We present a Lohner type algorithm for the computation of rigorous bounds for the solutions of ordinary differential equations and its derivatives with respect to the initial conditions up to an arbitrary order.

Character segmentation (i.e., splitting the images of handwritten words into pieces corresponding to single letters) is one of the required steps in numerous off-line cursive handwritten word recognition solutions. It is also a very important step, because improperly extracted characters are usually impossible to recognize correctly with currently used methods. The most common method of character segmentation is initial oversegmentation – finding some set of potential splitting points in the graphical representation of the word and then attempting to eliminate the improper ones. This paper contains a list of popular approaches for generating potential splitting points and methods of verifying their correctness.
 

The aim of this study was to describe some parametric estimation methods for the Weibull, gamma and Gompertz distributions and to identify among them estimators the most efficient in practical applications. Techniques which are considered as traditional methods, like the maximum likelihood (MLE) and the method of moments (MM) estimation but also some newer and less commonly used techniques like the Lmoment estimator (LME), least-square estimator (LSE), generalized spacing estimator (GSE) and percentile estimator (PE) were presented. The application of each method was demonstrated in a simulation study using data sets generated for different distribution parameters and sample sizes. Discussed estimators were compared in terms of their efficiency and bias measured by mean-square errors (MSE) based on the simulations results.

In this paper a new theorem about components of the mean squared error of Hierarchical Estimator is presented. Hierarchical Estimator is a machine learning meta-algorithm that attempts to build, in an incremental and hierarchical manner, a tree of relatively simple function estimators and combine their results to achieve better accuracy than any of the individual ones. The components of the error of a node of such a tree are: weighted mean of the error of the estimator in a node and the errors of children, a non-positive term that descreases below 0 if children responses on any example dier and a term representing relative quality of an internal weighting function, which can be conservatively kept at 0 if needed. Guidelines for achieving good results based on the theorem are brie discussed.

In this paper a genetic algorithm for clustering is proposed. The algorithm is based on the variable length chromosomes and the notion of local points density in the clustered set. Its role is to identify the number of clusters in the clustered set and to partition this set into particular clusters. The tests were conducted for two different sets of two dimensional data. The algorithm performed well in both cases. The tests presented the ability of the algorithm to partition the subsets combined with the thin dense area into separate clusters.

We consider a mathematical model which describes the adhesive contact between a linearly elastic body and an obstacle. The process is static and frictionless. The normal contact is governed by two laws. The first one is a Signorini law, representing the fact that there is no penetration between a body and an obstacle. The second one is a Winkler type law signifying that if there is no contact, the bonding force is proportional to the displacement below a given bonding threshold and equal to zero above the bonding threshold. The model leads to a variational-hemivariational inequality. We present the numerical results for solving a simple two-dimensional model problem with the Proximal Bundle Method (PBM). We analyze the method sensitivity and convergence speed with respect to its parameters.

This paper shows a new combinatorial problem which emerged from studies on an artificial intelligence classification model of a hierarchical classifier. We introduce the notion of proper clustering and show how to count their number in a special case when 3 clusters are allowed. An algorithm that generates all clusterings is given. We also show that the proposed approach can be generalized to any number of clusters, and can be automatized. Finally, we show the relationship between the problem of counting clusterings and the Dedekind problem.

The following paper discusses the topic of edge detection in X-ray hand images. It criticises the existing solution by highlighting a design fault, which is a carelessly chosen function and then proposes a way to eliminate the fault by replacing it with a better suited function. The search for this function and its results are also discussed in this paper. It also presents the aspect of pre- and postprocessing through filtering as another improvement in edge detection.

INTRODUCTION
Pattern recognition is one of principle problems in computer science. Many issues such as controlling, making decisions or predictions are related to it. It also has the main position in robotics. Therefore, this branch of computer science has been developing for a long time both in theoretical and implementation aspects. In a lot of cases pattern recognition can be a difficult problem and consequently the only method commonly used to sort out this issue does not exist. Presently, a wide range of methods based on various elements of mathematics, for instance calculus of probability or approximation theory, is applied. However, a universal recognition method does not exists - a given one can be effective for a specific sort of tasks and can fail for others. This is the reason why new methods are created and the existing ones developed. For example, syntactic methods are supported with probabilistic mechanisms and methods, which are combination of different basic methods such as neural-fuzzy ones, are created or hybrid expert systems are built. This paper concerns recognition curves in relation to their structural features. The considered problem is situated in a group of problems where pattern representation is a sequence of primitives being elements of a context language. For this group of languages, admittedly, automata which analyze these languages exist but their complexity is non-polinominal and consequently their usefulness in practical applications is limited. Moreover, an algorithm of grammar inference does not exist, consequently a method of automatic creation of tables controlling parsers (conversion functions in automata) does not exist, which in a practical nontrivial application disqualifies these languages. So, for structural patterns whose representations belong to context languages syntactic methods allowing to analyze them do not exist. Therefore, an application of nonsyntactic methods to structural features analyzing seems to be valuable. The aim of this paper is to propose a new methodology of curves recognition in relation to their structural features taking advantage of fuzzy methods statistically aided. The possibility of a neural implementation of a recognition system based on the proposed methodology is tested. In the second chapter of this paper, the methodology of a decision function construction in an axiomatic recognition of patterns is presented. In the third chapter the proposed methodology is applied to classification curves describing relative changes in the cardiac rhythm between different people with and without a cognitive load, respectively. The curves were obtained in the Department of Psychophysiology of the Jagiellonian University. The experiment is described in details in [14], [15], [27]. The fourth chapter contains the description of a neural network computing the value of membership functions for each class.

The aim of this work was to analyze the cooperation efficiency of the distributed objects based on the CORBA standard. The obtained results show the possibilities of application to the object-relational databases or object oriented computation of data received via the network from the object managed data base. The distributed objects for the client-server model were implemented in Java and C++ languages. All possible configurations of the implementation for the client and the server were analyzed. Best results were received for the client and the server implementation in C++ language. The worst results were received for the client and the server implementation in Java.

Pre-processing of mammograms is a crucial step in computer-aided analysis systems. The aim of segmentation is to extract a breast region by estimation of a breast skin-line and a pectoral muscle as well as removing radiographic artifacts and the background of the mammogram. Knowledge of the breast contour also allows further analysis of breast abnormalities such as bilateral asymmetry. In this paper we propose a fully automatic algorithm for segmentation of a breast region, based on two types of global image thresholding: the multi-level Otsu and minimizing the measure of fuzziness as well as the gradient estimation and linear regression. The results of our experiments showed that our method can be used to find a breast line and a pectoral muscle accurately

In this paper we present two methods of binarization of corneal endothelial images. The binarization is a first step of advanced image analysis. Images of corneal endothelial obtained by the specular microscopy have a poor dynamic range and they are usually non-uniformly illuminated. The binarization endothelial images is not trivial. Two binarization algorithms are proposed. The output images are presented. The quality of algorithms is discussed.