Indefinite quadratic with linear costs optimal control of Markov jump with multiplicative noise systems

In this paper we consider the stochastic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The performance criterion is assumed to be formed by a linear combination of a quadratic part and a linear part in the state and control variables. The weighting matrices of the state and control for the quadratic part are allowed to be indefinite. We present a necessary and sufficient condition under which the problem is well posed and a state feedback solution can be derived from a set of coupled generalized Riccati difference equations interconnected with a set of coupled linear recursive equations. For the case in which the quadratic-term matrices are non-negative, this necessary and sufficient condition can be written in a more explicit way. The results are applied to a problem of portfolio optimization.     

Practical output regulation for bounded linear infinite-dimensional state space systems

We develop the mathematical foundations of practical state space output regulation for bounded infinite-dimensional linear systems. By practical output regulation we mean asymptotic tracking of references and rejection of disturbances with a given accuracy. Our main results are general upper bounds for the norms perturbations to the parameters of the exosystem, the plant and a controller which achieves exact output regulation. These bounds depend explicitly on the desired tracking accuracy ε>0. In this paper, all perturbations are assumed to be bounded, additive and linear. Our results apply for both feedforward and error feedback controllers, and for arbitrary bounded uniformly continuous reference/disturbance signals.     

An investigation of the modified direction feature for cursive character recognition

This paper describes and analyses the performance of a novel feature extraction technique for the recognition of segmented/cursive characters that may be used in the context of a segmentation-based handwritten word recognition system. The modified direction feature (MDF) extraction technique builds upon the direction feature (DF) technique proposed previously that extracts direction information from the structure of character contours. This principal was extended so that the direction information is integrated with a technique for detecting transitions between background and foreground pixels in the character image.In order to improve on the DF extraction technique, a number of modifications were undertaken. With a view to describe the character contour more effectively, a re-design of the direction number determination technique was performed. Also, an additional global feature was introduced to improve the recognition accuracy for those characters that were most frequently confused with patterns of similar appearance. MDF was tested using a neural network-based classifier and compared to the DF and transition feature (TF) extraction techniques. MDF outperformed both DF and TF techniques using a benchmark dataset and compared favourably with the top results in the literature. A recognition accuracy of above 89% is reported on characters from the CEDAR dataset.     

Model-based evaluation of clustering validation measures

A cluster operator takes a set of data points and partitions the points into clusters (subsets). As with any scientific model, the scientific content of a cluster operator lies in its ability to predict results. This ability is measured by its error rate relative to cluster formation. To estimate the error of a cluster operator, a sample of point sets is generated, the algorithm is applied to each point set and the clusters evaluated relative to the known partition according to the distributions, and then the errors are averaged over the point sets composing the sample. Many validity measures have been proposed for evaluating clustering results based on a single realization of the random-point-set process. In this paper we consider a number of proposed validity measures and we examine how well they correlate with error rates across a number of clustering algorithms and random-point-set models. Validity measures fall broadly into three classes: internal validation is based on calculating properties of the resulting clusters; relative validation is based on comparisons of partitions generated by the same algorithm with different parameters or different subsets of the data; and external validation compares the partition generated by the clustering algorithm and a given partition of the data. To quantify the degree of similarity between the validation indices and the clustering errors, we use Kendall's rank correlation between their values. Our results indicate that, overall, the performance of validity indices is highly variable. For complex models or when a clustering algorithm yields complex clusters, both the internal and relative indices fail to predict the error of the algorithm. Some external indices appear to perform well, whereas others do not. We conclude that one should not put much faith in a validity score unless there is evidence, either in terms of sufficient data for model estimation or prior model knowledge, that a validity measure is well-correlated to the error rate of the clustering algorithm.     

Retrieval of textured images through the use of quantization and modal analysis

This paper proposes a new method for textured image retrieval, by the modal analysis of quantized spectral point patterns as the modal correspondence method of Shapiro and Brady, to match point sets by comparing the eigenvectors of a pairwise point proximity matrix taken from the power spectrum peaks. A variant of the Carcassoni, Ribeiro and Hancock method for performing recognition is taken into account. For choosing image features to represent an image, a quantization scheme is applied. This quantization scheme acts in the spectral space given by the Fourier transform of each image. Its goal is to find a small set which represents an image efficiently, where the most important features are presented. The proposed technique is invariant to rotation and is robust in the presence of noise and damaged images. The techniques here presented are compared, and the commonly used retrieval performance measurement—precision and recall—is used as evaluation of the query results.     

A mean field annealing approach to accurate free form shape matching

The SoftAssign algorithm is an elegant free form shape matching algorithm. While its objective function can be interpreted as consisting of three desired terms: minimising a weighted sum of matching errors of combinations of all the points in the two free form shapes to be matched, equalising their weights (probabilities) of being real ones and also maximising the overlapping area between the free form shapes to be matched, the last term has no effect on the optimisation of the parameters of interest due to normalisation. In this paper, we reformulate the last two terms using the inequality about the geometric and algebraic averages and the sum of the powers of these probabilities. For the sake of computational efficiency, instead of considering combinations of all the points in the overlapping free form shapes to be matched, we employ the traditional closest point criterion to establish possible correspondences between the two overlapping free form shapes to be matched. The saddle point solution of the resulting objective function no longer yields a closed form solution to the parameters of interest. For easy computation, we then adopt a pseudo-linearisation method to linearise the first order derivative of the objective function, leading the parameters of interest to be tracked and estimated with a closed form solution. The parameters of interest are finally optimised using the efficient deterministic annealing scheme with the camera motion parameters estimated using the quaternion method in the weighted least squares sense. A comparative study based on both synthetic data and real images with partial overlap has shown that the proposed algorithm is promising for the automatic matching of overlapping 3D free form shapes subject to a large range of motions.     

Design and formal proof of a new optimal image segmentation program with hypermaps

This article presents the design of a new functional 2D image segmentation algorithm by cell merging in a subdivision, its proof of total correctness, and the derivation of an optimal imperative program. The planar subdivisions are modeled by hypermaps. The formal specifications of hypermaps and segmentation are developed in the Calculus of Inductive Constructions. The proofs are assisted by the Coq system. The final program is written in C.     

An empirical investigation of competency factors affecting e-business success in European SMEs

In the last decade there was growing interest in strategic management literature about factors that influence a company's ability to use IT. There is general consensus that knowledge and competency are necessary in developing an IT capability, but there is very little understanding of what the necessary competencies are, and how they influence IS usage in different contexts. The small and medium-sized enterprise context is particularly interesting for two reasons: it constitutes a major part of the economy and it has been relatively unsuccessful in exploiting e-business.     

Gröbner bases with respect to several orderings and multivariable dimension polynomials

Let D=K[X]$D=K\left[X\right]$ be a ring of Ore polynomials over a field K$K$ and let a partition of the set of indeterminates into p$p$ disjoint subsets be fixed. Considering D$D$ as a filtered ring with the natural p$p$-dimensional filtration, we introduce a special type of reduction in a free D$D$-module and develop the corresponding Gröbner basis technique (in particular, we obtain a generalization of the Buchberger Algorithm). Using such a modification of the Gröbner basis method, we prove the existence of a Hilbert-type dimension polynomial in p$p$ variables associated with a finitely generated filtered D$D$-module, give a method of computation and describe invariants of such a polynomial. The results obtained are applied in differential algebra where the classical theorems on differential dimension polynomials are generalized to the case of differential structures with several basic sets of derivation operators.