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## Über dieses Buch

Prediction of behavior of the dynamical systems, analysis and modeling of its structure is vitally important problem in engineering, economy and science today. Examples of such systems can be seen

in the world around us and of course in almost every scientific discipline including such “exotic” domains like the earth’s atmosphere, turbulent fluids, economies (exchange rate and stock markets),

population growth, physics (control of plasma), information flow in social networks and its dynamics, chemistry and complex networks. To understand such dynamics and to use it in research or industrial

applications, it is important to create its models. For this purpose there is rich spectra of methods, from classical like ARMA models or Box Jenkins method to such modern ones like evolutionary

computation, neural networks, fuzzy logic, fractal geometry, deterministic chaos and more. This proceeding book is a collection of the accepted papers to conference Nostradamus that has been held in Ostrava, Czech Republic. Proceeding also comprises of outstanding keynote speeches by distinguished guest speakers: Guanrong Chen (Hong Kong), Miguel A. F. Sanjuan (Spain), Gennady Leonov and Nikolay Kuznetsov (Russia), Petr Škoda (Czech Republic).

The main aim of the conference is to create periodical possibility for students, academics and researchers to exchange their ideas and novel methods. This conference will establish forum for

presentation and discussion of recent trends in the area of applications of various predictive methods for researchers, students and academics.

## Inhaltsverzeichnis

### Constructing a Simple Chaotic System with an Arbitrary Number of Equilibrium Points or an Arbitrary Number of Scrolls

In a typical 3D smooth autonomous chaotic system, such as the Lorenz and the Rssler systems, the number of equilibria is three or less and the number of scrolls in their attractors is two or less. Today, we are able to construct a relatively simple smooth 3D autonomous chaotic system that can have any desired number of equilibria or any desired number of scrolls in its chaotic attractor. Nowadays it is known that a 3D quadratic autonomous chaotic system can have no equilibrium, one equilibrium, two equilibria, or three equilibria. Starting with a chaotic system with only one stable equilibrium, by adding symmetry to it via a suitable local diffeomorphism, we are able to transform it to a locally topologically equivalent chaotic system with an arbitrary number of equilibria. In so doing, the stability of the equilibria can also be easily adjusted by tuning a single parameter. Another interesting issue of constructing a 3D smooth autonomous chaotic system with an arbitrary number of scrolls is discussed next. To do so, we first establish a basic system that satisfies Shilnikovs inequalities. We then search for a heteroclinic orbit that connects the two equilibria of the basic system. Finally, we use a copy and lift technique and a switching control method to timely switch the dynamics between nearby sub-systems, thereby generating a chaotic attractor with multiple scrolls. Not only the number but also the positions of the scrolls in the chaotic attractor can be determined by our design method. This talk will briefly introduce the ideas and methodologies.

Guanrong Chen

### Dynamics of Partial Control of Chaotic Systems

In our chaotic lives we usually do not try to specify our plans in great detail, or if we do, we should be prepared to make major modifications. Our plans for what we want to achieve are accompanied with situations we must avoid. Disturbances often disrupt our immediate plans, so we adapt to new situations.We only have partial control over our futures. Partial control aims at providing toy examples of chaotic situations where we try to avoid disasters, constantly revising our trajectories. Moremathematically, partial control of chaotic systems is a newkind of control of chaotic dynamical systems in presence of disturbances. The goal of partial control is to avoid certain undesired behaviors without determining a specific trajectory. The surprising advantage of this control technique is that it sometimes allows the avoidance of the undesired behaviors even if the control applied is smaller than the external disturbances of the dynamical system. A key ingredient of this technique is what we call safe sets. Recently we have found a general algorithm for finding these sets in an arbitrary dynamical system, if they exist. The appearance of these safe sets can be rather complex though they do not appear to have fractal boundaries. In order to understand better the dynamics on these sets, we introduce in this paper a new concept, the asymptotic safe set. Trajectories in the safe set tend asymptotically to the asymptotic safe set. We present two algorithms for finding such sets. We illustrate all these concepts for a time-2

π

map of the Duffing oscillator. This is joint work with James A. Yorke (USA), Samuel Zambrano (Italy) and Juan Sabuco (Spain).

Miguel A. F. Sanjuan

### Prediction of Hidden Oscillations Existence in Nonlinear Dynamical Systems: Analytics and Simulation

From a computational point of view, in nonlinear dynamical systems, attractors can be regarded as self-excited and hidden attractors. Self-excited attractors can be localized numerically by a standard computational procedure, in which after a transient process a trajectory, starting from a point of unstable manifold in a neighborhood of equilibrium, reaches a state of oscillation, therefore one can easily identify it. In contrast, for a hidden attractor, a basin of attraction does not intersect neighborhoods of equilibria. While classical attractors are self-excited, attractors can therefore be obtained numerically by the standard computational procedure, for localization of hidden attractors it is necessary to develop special procedures, since there are no similar transient processes leading to such attractors. This keynote lecture is devoted to affective analytical-numerical methods for localization of hidden oscillations in nonlinear dynamical systems and their application to well known fundamental problems and applied models.

Gennady A. Leonov, Nikolay V. Kuznetsov

### Astroinformatics: Getting New Knowledge from the Astronomical Data Avalanche

The research in almost all natural sciences is facing the data avalanche represented by an exponential growth of information produced by big digital detectors and large-scale multi-dimensional computer simulations stored in the worldwide network of distributed archives. As the data volumes have been growing faster than computer technology can cope with, a qualitatively new research methodology called Data Intensive Science or X-informatics is required, based on an advanced statistics and data mining methods, as well as on a new approach to sharing huge databases in a seamless way by global research communities. This approach, sometimes presented as a Fourth Paradigm of contemporary science, promises new scientific discoveries as a result of understanding hidden dependencies and finding rare outliers in common statistical patterns extracted by machine learning methods from Peta-scale data archives. The implementation of X-informatics in astronomy, Astroinformatics, is a new emerging discipline, integrating computer science, advanced statistics, and astrophysics to yield new discoveries and better understanding of nature of astronomical objects. It has been fully benefitting from the long-term skill of astronomy of building well documented astronomical catalogues and automatically processed telescope and satellite data archives. The astronomical Virtual Observatory project plays a key role in this effort, being the global infrastructure of federated astronomical archives, web-based services, and powerful client tools supported by supercomputer grids and clusters. It is driven by strict standards describing all astronomical resources worldwide, enabling the standardized discovery and access to these collections as well as advanced visualization and analysis of large data sets. In our talk, we give a overview of the motivations, early history, and technological principles of Virtual Observatory, as well as a more philosophical view of data mining, Citizen Science, and new promises of Astroinformatics in the age of data-flooded astronomy.

Petr Škoda

### Engineering of Mathematical Chaotic Circuits

We introduce the paradigm of chaotic mathematical circuitry which shows some similarity to the paradigm of electronic circuitry especially in the frame of chaotic attractors for application purpose (cryptography, generic algorithms in optimization, control, …).

René Lozi

### Utilising the Chaos-Induced Discrete Self Organising Migrating Algorithm to Schedule the Lot-Streaming Flowshop Scheduling Problem with Setup Time

The dissipative Lozi chaotic map is embedded in the Discrete Self Organising Migrating (DSOMA) algorithm, as a pseudorandom generator. This novel chaotic based algorithm is applied to the constraint based Lot-Streaming Flowshop scheduling problem. Two new and unique data sets generated using the Lozi and Dissipative maps are used to compare the chaos embedded DSOMA (DSOMAc) and the generic DSOMA utilising the venerableMersenne Twister. In total, 100 data sets were tested by the two algorithms, for the idling and the non-idling case. From the obtained results, the DSOMA

c

algorithm is shown to significantly improve the performance of generic DSOMA.

Donald Davendra, Roman Senkerik, Ivan Zelinka, Michal Pluhacek, Magdalena Bialic-Davendra

### Hidden Periodicity – Chaos Dependance on Numerical Precision

Deterministic chaos has been observed in many systems and seems to be random-like for external observer. Chaos, especially of discrete systems, has been used on numerous occasions in place of random number generators in so called evolutionary algorithms. When compared to random generators, chaotic systems generate values via so called map function that is deterministic and thus, the next value can be calculated, i.e. between elements of random series is no deterministic relation, while in the case of chaotic system it is. Despite this fact, the very often use of chaotic generators improves the performance of evolutionary algorithms. In this paper, we discuss the behavior of two selected chaotic system (logistic map and Lozi system) with dependance on numerical precision and show that numerical precision causes the appearance of many periodic orbits and explain reason why it is happens.

Ivan Zelinka, Mohammed Chadli, Donald Davendra, Roman Senkerik, Michal Pluhacek, Jouni Lampinen

### Do Evolutionary Algorithms Indeed Require Random Numbers? Extended Study

An inherent part of evolutionary algorithms, that are based on Darwin theory of evolution and Mendel theory of genetic heritage, are random processes. In this participation, we discuss whether are random processes really needed in evolutionary algorithms. We use

$\mathcal{n}$

periodic deterministic processes instead of random number generators and compare performance of evolutionary algorithms powered by those processes and by pseudo-random number generators. Deterministic processes used in this participation are based on deterministic chaos and are used to generate periodical series with different length. Results presented here are numerical demonstration rather than mathematical proofs. We propose that a certain class of deterministic processes can be used instead of random number generators without lowering of evolutionary algorithms performance.

Ivan Zelinka, Mohammed Chadli, Donald Davendra, Roman Senkerik, Michal Pluhacek, Jouni Lampinen

### New Adaptive Approach for Chaos PSO Algorithm Driven Alternately by Two Different Chaotic Maps – An Initial Study

In this initial study a novel adaptive approach for chaos driven PSO algorithm is proposed. Two different chaotic maps are used as pseudorandom number generators and switched over during the run of chaos driven PSO algorithm. The new adaptive approach brings promising results that are presented and briefly analyzed.

Michal Pluhacek, Roman Senkerik, Ivan Zelinka, Donald Davendra

### On the Performance of Enhanced PSO Algorithm with Dissipative Chaotic Map in the Task of High Dimensional Optimization Problems

In this paper, it is proposed the utilization of discrete Dissipative standard map based chaos pseudorandom number generator to enhance the performance of PSO algorithm with linear decreasing inertia weight in the task of high dimensional optimization. The performance is tested on a set of four typical test functions and the results are briefly analyzed and compared against the standard PSO version with inertia weight.

Michal Pluhacek, Roman Senkerik, Ivan Zelinka, Donald Davendra

### Utilization of Analytic Programming for Evolutionary Synthesis of the Robust Controller for Set of Chaotic Systems

In this paper, it is presented a utilization of tool for symbolic regression, which is analytic programming, for the purpose of the synthesis of a new robust feedback control law. This universal synthesized robust chaotic controller secures the fully stabilization of selected set of three discrete chaotic systems. The paper consists of the descriptions of analytic programming as well as selected chaotic systems, used heuristic and cost function design. For experimentation, Self-Organizing Migrating Algorithm (SOMA) and Differential evolution (DE) were used.

Roman Senkerik, Zuzana Kominkova Oplatkova, Ivan Zelinka, Michal Pluhacek

### Chaos Powered Selected Evolutionary Algorithms

It is well known that the evolution algorithms use pseudo-random numbers generators for example to generate random individuals in the space of possible solutions, crossing etc. In this paper we are dealing with the effect of different pseudo-random numbers generators on the course of evolution and the speed of their convergence to the global minimum. From evolution algorithms the differential evolution and self organizing migrating algorithm have been chosen because they have different strategies. As the random generators Mersenne Twister and chaotic system - logistic map have been used.

Lenka Skanderova, Ivan Zelinka, Petr Šaloun

### Case Study of Evolutionary Process Visualization Using Complex Networks

This paper presents a case study of visualization of evolutionary process using complex network. Our previous research focused on application of evolutionary algorithms on finding global minimum of energetic function obtained in Force-directed graph drawing algorithm. This research has been combined with novel method for visualization of Differential Evolution (DE) and Self-Organizing Migration Algorithm (SOMA) process. We have developed and run our own algorithms, visualized and analyzed evolutionary complex networks obtained from their process. This paper presents improvements to the evolutionary network visualization by observing changes of some of the complex network properties during evolution. We also propose further improvements to the evolutionary network visualization.

Patrik Dubec, Jan Plucar, Lukáš Rapant

### Stabilization of Chaotic Logistic Equation Using HC12 and Grammatical Evolution

The paper deals with stabilization of simple deterministic discrete chaotic system. By means of proper utilization of meta-heuristic optimization tool, the HC12 algorithm stands alone and together with a symbolic regression tool, which is Grammatical Evolution (GE), and can synthesise a new control law. Given softcomputing tools appear as powerful optimization tool for an optimal control parameters tuning and general control law design too. The well known one dimensional discrete Logistic equation was used as a model of deterministic chaotic system. Satisfactory results obtained by both heuristics and propose objective function are also compared with previous research of other authors.

The chaotic system stabilization is based on time-delay auto-synchronization (TDAS, ETDAS) and proper combination with own synthesized control law. This synthesized chaotic controller is based on one or two compensator. The primary compensator generates the perturbation sequence using TDAS/ETDAS method, second one is own design using method of GE. The original design of the objective function takes inspiration from standard control theory. All tests are performed using Matlab/Simulink environment.

### Hypervolume-Driven Analytical Programming for Solar-Powered Irrigation System Optimization

In the field of alternative energy and sustainability, optimization type problems are regularly encountered. In this paper, the Hypervolume-driven Analytical Programming (Hyp-AP) approaches were developed. This method was then applied to the multiobjective (MO) design optimization of a real-world photovoltaic (PV)-based solar powered irrigation system. This problem was multivariate, nonlinear and multiobjective. The Hyp-AP method was used to construct the approximate Pareto frontier as well as to identify the best solution option. Some comparative analysis was performed on the proposed method and the approach used in previous work.

T. Ganesan, I. Elamvazuthi, Ku Zilati Ku Shaari, P. Vasant

### Forecasting of Time Series with Fuzzy Logic

There are different methods which can be used for the support of forecasting. Nowadays the new theories of soft computing are used for these purposes. There could be mentioned fuzzy logic, neural networks and some other methods. The aim of the paper is focused on the use of fuzzy logic for forecasting purposes. The advantage of the use of fuzzy logic is in processing imprecision, uncertainty, vagueness, semi-truth, or approximated and nonlinear data. The applications on the stock market have specific features in comparison with others. The processes are focused on private corporate attempts at money making; therefore, the details of applications, successful or not, are not published very often. The fuzzy logic helps in decentralization of decision-making processes to be standardized, reproduced, and documented, that is an important factor in the business field. It was proved by the tests in the practice that the presented case studies had their justness to be used as a support for a decision making on the stock market.

Petr Dostál

### Unknown Input Proportional Integral Observer Design for Chaotic TS Fuzzy Models

In this paper, the chaos synchronization problem is treated by an unknown input proportional integral observer (PIO) for a Takagi-Sugeno (TS) fuzzy chaotic model subject to unknown input and unmeasurable decision variables. This unknown input is considered like a message to encode by a chaotic system then to decode or to reconstruct by the PIO after to be transmitted by a public transmission canal in order to a secure communication system. In our case, the unknown input affects both state and output of the chaotic system. The synthesis conditions of this PIO are based on the hypothesis that the unknown input is under polynomial form with its kth derivative zero. At the end the measurable decision variables are also considered in this work like a particular case. The Lyapunov theory is used to develop the stability conditions of the unknown input PIO in LMIs formulation. A simulation example is proposed through a TS fuzzy chaotic model to validate the proposed design.

### Modeling of EEG Signal with Homeostatic Neural Network

Prediction and modeling of signal are tasks that can be done by many methods among which the neural networks have an important place due to the fact that it is data driven method that doesn´t require extensive understanding of the process. This paper presents a new type of neural network that was tested on the modeling of EEG signal. The performance of this network was compared to traditional NN methods. The novelty of this network consists in the fact that each neuron is processing its learning as an independent unit, without any higher process or structure. The learning rule can be simply described as ´improving the significance of the neuron for the rest of the network´. The growth of computational power in recent years opens new possibilities to the use of neural networks in artificial intelligence.

Martin Ruzek

### Model Identification from Incomplete Data Set Describing State Variable Subset Only – The Problem of Optimizing and Predicting Heuristic Incorporation into Evolutionary System

Presented paper describes the application of evolutionary system GPA-ES in difficult task of chaotic system symbolic regression from incomplete training data set describing only some of model variables. The algorithm uses many heuristics which are described below and which will be subject of future development. The first test of algorithm was applying the Lorenz attractor system data, where only the original system x and y variable data were used and z variable data were estimated.

Tomas Brandejsky

### Supervised and Reinforcement Learning in Neural Network Based Approach to the Battleship Game Strategy

In our study the Battleship game we concern as an example of a simple pattern matching problem in correspondence with the Partially observable Markov decision process. We provide comparison of supervised and reinforcement learning paradigms used as neural network learning mechanisms applied by solving the Battleship game.We examine convergence of the neural network adaptation process by using these techniques.While concerning our pattern matching problem of the Battleship game solution by the neural network the reinforcement learning technique is not as straightforward as the supervised learning. On the other hand the neural network adaptation by the supervised learning mechanism has a faster convergence in our case. We use the Battleship game probability model to determine next position in an environment to be shot at with the highest probability of resulting into a successful hit attempt.

### Evolutionary Algorithms for Parameter Estimation of Metabolic Systems

For many years, computational tools have been widely applied to study such complex systems as metabolic networks. One of the principal questions in modeling of metabolic systems is the parameter estimation of model, which is related to a nonlinear programming problem. Two types of evolutionary algorithms, Differential Evolution and Self-Organizing Migrating Algorithm, are applied to the well-studied metabolic system, the urea cycle of the mammalian hepatocyte. The algorithms provide an effective approach in parameters identification of the model.

### Evolutionary Synthesis of Complex Structures – Pseudo Neural Networks for the Task of Iris Dataset Classification

This research deals with a novel approach to classification. This paper deals with a synthesis of a complex structure which serves as a classifier. Classical artificial neural networks, where a relation between inputs and outputs is based on the mathematical transfer functions and optimized numerical weights, were an inspiration for this work. The proposed method utilizes Analytic Programming (AP) as the tool of the evolutionary symbolic regression. AP synthesizes a whole structure of the relation between inputs and output. Iris data (a known benchmark for classifiers) was used for testing of the proposed method. For experimentation, Differential Evolution for the main procedure and also for meta-evolution version of analytic programming was used.

Zuzana Kominkova Oplatkova, Roman Senkerik

### Speech Emotions Recognition Using 2-D Neural Classifier

This article deals with a speech emotion recognition system. We discuss the usage of a neural network as the final classifier for human speech emotional state. We carried our research on a database of records of both genders and various emotional states. In the preprocessing and speech processing phase, we focused our intent on parameters dependent on the emotional state. The output of this work is a system for classifying the emotional state of a man’s voice, which is based on a neural network classifier. For output-stage classifier was used self-organizing feature map, which is specific type of artificial neural nets. The number of input parameters must be limited for hardware and time consuming computation of neurons positions. Therefore we discuss the accuracy of the classifier whose input is the fundamental frequency calculated by different methods.

Pavol Partila, Miroslav Voznak

### Predictive Control of Radio Telescope Using Multi-layer Perceptron Neural Network

Radio telescope (RT) installations are highly valuable assets and during the period of their service life they need regular repair and maintenance to be carried out for delivering satisfactory performance and minimizing downtime. With the growing automation technologies, predictive control can prove to be a better approach than the traditionally applied visual inspection policy and linear models. In this paper, Irbene Radio telescope RT-16 disk rotation control motors are analysed. Retrieved data from the small DC motor is used for the predictive control approach. A Multilayer Perceptron (MLP) network approach is used for prediction of the indicator voltage output which affects the monitoring of the disk rotating angle.

Sergej Jakovlev, Miroslav Voznak, Kestutis Ruibys, Arunas Andziulis

### Modeling and Simulation of a Small Unmanned Aerial Vehicle

This paper aims to demonstrate a design of low-cost, and Inertial Measurement Unit (IMU) based autopilot that is ArduPilot, and its applications. ArduPilot’s control algorithm possesses two control loops, which are used to control the navigation and the control surfaces such as actuators. Due to using PID control and being able to tune and update the PID parameters (Kp, Ki, Kd) even during the flight, ArduPilot becomes very efficient autopilot also. It’s also possible to export and analyze the data such as airspeed, air pressure, latitude-longitude-altitude, roll-pitch-yaw angles, accelerometer-gyro information, servo outputs, and moreover on Matlab

®

, after or during the flight. In order to go one step further, a model aircraft, which has nearly the same physical parameters as the one used for the real tests, designed on Plane Maker

®

, and simulated on Xplane

®

simulator. Using the simulator made this study easy to tune and test the whole flight parameters before real flight. This paper will lead the students who are interested in automatic control applications especially Unmanned Aerial Vehicles (UAV).

Ozan Eren Yuceol, Ahmet Akbulut

### Mathematical Models of Controlled Systems

The paper is focused on the build of a mathematical model of digital controlled systems. This article describes the creation of mathematical models of one-dimensional systems by the method of experimental identification. The created model is used for predicting the static and dynamic behavior of the controlled system in the closed loop. Dynamic properties of systems are described by the differential equations. In the experimental part are identified the parameters of the mathematical model of rectifying column. As an example, the one-dimensional controlled system, in this case is described the dependence of concentration distilled mixture on change the reflux.

### Effect of Weighting Factors in Adaptive LQ Control

An adaptive control is a technique with strong theoretical background and lots of applications to the abstract and real systems. The big advantage can be found in usability of this control method for systems with negative control properties such as nonlinearity, time-delay, non-minimum behavior etc. The adaptive approach here is based on the choice of the external linear model of the originally nonlinear system parameters of which are updated in defined time moments via recursive identification. The control synthesis employs polynomial approach with linear-quadratic approach and spectral factorization. Resulted controller has two weighting factors as tuning parameters. This paper explores the effect these factors to the control. All proposed approaches were tested by simulations on the mathematical model of the continuous stirred-tank reactor as a typical member of the nonlinear lumped-parameters systems.

Jiri Vojtesek, Petr Dostal

### Unstable Systems Database: A New Tool for Students, Teachers and Scientists

The contribution presents a starting project of a site focused on unstable systems. It is a web-based database in the bilingual version (ENG/CZ) which can be used as an information database for models of unstable processes. The site contains mathematical models of such systems including their simulation files together with basic information about stability of dynamical systems. The paper outlines motivation for development of this database, presents its basic structure and discusses several models from the site. Areas of prospective usage are also suggested together with possible directions of further development of this project.

František Gazdoš, Jiří Marholt, Jaroslav Kolařík

### Nonlinear State Estimation and Predictive Control of pH Neutralization Process

In the paper the fuzzy Kalman filter (KF) is proposed to allow for adaptation to changing properties of the controlled process. The fuzzy KF is used to estimate both states and unmeasured disturbances of the nonlinear process. Further, a Model Predictive Control (MPC) based on the fuzzy representation of the nonlinear process is formulated. The performance of the proposed estimation fuzzy scheme and predictive controller is evaluated through computer simulations of the pH neutralization process. The pH neutralization process is widely recognized as a difficult control problem due to the strong nonlinearity of the process.

Jakub Novák, Petr Chalupa

### State Observers for Model Predictive Control

This paper deals with state observers with respect to their usage in the model predictive control (MPC) based on state space model of the controlled system. In case of immeasurable states a state observer (filter) is used to calculate current states in each control step. The paper is especially focused to finite impulse filters (FIR) as these filters do not require knowledge of initial state - contrary to infinite impulse response (IIR) filters. Several linear filters are tested and compared with proposed filters based on quadratic and linear programming. Different filter lengths (horizons) were tested to investigate filters’ performance. Filters were tested in very noisy conditions to evaluate filter robustness and therefore its usability in real-time deployment. The simulations were carried out using data from a real-time laboratory (Amira DR300 Servo system). All the measurements and simulations were carried out in MATLAB/Simulink environment.

Petr Chalupa, Peter Januška, Jakub Novák

### Characteristics of the Chen Attractor

Within the paper a mathematical representation of the so-called Chen model is described as a particular parametric three-dimensional chaotic dynamical system, i.e. a system of three nonlinear differential equations evolving in time. The main aim of this paper is to find for the Chen system the properties that are known for the Lorenz system and its famous Lorenz attractor. First, the integrals of motion are derived for some parameters of the Chen system. The integrals of motions play an important role in physics, e.g. for conservation laws. Next, the shape of the global attractor of this system is approximated by volumes that contain the attractor. The shape predicts the future behavior of the system. To obtain these results, the already proved fact that the Chen system is a continued transition of the Lorenz system is used. According to our knowledge, the same approach of shifting the known facts about the Lorenz system to a newdynamical system, the Chen system in this context, has not been presented yet.

Petra Augustová, Zdeněk Beran

### Message Embedded Synchronization for the Generalized Lorenz System and Its Use for Chaotic Masking

This paper implements and analyzes the well-known message embedded synchronization scheme for the case of the generalized Lorenz system. Such a synchronization may be used for chaotic masking scheme using a single channel only. This method was already discussed in the earlier literature for the particular classes of systems. In this paper, a more general class wheremessage embedded synchronization is possible is described. Then, it is shown that the generalized Lorenz system falls within that class. Furthermore, using the resulting synchronization, the novel secure encryption scheme is proposed. It requires very reasonable amount of data to encrypt and time to decrypt one bit. Basically, to encrypt one bit, only one iteration (i.e. only one real number of 6 valid digits) is needed. At the same time, 100 percent of the carrying chaotic signal can be used. The method is also demonstrated by numerical simulations of a digital data encryption and decryption.

Sergej Čelikovský, Volodymyr Lynnyk

### Using Complex Network Topologies and Self-Organizing Maps for Time Series Prediction

A Self-organizing Map (SOM) is a competitive learning neural network architecture that make available a certain amount of classificatory neurons, which self-organize spatially based on input patterns. In this paper we explore the use of complex network topologies, like small-world, scale-free or random networks; for connecting the neurons within a SOM, and apply them for Time Series Prediction (TSP).We follow the classical VQTAMmodel for function prediction, and consider several benchmarks to evaluate the quality of the predictions. The results presented in this work suggest that the most regular the network topology is, the better results it provides in prediction. Besides, we have found that not updating all the cells at the same time provides much better results.

Juan C. Burguillo, Bernabé Dorronsoro

### Initial Errors Growth in Chaotic Low-Dimensional Weather Prediction Model

The growth of small errors in weather prediction is exponential. As an error becomes larger, the growth rate decreases and then stops with the magnitude of the error about at a value equal to the size of the average distance between two states chosen randomly.

This paper studies an error growth in a low-dimensional atmospheric model after the initial exponential divergence died away. We test cubic, quartic and logarithmic hypotheses by ensemble prediction method. Furthermore quadratic hypothesis that was suggested by Lorenz in 1969 is compared with the ensemble prediction method. The study shows that a small error growth is best modeled by the quadratic hypothesis. After the initial error exceeds about a half of the error saturation value, logarithmic approximation becomes superior.

Hynek Bednar, Ales Raidl, Jiri Miksovsky

### EEE Method: Improved Approach of Compass Dimension Calculation

In our research has improved an approach of compass dimension calculating for topological one-dimensional objects (especially signals, time series or dividing lines). The method was named

E

valuation of length changes with

E

limination of insignificant

E

xtremes (EEE). The method stems from an estimation of the fractal dimension, so it measures changes of lengths in sequential steps. The EEE method does not use a fixed “ruler” for measurement in every step, but the line is defined by local extremes (maxima and minima). Mathematically generated functions (e.g. based on the Hurst coefficient), time series from real production processes and dividing lines (surface profiles and surface roughness) were used for experiments. The results show good potential for applications in off-line evaluations of data sets and on-line monitoring and control.

Vlastimil Hotař

### Chaotic Analysis of the GDP Time Series

The goal of this paper is to analyze the Czech Gross domestic product (GDP) and to find chaos in the Czech GDP. At first we will estimate the time delay and the embedding dimension, which is needed for the Lyapunov exponent estimation and for the phase space reconstruction. Subsequently we will compute the largest Lyapunov exponent, which is one of the important indicators of chaos. Then we will calculate the 0-1 test for chaos. Finally we will compute the Hurst exponent by Rescaled Range analysis and by dispersional analysis. The Hurst exponent is a numerical estimate of the predictability of a time series. In the end we will display a phase portrait of detrended GDP time series. The results indicated that chaotic behaviors obviously exist in GDP.

### Daily Temperature Profile Prediction for the District Heating Application

We show an application of artificial neural networks for local weather prediction. By employment of appropriate network structure and proper selection of input/output signals, solid results can be achieved. Our system was implemented in the local district heating company, where it was used to predict daily temperature profile with period of 15 minutes. Further, weekly and yearly profiles were predicted, and also heat consumption profiles. Whole prediction system consists of several chained neural networks and data processing modules. Training data for neural networks were collected from meteorological stations around the Košice city. Additional training data were collected by web-robots from internet from several weather forecast agencies.

Juraj Koščák, Rudolf Jakša, Rudolf Sepeši, Peter Sinčák

### Adaptive Classifier of Candlestick Formations for Prediction of Trends

Candlestick charts have become in last decades a popular means in predicting trends on stock markets. Their properties enable in the form of the so-called formations to represent some symptoms of market changes in a user-friendly manner. Thus experienced businessmen are able using such kind of information to predict situations and in advance to correctly decide. However, candlestick charts are only one of many other indicators and their interpretation is not trivial. It depends e.g. on commodity, stage of a given trend, etc. To efficiently perform correct prediction using this graphical means a system utilizing ability to process vague information being able of adaptation is necessary. In this paper a design of such an fuzzy adaptive knowledge-based classification system using evolutionary optimization is proposed for categorization of characteristic candlestick formations and verified by a number of experiments in the area of exchange rates.

Ján Vaščák, Peter Sinčák, Karol Prešovský

### Identification of Economic Agglomerations by Means of Accounting Data from ERP Systems of Business Entities

The aim of this paper is to introduce the methodology of the identification of common economic agglomerations based on the accounting data gained from business entities in the Czech Republic. The identification of economic agglomerations by descriptive approach should reveal the geographical location and their extent within the country. Although the result of the examination cannot be fully generalised due to a limited data source, it should be considered as the contribution to regional studies of the Czech Republic in the broadest context.

Petr Hanzal, Ivana Faltová Leitmanová

### Nonlinear Spatial Analysis of Dynamic Behavior of Rural Regions

We aim to examine the impact of economic growth with a carbon dioxide

(CO

2

) emission factor, particularly, our investigation focuses on the dynamic behaviors of the functional regions of a rural area. A spatial analysis approach that incorporates three components and

CO

2

emission factor has been developed to evaluate the dynamic behaviors of the rural areas at an administrative county level.We adopt the Mendel genetic algorithm (Mendel-GA) to implement the technical computation, in which a Mendel genetic operator implies the random assignment by using the Mendel’s principles and the data of gross domestic product (GDP) has been utilised to estimate the

CO

2

emission of productive activities in the rural area. A functional region affecting index (FRAI) has been used to construct the fitness function in the Mendel genetic algorithm evaluation. The real data simulation for Chongqing rural region indicates that the index of FRAI works well in the modeling process and suggests its potential as a technical indicator for the rural policy-making.

Yi Chen, Guanfeng Zhang, Bin Zheng, Ivan Zelinka

### Complex System Simulation Parameters Settings Methodology

This article extends (Janošek and Kocian 2013) and deals with simulation parameters setting methodology proposal for complex system behaviour adaptation. Therefore the article focuses on system adaptation where there is an effort to find such means of mediating the system’s behaviour that would make it possible to adapt to the current state of the system and the environment and react to the changes so that the desired behaviour of the system is kept in specified limits or patterns of behaviour. The instruments of regulating the system’s behaviour are its parameters. In recognizing the parameters’ importance, this work is inspired by the leverage point theory (Meadows 1999) and builds on its approach to the system cognizance. The adaptation of the system’s behaviour itself consists of recognizing these characteristic patterns using neural networks and the subsequent mediation of the system’s behaviour through selected parameters and their action ranges based on pre-prepared expectations of what will happen if the system’s behaviour exhibits a known characteristic pattern.

Michal Janošek, Václav Kocian, Eva Volná

### Simulation Analysis of the Complex Production System with Interoperation Buffer Stores

The article highlights the problem of mathematical modelling and subsequent simulation of the highly complex synthetic environment illustrating the real production system consisting of parallel manufacturing plants equipped with interoperation buffer stores. The system can be arranged optionally by means of the simulator which was created on the basis of the presented assumptions in the C# programming language. The discussed system realizes orders set by defined customers. Production control is based on heuristic algorithms which choose an order to be realized and a manufacturing plant in which the production process is carried out. The criterion is to minimize the total time of realizing orders however, as seen in the case study, also either the remaining capacity of tools after realizing all orders or the total tool replacement time can be taken into account while dealing with the problem. The modelling and projecting stages are followed by the simulation study. This simulation study is realized for the specific list of orders. It all leads to the thorough analysis of the obtained results which are later compared with the results obtained for the system without interoperation buffer stores.

Bronislav Chramcov, Robert Bucki, Sabina Marusza

### Usage of Modern Exponential-Smoothing Models in Network Traffic Modelling

The article summarized current state of our works regarding usage of exponential smoothing Holt-Winters’ based models for analysis, modelling and forecasting Time Series with data of computer network traffic. Especially we use two models proposed by J. W. Taylor to deal with double and triple seasonal cycles for modelling network traffic in two local area networks and three campus networks. We use three time series with data of TCP, UDP and ICMP traffic (given by number of packets per interval) on each network.

Roman Jašek, Anna Szmit, Maciej Szmit

### On Approaches of Assessment of Tribo Data from Medium Lorry Truck

The paper deals with application of selected analytical methods in order to analyse field data from heavy off-road military vehicles. The information from the engine oil are interpreted in form of polluting particles like particles from wear process (e.g. Fe, Pb, Cu, etc.) and particles from oil deterioration itself (like Mn, Si, Zn, etc.). These particles can give us information both about system state and about oil state. We have reasonable set of oil data from field operation available. Based on the data we assume being able to determine the system condition and propose some changes (e.g. in residual operation life, in maintenance modifications in the intervals, in mission planning, etc.). Selected methods like regression analysis and fuzzy inference system are used for the data assessment.

David Valis, Libor Zak, Agata Walek

### Energy and Entropy of Fractal Objects: Application to Gravitational Field

Various different approaches to the definition of entropy and their connections with fractal dimensions of systems were described in the paper

Entropy of Fractal Systems

presented at the conference

. In the second part of the paper, the described findings were applied to study the fractal properties of image structures.

Further development is going to be presented in this paper. Conclusions of general fractal theory will be applied to the general fractal systems represented by elements (elementary particles) having fractal structure. An typical example may include the space and time distribution of mass and electric charge, i.e. the general energy. The properties of fractal fields of these quantities (gravitational, electric or other field) can be described by means of fractal geometry generally at Edimensional space, where

E

= 0, 1, 2, 3, ... The

density of energy

and

entropy

of these fractal elements will be also determined from the distribution of their quantity, field intensity and potential.

Oldrich Zmeskal, Michal Vesely, Petr Dzik, Martin Vala

### Wavelet Based Feature Extraction for Clustering of Be Stars

The goal of our work is to create a feature extraction method for classification of Be stars. Be stars are characterized by prominent emission lines in their spectrum. We focus on the automated classification of Be stars based on typical shapes of their emission lines. We aim to design a reduced, specific set of features characterizing and discriminating the shapes of Be lines. In this paper, we present a feature extraction method based on the wavelet transform and its power spectrum. Both the discrete and continuous wavelet transform are used. Different feature vectors are created and compared on clustering of Be stars spectra from the archive of the Astronomical Institute of the Academy of Sciences of the Czech Republic. The clustering is performed using the kmeans algorithm. The results of our method are promising and encouraging to more detailed analysis.

Pavla Bromová, Petr Škoda, Jaroslav Zendulka

### Upcoming Features of SPLAT-VO in Astroinformatics

During last decade was developed fully automatized (robotic) class of telescopes, that produce huge amount of data per each night. Amount of recorded data is usually in the scale of petabytes. To process properly all data and select an important events it is needed to use sophisticated software methods and algorithms. It caused an appearance of a new field of science - astroinformatics. In this paper we introduce a small part of our contribution to the astroinformatics field - a specialized software SPLAT-VO. It is used for processing and visualization of astrophysical data generated by nonlinear, complex or even chaotic processes in the space. Overview of new features so far prepared for new version of SPLAT-VO. The overview is focused on enhancements of user experience, work with SAMP protocol and other interoperability that improves work with global list of spectra, plot window and analysis menu.

Petr Šaloun, David Andrešič, Petr Škoda, Ivan Zelinka

### Mobile Sensor Data Classification Using GM-SOM

The paper uses a previously-introduced modification of standard Kohonen network (SOM), called GM-SOM. This approach uses partitioning the problem in case of insufficient resources (memory, disc space, etc.) and parallel processing of input data set to process all input vectors at once, with the use of modern multi-core GPUs to achieve massive parallelism. The algorithm pre-selects potential centroids of data clusters in the first step and uses them as weight vectors in the final calculation. In this paper, the algorithm has been demonstrated on a new UCI HAR dataset, representing activities recorded by smartphone sensors, which are prone to random noise due to the sensor behavior. Moreover the separation of classes is not linear, which introduces additional complexity and makes it hard to process the data by linear algebra methods.

Petr Gajdoš, Pavel Moravec, Pavel Dohnálek, Tomáš Peterek

### Tensor Modification of Orthogonal Matching Pursuit Based Classifier in Human Activity Recognition

Human physical activity monitoring is a relatively new problem drawing much attention over the last years due to its wide application in medicine, homecare systems, prisoner monitoring etc. This paper presents Orthogonal Matching Pursuit as a method for activity recognition and proposes a new modification to the method that significantly increases the recognition accuracy. Both methods show promising results in both total recognition and differentiation between certain activities even without the necessity of prior data preprocessing. The methods were tested on raw sensor data.

Pavel Dohnálek, Petr Gajdoš, Tomáš Peterek

### Global Motion Estimation Using a New Motion Vector Outlier Rejection Algorithm

Global Motion Estimation (GME) is mainly performed in either pixel or compressed domain. Compressed domain approaches usually utilize existing block matching motion data. On the other hand, in compressed domain based GME, there are many unwanted existing outliers because of noise and foreground objects which are obstacle for GME. In this paper, a new motion vector dissimilarity measure is proposed to remove motion vector (MV)-outliers to provide fast and accurate GME. In experimental results, it is shown that proposed method is fairly successive in terms of both accuracy and complexity compared to the state of the art methods.

Burak Yıldırım, Hakkı Alparslan Ilgın

### Searching for Dependences within the System of Measuring Stations by Using Symbolic Regression

This article deals with searching for dependences within the System of Measuring Stations.Weather measuring stations represent one of the most important data sources. The same could be said about stations that measure the composition of air and the level of pollutants. Knowledge of the current state of air quality resulting from the measured values is essential for citizens, especially in areas affected by heavy industry or dense traffic. Computation of such air quality indicators depends on values obtained from measuring stations which are more or less reliable. They can have failures or they can measure just a part of the required values. In general, searching for dependences represents a complex and non-linear problem that can be effectively solved by some class of evolutionary algorithms. This article describes a method that helps us to predict the levels of air quality in the case of station failure or data loss. The model is constructed by the symbolic regression with usage of the principles of genetic algorithms. The level of air quality of a given station is predicted with respect to a set of surrounding stations. All experiments were focused on real data obtained from the system of stations located in the Czech republic.

Petr Gajdoš, Michal Radecký, Miroslav Vozňák

### The Effect of Sub-sampling on Hyperspectral Dimension Reduction

Hyperspectral images which are captured in narrow bands in continuous manner contain very large data. This data need high processing power to classify and may contain redundant information. A variety of dimension reduction methods are used to cope with this high dimensionality. In this paper, the effect of sub-sampling hyperspectral images for dimension reduction techniques is explored and compared in classification performance and calculation time.

Ali Ömer Kozal, Mustafa Teke, Hakkı Alparslan Ilgın

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