-Comp Press.

Abstract
All over the world we have been assisting to a significant increase of the telecommunication systems usage. People are faced day after day with strong marketing campaigns seeking their attention to new telecommunication products and services. Telecommunication companies struggle in a high competitive business arena. It seems that their efforts were well done, because customers are strongly adopting the new trends and use (and abuse) systematically communication services in their quotidian. Although fraud situations are rare, they are increasing and they correspond to a large amount of money that telecommunication companies lose every year. In this work, we studied the problem of fraud detection in telecommunication systems, especially the cases of superimposed fraud, providing an anomaly detection technique, supported by a signature schema. Our main goal is to detect deviate behaviors in useful time, giving better basis to fraud analysts to be more accurate in their decisions in the establishment of potential fraud situations.

Abstract
The problem of discovering previously unknown frequent patterns in time series, also called motifs, has been recently introduced. A motif is a subseries pattern that appears a significant number of times. Results demonstrate that motifs may provide valuable insights about the data and have a wide range of applications in data mining tasks. The main motivation for this study was the need to mine time series data from protein folding/unfolding simulations. We propose an algorithm that extracts approximate motifs, i.e. motifs that capture portions of time series with a similar and eventually symmetric behavior. Preliminary results on the analysis of protein unfolding data support this proposal as a valuable tool. A.dditional experiments demonstrate that the application of utility of our algorithm is not limited to this particular problem. Rather it can be an interesting tool to be applied in many real world problems.

Abstract

Abstract
The INteger-valued AutoRegressive (INAR) processes were introduced in the literature by Al-Osh and Alzaid [1987. First-order integer-valued autoregressive (INAR(l)) process. J. Time Ser. Anal. 8, 261-275] and McKenzie [1988. Some ARMA models for dependent sequences of Poisson counts. Adv. Appl. Probab. 20, 822-835] for modelling correlated series of counts. These processes have been considered as the discrete counter part of AR processes, but their highly nonlinear characteristics lead to some statistically challenging problems, namely in parameter estimation. Several estimation procedures have been proposed in the literature, mainly for processes of first order. For some of these estimators the asymptotic properties as well as finite sample properties have been obtained and studied. This paper considers Yule-Walker parameter estimation for the pth-order integer-valued autoregressive, INAR(p), process. In particular, the asymptotic distribution of the Yule-Walker estimator is obtained and it is shown that this estimator is asymptotically normally distributed, unbiased and consistent.