## Contents of Volume 12 (2002)

5/2002 4/2002 2/2002 2/2002 1/2002

### 6/2002

• [1] Editorial, 517.
• [2] Devon D., Juliano B. (USA): Modifying XCS for size-constrained systems, 519-531.

Extended Classifier Systems, or XCS, is a soft-computing approach to machine learning in rule-based systems. While XCS has been shown effective in learning accurate, compact and complete mappings of an environment's payoff landscape, it can require significant resources to do so. This paper presents four modifications that allow XCS to achieve high performance even in highly size-constrained populations. By modifying the genetic algorithm trigger function, the classifier deletion-selection mechanism, the frequency of classifier parameter updates and the genetic algorithm selection function - the modified system more efficiently uses the available population resources. Experimental results demonstrate the improvement in performance achieved with the proposed modifications in both the single-step 6-Multiplexer problem and the multi-step Woods-2 problem.

• [3] Domínguez J. J., Lozano S., Calle M. (Spain), Smith K. (Australia): A new method for combinatorial optimization: genetic neighborhood search, 533-547.

Combinatorial optimization is a discipline of decision making in the case of discrete alternatives. The Genetic Neighborhood Search (GNS) is a hybrid method for these combinatorial optimization problems. The main feature of the approach is iterative use of local search on extended neighborhoods, where the better solution will be the center of a new extended neighborhood. When the center of the neighborhood would be the better solution the algorithm will stop. We propose using a genetic algorithm to explore the extended neighborhoods. This GA is characterized by the method of evaluating the fitness of individuals and useing two new operators. Computational experience with the Symmetric TSP shows that this approach is robust with respect to the starting point and that high quality solutions are obtained in a reasonable time.

• [4] Haber R. E., Alique A., Ros S., Alique J. R. (Spain), Haber R. H. (Cuba), Jiménez J. E. (Spain): Nonlinear output error model using a single hidden layer neural network. An application case study, 549-558.

This work is focused on determining a nonlinear output error (OE) model, i.e., a dynamic system, by training a two layer neural network with a Levenberg-Marquardt method. Selected as a case study is application of a dynamic model to predict cutting force in machining processes. A model created by using Artificial Neural Networks (ANN), able to predict the process output, is introduced in order to deal with the characteristics of such an ill-defined process. This model describes the dynamic response of the output before the changes in the process input command (feed rate) and the process parameters (depth of cut). The model provides a sufficiently accurate prediction of cutting force, since the process-dependent specific dynamic properties are adequately reflected.

• [5] Hakl F., Hlaváček M., Kalous R.(Czech Republic): $M_{bb}$ distribution of subsets of Higgs bosson decay events defined via neural networks, 559-571.

This paper describes an application of a neural network approach to the SM (standard model) and the MSSM (minimal supersymetry standard model) Higgs search in the associated production $t^{\bar&space;t}&space;H$ with $H&space;\to&space;b^{\bar&space;b}$. This decay channel is considered as a discovery channel for Higgs scenarios for Higgs boson masses in the range 80 - 130 GeV. A neural network model with a special type of data flow is used to separate $\bar&space;t_{jj}$ background from $H&space;\to&space;b^{\bar&space;b}$ events. The neural network used combines together a classical neural network approach and a linear decision tree separation process. The parameters of these neural networks are randomly generated and the population of the predefined size of those networks is learned to get initial generation for the following genetic algorithm optimization process. A genetic algorithm principles are used to tune parameters of further neural network individuals derived from previous neural networks by GA operations of crossover and mutation. The goal of this GA process is optimization of the final neural network performance.

Our results show that the NN approach is applicable to the problem of Higgs boson detection. Neural network filters can be used to emphasize the difference of the $M_{bb}$ distribution for events accepted by filter (with better $\frac{signal}{background}$ rate) from the $M_{bb}$ distribution for original events (with original $\frac{signal}{background}$ rate) under condition that there is no loss of significance. This improvement of the shape of the $M_{bb}$ distribution can be used as a criterion of existence of Higgs boson decay in the discovery channel considered.

• [6] Neruda R., Kudová P. (Czech Republic): Hybrid learning of RBF networks, 573-585.

Three different learning methods for RBF networks and their combinations are presented. Standard gradient learning, three-step algorithm with unsupervised part, and evolutionary algorithm are introduced. Their performance is compared on two benchmark problems: Two spirals and Iris plants. The results show that the three-step learning is usually the fastest, while the gradient learning achieves better precision. The combination of these two approaches gives the best results.

• [7] Neruda R., Štědrý A., Drkošová J. (Czech Republic): Variants of learning algorithm based on Kolmogorov theorem, 587-597.

A thorough analysis of theoretical and computational properties of Kolmogorov learning algorithm for feedforward neural networks lead us to proposal of efficient sequential and parallel implementation. A novel approach to parallelization is presented which combines our previous results in order to achieve higher parallel speed-up.

• [8] Wang L., Li S., Lay S. C., Yu W. H., Wan C.(Singapore): Genetic algorithms for optimal channel assignments in mobile communications, 599-619.

The demand for mobile communication has been steadily increasing in recent years. With the limited frequency spectrum, the problem of channel assignment becomes increasingly important, i.e., how do we assign the calls to the available channels so that the interference is minimized while the demand is met? This problem is known to belong to a class of very difficult combinatorial optimization problems. In this paper, we apply the formulation of Ngo and Li with genetic algorithms to ten benchmarking problems. Interference-free solutions cannot be found for some of these problems; however, the approach is able to minimize the interference significantly. The results demonstrate the effectiveness of genetic algorithms in searching for optimal solutions in this complex optimization problem.

• [9] Zacharias J., Hartmann C., Delgado A. (Germany): Application of Neuro-Numerics for the damage recognition on crates of beverages, 621-633.

A new method to detect damages on crates of beverages is investigated. It is based on a pattern-recognition-system by an artificial neural network (ANN) with a feedforward multilayer-perceptron topology. The sorting criterion is obtained by mechanical vibration analysis which provides characteristic frequency spectra for all possible damage cases and crate models. To support the network training, a large number of numerical data-sets is calculated by finite-element-method (FEM). The combination of artificial neural networks with methods of numerical simulation is a powerful instrument to cover the broad range of possible damages. First results are discussed with respect to the influence of modelling inaccuracies of the finite-element-model and the support of ANN by training-data obtained from numerical simulation. Also the feasibility of neuro-numerical ANN training will be dwelled on.

### 5/2002

• [1] Editorial, 405.
• [2] Aguzzoli S., Gerla B. (Italy): On countermodels in Basic Logic, 407-420.

In [3] the tautology problem for Hájek's Basic Logic BL is proved to be co-NP-complete by showing that if a formula ? is not a tautology of BL then there exists an integer m > 0, polynomially bounded by the length of ?, such that ? fails to be a tautology in the infinite-valued logic m£ corresponding to the ordinal sum of m copies of the £ukasiewicz t-norm. In this paper we state that if ? is not a tautology of BL then it already fails to be a tautology of a finite set of finite-valued logics, defined by taking integers m, k > 0 only depending on polynomial-time computable features of ?. This result allows the definition of a calculus for m£ along the lines of [1], [2], while the analysis of the features of functions associated with formulas of m£ constitutes a step toward the characterization of finitely generated free BL-algebras as algebras of [0,1]-valued functions.

• [3] Barták R. (Czech Republic): Modelling soft constraints: A survey, 421-431.

Constraint programming is an approach for solving (mostly combinatorial) problems by stating constraints over the problem variables. In some problems, there is no solution satisfying all the constraints, so the problem formulation must deal with uncertainty, vagueness, or imprecision. In such a case the standard constraint satisfaction techniques dealing with hard constraints cannot be used directly and some form of soft constraints is required. In the paper we survey four generic models for soft constraints, namely hierarchical, partial, valued, and semiring-based constraint satisfaction.

• [4] Byrski A., Kisiel-Dorohinicki M. (Poland): Evolving RBF networks in a multi-agent system, 433-440.

In the paper an agent system of evolving neural networks, being an example of collective intelligence, is presented. A concept of decentralised evolutionary computation realised as an evolutionary multi-agent system (EMAS) may help to avoid some of the shortcomings of classical evolutionary optimisation techniques. As an addition, several methods of managing such a collective intelligent system are mentioned. General considerations are illustrated by a particular system dedicated to the problem of time-series prediction. Selected experimental results conclude the work.

• [5] Ciabattoni A. (Austria), Esteva F., Godo L. (Spain): T-norm based logics with n-contraction, 441-452.

We consider two families of fuzzy propositional logics obtained by extending MTL and IMTL with the n-contraction axiom, for $n\geqslant&space;2$. These logics - called $C_n$-MTL and $C_n$-IMTL - range from Gödel and classical logic (when n = 2) to MTL and IMTL (when n tends to infinity), respectively. We investigate the t-norm based semantics and the proof theory for $C_n$-MTL and $C_n$-IMTL. We show standard completeness and suitable analytic hypersequent calculi for them.

• [6] Haniková Z. (Czech Republic): A note on the complexity of propositional tautologies of individual t-algebras, 453-460.

For any t-algebra, the set of its propositional tautologies is coNP complete.

• [7] Katarzyniak R. P., Pieczyńska - Kuchtiak A.(Poland): A consensus based algorithm for grounding belief formulas in internally stored perceptions, 461-472.

In this paper an original algorithm for the choice of a relevant belief formula is presented. Belief formulas are treated as external representations of internal states of cognition directed at an ontologically existing atom object. This algorithm is based on the idea of intentional semantics and uses soft methods based on the theory of consensus and choice.

• [8] Kramosil I. (Czech Republic): On inner and outer extensions of non-numerical fuzzy and possibilistic measures, 473-482.

Non-numerical fuzzy and possibilistic measures taking their values in partially ordered sets, semilattices or lattices are introduced. Using the operations of supremum and infimum in these structures, the inner and outer (lower and upper) extensions of the original measures are investigated and defined. The conditions under which the resulting functions extend conservatively the original ones and possess the properties of fuzzy or possibilistic measures, are explicitly stated and relevant assertions are proved.

• [9] Pokorný D. (Germany), Stigler M. (Switzerland): A cluster procedure for small frequencies: crisp data, fuzzy distances, crisp clusters, 483-497.

(i) The procedure introduced here for the clustering of frequency vectors takes into account the uncertainty arising from dealing with small observed frequencies. The smaller observed absolute frequencies, the more uncertainty about the "true" probability vector. The object is not represented by a single point in the multidimensional space but rather by the fuzzy set spread around this point. Consequently, the distance between two such objects is a fuzzy value, too. The expected mean distance between two objects generally differs from the simple distance: for instance, two objects with the same frequency vectors have a positive mean distance. The exact formula for estimation of the mean distance is given; this makes the algorithmization of the proposed procedure possible. The approach corresponds to that of the Bayesian estimation. The matrix of expected mean distances is an input to the hierarchical cluster analysis. (ii) The conventional hierarchical cluster analysis investigates similarities between objects from a given class. A modified general procedure is proposed seeking analogies between two classes of objects. The "two-class cluster analysis" is applicable to any kind of objects to be clustered; it is not confined to the herein discussed special case of frequency vectors. (iii) The development of the procedure was developed initially for the field of the psychotherapy research - investigation of relationship patterns found within verbatim protocols of sessions using the "guided imagery", a psychotherapy technique dealing with evoked daydreams. This constitutes an application example.

• [10] Valdés J. J. (Canada): Similarity-based heterogeneous neurons in the context of general observational models, 499-507.

This paper presents a framework for processing heterogeneous information based on the construction of general observational domains, and similarity-based function calculi suitable for data mining in domains which can be described by corresponding observational models. These calculi are intuitive, simple, and sufficiently general for classification and pattern recognition tasks. Functions in these calculi are represented by a particular kind of neuron models and their behavior is illustrated with examples from real-world domains showing their capabilities in processing heterogeneous, incomplete and fuzzy information.

• [11] Wiedermann J. (Czech Republic): On the super-Turing computational power of non-uniform families of neuromata, 509-516.

It is shown that the computational power of non-uniform infinite families of (discrete) neural nets reading their inputs sequentially (so-called neuromata), of polynomial size, equals to PSPACE/poly, and of logarithmic size to LOGSPACE/log. Thus, such families posses super-Turing computational power. From computational complexity point of view the above mentioned results rank the respective families of neuromata among the most powerful computational devices known today.

### 4/2002

• [1] Dündar P. (Turkey): Results on the integrity of double star graphs, 311-317.

A network begins losing nodes or links, or there may be a loss in its effectiveness. Thus, the communication network must be constructed to be as stable as possible, not only with respect to the initial disruption, but also with respect to the possible reconstruction of the network. Stability numbers of a communication network measure its durability with respect to a break down. If we consider a graph as modelling of a communication network, connectivity is an important measure of reliability or stability of a graph, but not enough. Integrity is a new measurement of stability. It takes into consideration the number of vertices of the remaining components after some disruption. Also the edge-integrity is defined. In this paper, we study integrity (or vertex-integrity) and edge-integrity of Double Star Graphs and some of its compounds.

• [2] Muro E. M. (Spain), Andrade M. A. (Germany), Morán F. (Spain): A self-organizing model for the development of orientation selectivity and ocular dominance patterns in the visual nervous system, 319-332.

A binocular model for the prenatal development of the visual nervous system is proposed. The model is able to reproduce some properties observed in mammals at the moment of birth such as retinotopy, oriented receptive fields, and ocular dominance. One of the outstanding features of the model architecture is the existence of dendrodendritic interaction within each layer. The spontaneous activity of the neurons of the input layer is modeled by spatially and temporally decorrelated activity. The evolution of a connection depends on the output activity of both connected neurons. Hebbian learning has been used for the afferent excitatory connections and anti-Hebbian learning for the lateral inhibitory connections. The model is reduced to a set of ordinary differential equations obtained from a statistical treatment of the dynamics that avoids its explicit dependence on the spontaneous activity.

• [3] Majerová D., Kukal J. (Czech Republic): Multicriteria approach to 2D image de-noising by means of Łukasiewicz algebra with square root, 333-348.

The image de-noising is a practical application of image processing. Both linear and nonlinear filters are used for the noise reduction. The filters which are realizable in Łukasiewicz algebra with square root were analyzed first and then they were used for the 2D image de-noising. There is a set of quality measures recommended for the evaluation of de-noising quality. In case of various quality measures we can find the best filter. The Pareto optimality principle and the AIA technique were used for this purpose. The procedures were demonstrated on a set of MRI biomedical images.

• [4] Koshur V. D. (Russia): Modelling of laminated metal-ceramic composites with neural network control of elastic waves transformations, 349-360.

Intelligent materials, structures and structronic (structure + electronic) systems can function autonomously in response to the varying environmental and operating conditions [1-4]. This paper describes the application of artificial neural networks as adaptive controllers for elastic waves transformations. The results presented are connected to the modelling of smart composite materials proposed as an integral, mechanical, neural network and electronic systém which has been named as the Matrix Electronic Materials (MEM). A converse piezoelectric effect is used to suppress the amplitudes or to modify the frequency of elastic waves which propagate along the thickness of a laminated metal-ceramic plate when on the front surface of the plate the oscillating pressure is applied. The investigation of such problems relating to the elaboration of smart materials and structures, can be used for diverse technical applications, in particular, for suppression of vibrations and noise.

• [5] Güney K., Sagiroglu S., Erler E. (Turkey): Design of rectangular microstrip antennas with the use of artificial neural networks, 361-370.

A model for the design of rectangular microstrip antennas, based on artificial neural networks, is presented. The multiple output design parameters are calculated by using only one network. The extended delta-bar-delta algorithm is used to train the network. The neural model is simple and is useful for the computer-aided design (CAD) of microstrip antennas. The design results obtained by using the neural model are in very good agreement with the results available in the literature.

• [6] Cavalli E., Moriggia V. (Italy): Logical data analysis vs. neural networks in the creditworthines, 371-392.

Statistics, Operations Research and Artificial Intelligence are often used to identify the factors that influence certain phenomena of real life based on samples of data. In the variety of data analysis techniques suggested by these disciplines, the classification capability of Logical Analysis of CORRETTOv: Data Data, proposed by Hammer in [12], is compared to the neural networks in the well-known financial classification problem of insolvency.

• [7] Book review, 393-394.
• [8] Book review, 395-396.
• [9] Book review, 397-398.
• [10] Book review, 399-401.
• [11] Book review, 401-403.

### 3/2002

• [1] Vlček J., Kuűerová J. (Czech Republic): Genetic algorithms in systém procedures, 211-221.

The structure of procedures with genetic algorithms using methodological tools of constructive system theory is described. The model of genetic code of system is used for the transmission of species characteristics with the emphasis on non-living and formal objects.

• [2] Jiřina M. (Czech Republic): Preprocessing of initial weights in the SOM, 223-239.

In this paper we introduce a new approach to the preprocessing (initial setting) of weight vectors and thus a speed-up of the well-known SOM (Kohonen's, SOFM) neural network. The idea of the method (we call it Prep through this paper) consists in spreading a small lattice over the pattern space and consequently completing its inner meshes and boundaries to obtain a larger lattice. This large lattice is then tuned by its training for a short time. To justify the speed up of the Prep method we give a detailed time analysis. To demonstrate the suggested method we show its abilities on several representative examples.

• [3] Peček B. L., Grabec I. (Slovenia): Forecasting electric power consumption by a normalised radial-basis function neural network, 241-254.

An empirical model for forecasting electric power consumption is formulated. The research concerns the preparation and optimal selection of characteristic variables. Prototype patterns of electric power consumption over a day are described by proper by encoding the day-types and their self-organised adaptation to the data recorded in the past. In this procedure, holidays are treated by specific prototype patterns. The influence of the environmental temperature on the consumed power is accounted for by including the extreme values of temperature in a day into prototype patterns. These patterns are employed as parameters of a normalised radial basis function neural network, which is used to forecasting the consumption process. The performance of forecasting and the applicability of various input variables is tested, based on one- and four-year-long records of electric power consumption in Slovenia.

• [4] Svoboda P. (Czech Republic): Alternative methods of EEG signal analysis, 255-266.

Methods of analyses of biological time series are presented and compared to the traditional techniques based on the Fourier transform. Parametric methods are used for computation of the autoregressive estimator, for the model order selection and for the spectrum estimation. A nonlinear analysis deals with the state-space trajectory reconstruction and with the fractal and embedding dimension estimation. Experimental results compare the abilities of traditional, parametric and nonlinear methods to distinguish different cognitive states of the human operator by an analysis of an EEG curve.

• [5] Brunner J., Koutník J. (Czech Republic): SiMoNNe - Simulator of modular neural networks, 267-278.

In this paper, the description of the new neurosimulator SiMoNNe is presented. This simulator should facilitate the design of a new artificial neural network paradigm to a designer. A user can fully concentrate on the network design while working with SiMoNNe instead of the low-effective adaptation of the existing neural network paradigm or simulator. The crucial thing for the SiMoNNe simulator is a language containing resources for description, execution and debugging of a neural network. The SiMoNNe simulator can be optimized for a particular application. The architecture of SiMoNNe assumes taking advantages of the internet.

• [6] Olej V. (Slovakia): Prediction of gross domestic product development by frontal neural networks with learning process on the basic genetic and eugenic algorithms, 279-291.

The paper presents the possibility of application of frontal neural networks, genetic and eugenic algorithms in predicting gross domestic product development by designing a prediction model whose accuracy is superior to the model used in practice [1]. The learning process is implemented by means of a newly designed algorithm based on the EuSANE algorithm [2].

• [7] JiŘina M., Cahlík T. (Czech Republic): Growing hyperspheres neural classifier and its utilization for an economical analysis, 293-306.

This article introduces an improved growing hyperspheres (GHS) neural classifier that is based on a proper distribution of hyperspheres over patterns to properly cover all the patterns of a given class. The union of these hyperspheres then form a discrimination surface among the classes. The article describes a complete general algorithm together with all up-to-date modifications and shows its abilities on an economical problem. A comparison with results obtained by the multilayer perceptron (MLP) neural network is presented. The problem consists in a detection of peaks (steep time changes) in a time sequence of the total factor productivity - a residual factor in the production function. The peaks can be interpreted - at least in the Real Business Cycles (RBC) Theory - as shocks caused by sudden technological innovations. The results from the GHS and MLP neural network are compared with results obtained by means of empirical rules compiled by an economic expert.

• [8] Conference announcement, 307-309.

### 2/2002

• [1] Brandejsky T. (Czech Republic): Qualitative behaviours similarity measure, 105-112.

The paper presented deals with a method of calculation of Qualitative Behaviours Similarity Measure. At the beginning, the measure of the qualitative distance of qualitative states in a given time-point is defined. Then the paper solves practical problems of landmark sets unification. Compared qualitative behaviours are each described by a different set of landmarks and distinguished time-points. All work is summarised in a measure of the similarity definition and the algorithm of similarity calculation.

• [2] Dunis Ch. L., Jalilov J. (United Kingdom): Neural network regression and alternative forecasting techniques for predicting financial variables, 113-139.

In this paper, we examine the use of Neural Network Regression (NNR) and alternative forecasting techniques in financial forecasting models and financial trading models. In both types of applications, NNR models results are benchmarked against simpler alternative approaches to ensure that there is indeed added value in the use of these more complex models.

The idea to use a nonlinear nonparametric approach to predict financial variables is intuitively appealing. But whereas some applications need to be assessed on traditional forecasting accuracy criteria such as root mean squared errors, others that deal with trading financial markets need to be assessed on the basis of financial criteria such as risk adjusted return.

Accordingly, we develop two different types of applications. In the first one, using monthly data from April 1993 through June 1999 from a UK financial institution, we develop alternative forecasting models of cash flows and cheque values of four of its major customers. These models are then tested out-of-sample over the period July 1999-April 2000 in terms of forecasting accuracy.

In the second series of applications, we develop financial trading models for four major stock market indices (S&P500, FTSE100, EUROSTOXX50 and NIKKEI225) using daily data from 31 January 1994 through 4 May 1999 for in-sample estimation and leaving the period 5 May 1999 through 6 June 2000 for out-of-sample testing. In this case, the trading models developed are not assessed in terms of forecasting accuracy, but in terms of trading efficiency via the use of a simulated trading strategy.

In both types of applications, for the periods and time series concerned, we clearly show that the NNR models do indeed add value in the forecasting process.

• [3] Frolov A. A. (Russia), Rachkovskij D. A. (Ukraine), Húsek D. (Czech Republic): On informational characteristics of Willshaw-like auto-associative memory, 141-157.

A sparsely encoded Willshaw-like attractor neural network based on the binary Hebbian synapses is investigated analytically and by computer simulations. A special inhibition mechanism which supports a constant number of active neurons at each time step is used. The informational capacity and the size of attraction basins are evaluated for the Single-Step and the Gibson-Robinson approximations, as well as for experimental results.

• [4] Hájek P. (Czech Republic): Some hedges for continuous t-norm logics, 159-164.

The basic fuzzy logic BL is extended by two unary connectives L, U (lower, upper) whose standard semantics is, given a continuous t-norm, the function assigning to each x$\in$[0,1] the biggest idempotent $\le$x (least idempotent $\ge$x). An axiom system is presented and shown complete with respect to the corresponding class of algebras. But the set of tautologies for a fixed continuous t-norm may have an arbitrarily high degree of insolvability.

• [5] Mendes A. S., Franca P. M., Moscato P. (Brazil): Fitness landscapes for the total tardiness single mechine scheduling problem, 165-180.

This paper addresses several issues related to the approximate solution of the Single Machine Scheduling problem with sequence-dependent setup times using metaheuristic methods. Instances with known optimal solution are solved using a memetic algorithm and a multiple start approach. A fitness landscape analysis is also conducted on a subset of instances to understand the behavior of the two approaches during the optimization process. We also present a novel way to create instances with known optimal solutions from the optimally solved asymmetric travelling salesman problem (ATSP) instances. Finally we argue for the test set of instances to be used in future works as a convenient performance benchmark.

• [6] Sfetsos A. (Greece): The application of neural logic networks in time series forecasting, 181-199.

This paper discusses the application of Neural Logic Networks in time series forecasting. Neural Logic Networks are systems that are developed to incorporate the strengths of neural networks and expert systems, which is equivalent to the human processes of logic and intuition [1]. This paper examines their prospect in forecasting of time series and compares their performance with linear models and the Feed Forward Neural Network. Additionally, the suitability of logic rules, generated from a Neural Logic Network, as potential inputs to forecasting systems is also examined. They are applied on two different meteorological series with strong features: a mean hourly wind speed series that exhibits behavior similar to random walk and an hourly solar radiation series selected because of its seasonal nature with discontinuities.

• [7] Book review, 201-202.
• [8] Book review, 203-204.
• [9] Conference announcement, 205.
• [10] Conference announcement, 207-209.

### 1/2002

• [1] Editorial, 1.
• [2] Chen Q., Zheng Q., Ling W. (China): Implementation of an on-chip learning artificial neural network, 3-14.

An on-chip learning Artificial Neural Network (ANN) implementation using the Pulse Width Modulation (PWM) technique is proposed in this paper. Synapse and neuron are analog circuits, while digital counters are utilized to store the weights. Through the PWM circuit, the digital weight is converted into a pulse signal as the input of the analog synapse circuit. The analog modified quantity of weight is transformed into a weight-update pulse signal whose width is proportion to the value of the weight modification quantity. The learning rule is based on the weight perturbation algorithm. In this way, the weight can be long-term-stored and easily modified, thereas the synapse and the neuron are of a small size in the silicon area and the learning circuit is feasible for implementation. Taking the advantages of both the analog and the digital realizations of the ANN, this method is a meaningful way to the implementation of on-chip ANN and fuzzy processors.

• [3] Goltsev A., Húsek D. (Czech Republic): Some properties of the assembly neural networks, 15-32.

Generalization phenomena which take place in two different assembly neural networks are considered in the paper. Either of these two assembly networks is artificially partitioned into several subnetworks according to the number of classes that the network has to recognize. Hebb's assemblies are formed in the networks. One of the assembly networks is with binary connections, the other is with analog ones. Recognition abilities of the networks are compared on the task of handwritten character recognition. The third neural network of a perceptron type is considered in the paper for comparison with the previous ones. This latter network works according to the nearest-neighbor method. Computer simulation of all three neural networks was performed. Experiments showed that the assembly network with binary connections has approximately the same recognition accuracy as the network realizing the nearest-neighbor technique.

• [4] Isasi P., Velasco M., Segovia J. (Spain): Selecting coefficients for emage processing using non-supervised neural nets, 33-43.

This paper introduces a new sensitivity analysis method using non-supervised neural nets, based on the Adaptive Resonance Theory (ART).This new method introduces the possibility of a sensitivity analysis being adaptive and being conducted at the same time as net learning is taking place, taking advantage of the property of continuous (as opposed to phase-wise) learning of ART models. A sensitivity analysis can be conducted likewise, i.e. continuous by and capably adapting to any new relationships appearing among the input data. The method has been validated in the field of feature detection for image classification and, more specifically, for face recognition.

• [5] Kukal J., Majerová D., Procházka A. (Czech Republic): Fuzzy prediction based on £ukasiewicz algebra, 45-66.

Noisy time series are typical results of observations or technical measurements. Noise reduction and signal structure saving are contradictory but useful aims. Non-linear time series processing is a way for non-gaussian noise suppression. Many valued algebras enriched by square root are able to realize the operators close to the weighted averages. Fuzzy data processing based on £ukasiewicz algebra [3] with square root satisfies the Lipschitz condition and causes constrained sensitivity of the mapping. The paper presents a fuzzy neural network based on Modus Ponens [1] with fuzzy logic function [6] preprocessing in the hidden layer. All the fuzzy algorithms were realized in the Matlab system and in C++. The fuzzy processing is applied to prediction of sunspot numbers. The systematic approach based on filter selection is combined with weight optimization.

• [6] Sarkar D. (USA): An algorithm for computation of inter-pattern interference noise in BAM, 67-73.

Standard Bidirectional Associative Memory (BAM) stores sum-of-the-correlation-matrices of the pairs of patterns. When a pattern of an encoded pair is presented, the other is expected to be recalled. It has been shown that standard BAM cannot correctly recall a pattern pair if it is not at local minima of the energy function. To overcome this problem, novel methods for encoding have been proposed. The efficient novel-encoding methods require knowledge of the interference noise in the standard BAM. In this paper, we propose an algorithm for computing the exact amount of interference noise in standard encoding of BAM. The computational complexity of the algorithm is the same as that of computing the correlation matrix for the standard BAM.

• [7] Ratsimalahelo Z. (France): On approximate systems identification, 75-95.

In this paper, concepts and techniques of the system theory are used to obtain state-space (Markovian) models of dynamic economic processes instead of the usual VARMA models. In this respect, the concept of state is reviewed as are Hankel norm approximations and balanced realizations for stochastic models. We clarify some aspects of the balancing method for state space modelling of the observed time series. This method may fail to satisfy the so-called positive real condition for stochastic processes. We use a state variance factorization algorithm, which does not require us to solve the algebraic Riccati equation. We relate the Aoki-Havenner method to the Arun-Kung method.

• [8] Contens volume 11 (2001), 97-99.
• [9] Author's index volume 11 (2001), 101-104.

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