Department of Nonlinear Modelling is divided into the following sections and research groups:

- Research Group of Environmental Informatics (head Krystof Eben)
- Research Group of New estimation methods in statistics (head Zdenek Fabian)
- Research Group of New methods for Knowledge & Data Engineering - (head Dusan Husek)
- Research Group of Nonlinear Dynamics (head Milan Palus)
- Research Group of Energy Consumption Modelling (head Emil Pelikan)
- Research Group of Softcomputing (head Marcel Jirina)
- Research Group of Software Engineering (head Frantisek Plasil)
- Laboratory of the System Reliability (in cooperation with the Faculty of Transportation, Czech Technical University) (head Vasek Sebesta)
- Research Group of Web-Sensor Collaborative Networks (head Petr Klan)

### Environmental informatics

Data assimilating methodsfor weather and air quality prediction are extensively developed. The results are available for the general public on the internetunder the acronym MEDARD (Meteorological and Environmental Data Assimilating system for Regional Domains). The forecasts update four times daily and are available on the internet address www.medard-online.cz. The research is supported by the Grant Agency of the Academy od Sciences, CR and the research team closely cooperate with Charles University and with the Czech Hydrometeorological Institute in Prague

### New estimation methods in statistics

Scalar inference function of mathematical statistics was developed and its possible use is studied. The function has not a fixed shape as psi-functions of robust statistics; it is expressed by means of the probability density, its derivative according the variable and Jacobian of the corresponding Johnson transformation. It appeared that the function makes possible to change view of parametric estimation: instead of parameters of a parametric family, some fictive parameters are estimated. These fictive parameters describe thecentral tendency and variability of probability distributions, including the heavy-tailed ones, not possessing the usual moments. We believe that the inference function could be successfully used in other fields of mathematical statistics as well.

### Knowledge & Data Engineering

This group of researchers aim is to make advances in research on aspects of artificial Intelligence and data analysis mainly by developing new biologically motivated methods, machine learning including tenzor methods. These methods are developed in the context of pure mathematics, including statistics. Among other our theoretical works are mainly focused on developing and analysis new architectures of NN networks but we do not restrict only on them. New method application areas include information retrieval, data mining, reduction dimensionality, social networks, modeling and adaptive systems, data compression, multidimensional data indexing, XML indexing, stringology, ordered sets, universal algebra, information retrieval and semantic Web (http://arg.vsb.cz/arg/, http://www.cs.cas.cz/semweb/).

Contributions should be made in new directions, both in the development of the theory and technology and in the exploration of opportunities and challenges.

Collaborative opportunities for work with other research groups of the Centre / institute are actively sought. The staff have developed strong links with other academic disciplines, for example statistics (http://nb.vse.cz/~rezanka, http://cedric.cnam.fr/~saporta/) linear algebra and optimization (http://www.cs.cas.cz/mweb/, Brain research ( http://www.ihna.ru , http://anim.snv.jussieu.fr ) Power Engineering (http://homen.vsb.cz/~hra50/index_en.htm), Robotics, Computer science as such (http://www.cs.utk.edu/~berry/) and with a wide range of industrial collaborators and users. Other areas with huge amount of high-dimensional data are in the scope of the qroup as well.

The aim of the local project is the development of the neural network approaches http://www.cs.cas.cz/~dusan (but not only) to the data dimension reduction, features extraction, clustering, classification, semantics web, basket market analysis and even knowledge organization, including modeling of brain functions.

### Research Group of Nonlinear Dynamics

Detection and characterization of nonlinear phenomena in time series recorded in complex systems is the main task of the research group of nonlinear dynamics[http://ndw.cs.cas.cz/].

Based on ideas from theory of nonlinear dynamical systems, deterministic chaos, and information theory we develop methods and algorithms suitable for analysis of multivariate time series recorded in complex systems of various origins, ranging from the atmospheric dynamics to signals capturing the activity of the human brain. Inferences about mechanisms underlying observed complex behaviour are done as a part of the data analysis, a range of phenomena, from nonlinearity to causality are identified. Tools for studying interactions, namely for identification of dependence, synchronization and causality are currently developed, with the main application field of uncovering interactions among the main rhythms in the human body - the respiratory rhythm, the heart rhythm, and the complex rhythmical dynamics of the brain - in the normalphysiological state and their changes during the anaesthesia. This research is conducted due to the involvement of our group in theEC FP6 project BRACCIA [http://www.cs.cas.cz/nlm/bracciaindex-en.htm] (Brain, Respiration And Cardiac Causalities In Anaesthesia). The interactions and synchronization in the brain activity are studied using the ideas of the theory of complex networks.

### Energy consumption modelling

The main aim of this research is development of statistical models for estimation and forecasting of energy (electricity and natural gas) consumption. In particular, our activities are focused on:

- forecasting of the energy consumption for different regions and specific segments of customers of for short-term (hours, days),middle-term(months) and long-term (years) prediction horizons
- modelling of energy consumption for individual consumers whose consumption is not measured on a daily or monthly basis, modelling of energy consumption for different segments of the gas market
- reliability assessment in energy sector, extreme value analysis

For forecasting tasks we have developed mathematical models for the decision-supporting system (called ELVIRA). ELVIRA is a complex modular system developed in collaboration between experts from natural gas distributing companies and Department of Non-linear Modeling of the ICS. The system is used for utility (presently natural gas) load prediction in different scales and various time horizons. The statistical and CI models embedded in the system offer forecast values and diagrams with scales ranging from single hours through days and weeks to months with horizons from one hour ahead up to five years ahead. Additionally, there is a special module for load corrections with respect to the different weather forecast scenarios. The input variables - consumptions, gas pressure, outdoor temperature and perhaps even weather forecast - are automatically imported into system-s archive every hour.

For the modelling tasks we have developed the mathematical model GAMMA which is used for the problem of accurate estimation of unbilled revenues. The GAMMA model is a result of an effective cooperation between West Bohemian Gas Distribution Company in Pilsen, Czech Republic and the Institute of Computer Science of the Academy of Science of the Czech Republic in Prague. The research is also supported by the Grant Agency of the Academy od Sciences, CR[http://www.cs.cas.cz/gamma/index.htm].

The statistical relationship between different meteorological factors and reliability assessment and network outages was studied inthe project called NORA. We cooperated with the CEZ company - the main producerand distributor of the electricity in the Czech Republic.

### Soft-Computing

One of themes of nonlinear modeling is softcomputing. Softcomputing consists of approaches inspired by processes in nature, specifically neural networks, evolutionary computation, and cognitive modeling. This theme is solved in frame of department of artificial intelligence of the Center of applied cybernetics (CAK) [http://www.c-a-k.cz]. One of many problems solved in CAK is a problem which encounters nearly in all tasks solved, namely so called curse of dimensionality. The curse of dimensionality is aphenomenon when computational complexity extremly grows with dimensionality of the task. Searching of solution is one of planned targets in this project and is linked to successful results of previous projects solved in the ICS up to now.

In ICS the work on problems of softcomputing is divided into four problem areas:

- Design of theoretical models for cognitive computation and hybrid methods of computational intelligence and stating their computational force and complexity [http://www.cs.cas.cz/~vera].
- Testing of different software and robotic models on classification, control, and cognitive tasks[http://www.cs.cas.cz/~roman].
- Research of neural networks and other approaches to tasks with multivariate data, problem of effective data dimensionality [http://www.cs.cas.cz/~jirina].
- Study and testing of other than classic types neural networks and other approaches with the use of compressed data [http://www.cs.cas.cz/~hakl][http://www.cs.cas.cz/~husek].

Public accessible realized outputs:

- Multivariate function approximation and data classification tool NNSU[http://www.cs.cas.cz/nnsu]
- Multiagent robotic system [http://www.cs.cas.cz/~roman/cak]

We use our methods and cooperate with

- Faculty of Electrical Engineering of the Czech Technical University in Prague in the frame of the Center of Applied Cybernetics [http://www.c-a-k.cz]
- Institute of Physics AS CR in Prague and with CERN in Geneva, Switzerland on Higgs boson search problems
- Faculty of Transportation of the Czech Technical University in Prague on problems of microsleeps
- Universita do Genova, Italy
- Georgetown University, USA

### Software Engineering

The research group conducts research in the area of software engineering and formal verification, specifically in the context ofdistributed component-based systems. In particular, our activities are focused on:

- design and construction of runtime environment for component applications, including deployment and configuration of heterogeneous component-based applications [1] [2]
- software connectors and their automatic generation from high-level specification, including investigation of other parts of component runtime environment (component controllers) suitable for automatic code generation [3]
- methods and technical infrastructure for continuous evaluation of software performance during development in order to detects undesired changes in performance, including application of the methods in the context of component-based applications [4] [5]
- methods for modeling behavior of software components, formal verification of compliance at different levels of component application architecture, including compliance of component implementation code with the specification of its behavior [6]

Even though at conceptual level our research is generally applicable in the area of component-based software engineering, we are using the SOFA 2 [ http://sofa.objectweb.org] and the Fractal [http://fractal.objectweb.org] component systems for prototyping and validation of our methods.

*[1] Bures, T., Hnetynka, P., Plasil, F., Klesnil, J., Kmoch, O., Kohan, T.,and Kotrc, P. Runtime Support for Advanced Component Concepts. To appearin Proceedings of SERA 2007, Busan, Korea, Aug 2007.[2] Bures, T., Hnetynka, P., and Plasil, F. SOFA 2.0: Balancing AdvancedFeatures in a Hierarchical Component Model. Proceedings of SERA 2006,Seattle, USA, IEEE CS, ISBN 0-7695-2656-X, pp. 40-48, Aug 2006.[3] Galik, O., and Bures, T. Generating Connectors for HeterogeneousDeployment. Proceedings of the 5th international Workshop on SoftwareEngineering and Middleware (SEM 2005), Lisbon, Portugal, ACM Press,ISBN 1-59593-204-4, pp. 54-61., Sep 2005.[4] Bulej, L., Kalibera, T., and Tuma, P. Repeated Results Analysis forMiddleware Regression Benchmarking. Performance Evaluation: AnInternational Journal, Performance Modeling and Evaluation ofHigh-Performance Parallel and Distributed Systems, vol. 60, pg. 345-358,Elsevier B.V., ISSN 0166-5316, May 2005.[5] Kalibera, T., Bulej, L., and Tuma, P. Automated Detection of PerformanceRegressions: The Mono Experience. Proceedings of the 13th IEEEInternational Symposium on Modeling, Analysis, and Simulation of Computerand Telecommunication Systems (MASCOTS 2005), Atlanta, GA, USA,IEEE CS, ISBN 0-7695-2458-3, ISSN 1526-7539, pp. 183-190, Sep 2005.[6] Adamek, J., and Plasil, F. Component Composition Errors and UpdateAtomicity: Static Analysis. Journal of Software Maintenance andEvolution: Research and Practice 17(5), pp. 363-377, ISSN: 1532-060X,Sep 2005.*

### System Reliability

The problem of the reliability of interaction between human subject and artificial system, especially the system operators (e.g. drivers) attention degradation and micro-sleep appearance is investigated in cooperation with the Faculty of Transportation Czech Technical University [http://www.fd.cvut.cz/pracoviste/laboratore.html]in the framework of joint project entitled -Development of Neuroinformatic Databases and respective data-mining-. Several methods for the micro-sleep detection and prediction based on the analysis of EEG spectrograms by the classification trees, by the GUHA (General Uniform Hypotheses Automaton) method and by the neuro-fuzzy classification models have been developed and tested. A new hypothesis about increasing of alfa activity and decreasing of delta activity in the case of somnolence in comparison with mentation and relaxation was found and verified.

[1] Klaschka, J.: Decision Trees and Forests as EEG Classification Tools. In: Neurodynamics and Neuroinformatic Studies (Second book on microsleeps), Neural Network World, 2005, pp. 115 - 127, ISBN 80-903298-3-7.[2] Fabian, Z.: Perspectives of Detection of Micro-sleep by Spectral Analysis of EEG Signals, In: Neurodynamics and Neuroinformatic Studies (Second book on microsleeps), Neural Network World, 2005, pp. 128 - 143, ISBN 80-903298-3-7.[3] Holeňa, M.: Knowledge Extraction from EEG Data Using Fuzzy Neural Networks, In: Neurodynamics and Neuroinformatic Studies (Second book on microsleeps), Neural Network World, 2005, pp. 144 - 157, ISBN 80-903298-3-7.[4] Coufal, D., Šebesta, V.: GUHA Method Supported Analysis of EEG Signal and their Spectograms, In: Neurodynamics and NeuroinformaticStudies (Second book on microsleeps), Neural Network World, 2005, pp. 158 - 181, ISBN 80-903298-3-7.

### Web-Sensor Collaborative Networks for Application Modelling

It is a research project concerning information and collaborative sensor networks. It will address the merge of several components: distributed information processing, Internet communication, and mobile Web server computing. The goal of the project is to develop a framework that will involve:

- networks of inexpensive and ubiquitous web-sensors and web-actuators,
- universal communication of the network nodes,
- automatic knowledge insertion into the nodes (no programming),
- useful network-based tools.

The nodes of the network will collaborate and support a large variety of application modelling. Several instances of this framework are implemented, see e.g. [http://pekcam.cs.cas.cz].