Current grants
(grants in alphabetical order)

A Multivalued Approach to Optima and Equilibria in Economics

A multivalued approach offers effecient tools for dealing with game-theoretic models and analysing optima and economic equilibria. The goal of this project is to use the methods based on multivalued analysis and logics for the investigation of several selected challenging problems that arise in game theory. This will include both cooperative and non-cooperative games. We will analyse the stability and sensitivity of generalized Nash equilibrium problems and optimise the construction of the bidding strategy at the electricity spot market of the European Energy Exchange. A particular attention will be paid to solutions of cooperative games with fuzzy coalitions. New dynamic bargaining procedures for the core of such cooperative games will be developed. The applications of many-valued and dynamic epistemic logics will enable us to capture the flow of information and knowledge in games and to model the imprecision of data. The multivaluedness is present in all considered game models both on the side of the game description and the game solutions.

01. 01. 2012 - 31. 12. 2014

Advanced random field methods in data assimilation for short-term weather prediction

An indispensable feature of weather nowcasting is data assimilation (DA), which includes the newest data, e.g. radar and satellitedata, into the numerical weather prediction model. The goal of the project is to introduce qualitatively new DA techniques.These techniques (automatic registration, morphing) have arisen in the theory of pattern recognition. They perform a correctionof shape and position of objects by means of a horizontal motion ?eld at the same time as the correction of the values of thephysical variables. The methods will be generalized so as to be able to use radar data. This will result in better timing andposition of atmospheric fronts or precipitation ?elds and in an improvement of the forecast.Many DA techniques are computationally demanding. New methods which rely on the theory of random ?elds and WaveletTransform will be developed. Expensive computations with large matrices in the Ensemble Kalman Filter analysis will bereplaced by cheap wavelet transform calls. The methods also can substantially reduce the number of ensemble membersrequired.

01. 02. 2013 - 31. 01. 2017

Algebraic Methods in Proof Theory

It is a recent trend in proof theory in non-classical logic to employ more algebraic methods and to develop the so-called algebraic proof theory. A typical example of a result in this direction is proving cut elimination in the same way that closedness w.r.t. Dedekind-MacNeille completion is proved in algebra. Other results in this direction show that current proof theory, based on Gentzen sequent calculi, works only for logics eith structural axioms of low complexity. Our project aims at generalizing the current methods and thus widening the applicability of(generalized) Gentzen calculi. A related target is a study of computational complexity of nonclassical logics.

01. 01. 2011 - 31. 12. 2015

An Order-Based Approach to Non-Classical Propositional and Predicate Logics

Formal systems of (non-)classical logics are essential in many areas of computer science. Their appreciation is due to theirdeductive nature, universality and portability, and the power they gain from their mathematical background. Such a diverselandscape of logical systems has greatly benefited from a unified approach offered by Abstract Algebraic Logic. The purpose ofthis project is to develop a variant of this theory, based on the notion of ordered semantics and its interplay with implicationconnective. We aim at a stronger, better applicable abstract theory for both propositional and predicate logics. As a showcase,we plan to illustrate the power of the resulting theory on two important families of non-classical logics: substructural and fuzzyones.

01. 02. 2013 - 31. 01. 2017

Center of Excellence - Institute for Theoretical Computer Science

Center of Excellence - Institute for Theoretical Computer Science (CE-ITI) is a research center for theoretical computer science and discrete mathematics. CE-ITI aims at becoming an international leader recognized world-wide, and also a driving force of Czech theoretical computer science and discrete mathematics. To achieve that, CE-ITI includes best professors, young researchers, and students from several top institutes in the Czech Republic, and integrates the following key activities: 1) conducting research of highest quality, addressing major challenges and open problems, and initiating new lines of research. 2) Educating a new generation of researchers and active searching for new talents. 3) Coordinating and fostering international cooperation, strengthening the standing of Czech computer science and mathematics in world-wide context.

01. 01. 2012 - 31. 12. 2018

Constructing Advanced Comprehensible Classifiers

The proposed project will further develop key directions of research into methods attempting to alleviate the discrepancybetween accurate and comprehensible classifiers. These are the extraction of logical rules from trained neural networks, and theevolution of sets of comprehensible classification rules by means of genetic, ant colony, and similar optimization algorithms.The project aims at increasing the accuracy of rule induction in classification rules mining, and at the elaboration of newmethods for inferring comprehensible rules from accurate classifiers, such as support vector machines. It will also performtheoretical research in this area, in particular research into the relationship that the accuracy-comprehensibility trade-off has tothe difference between descriptive and generative classifiers, and will search for a suitable formalization of the concept ofclassification comprehensibility.

01. 02. 2013 - 31. 01. 2016

Distribution and metric properties of number sequences and their applications

The aim of the project is to develop new and to generalize used methods of the analytic and combinatorialnumber theory employed in the study of distribution and metric properties of number sequences or theirfamilies. In the area of distribution properties the aim of study will be global characteristics of the set ofall distribution functions, as well as conditions for the existence of their specic properties indicating thedistribution type and their impact on the randomness and the arithmetics of the underlying sequences.The aim of the study will also be the interference between arithmetic characteristics (discrepancy, densityetc.) of sequences and their sets of distribution functions and the sets of distribution functions of derivedsequences (e.g. block, triangle, etc.), as well as the mutual relationships of these two sets. The aim of studywill also be the interference between distribution and metric characteristics (as Hausdor dimension, Bairesclassication, etc) of number sequences and their arithmetic properties, as irrationality, or measures ofirrationality.

01. 01. 2012 - 31. 12. 2015

Game - theoretical approach to many - valued logics

The goal of the project is to continue the longstanding cooperation between Prague and Vienna on the application of game and theory fuzzy logic. The project will focus particulary on the following research issues:a) the relationship between game semantics for fuzzy logic (dialogical/evaluation games) and their relationship to other game–theoretical many–valued semantics (probalistic semantics for independent-friendly logic)b) consequences of the game semantics for the study of fuzzy logics (e.g., the problem of safe models)c) application of kooperative games in many-valued logics – the formativ of fuzzy coalitions and bargainingd) applicatin of dialogical games in linguistics with a focus on generalized quantifiersThe output of the project will consist of papers in etablished international journals.

01. 01. 2013 - 31. 12. 2014

Geometry of associative structures

This project intends to investigate associative operations and structures from a geometrical point of view.The main motivation comes from the study of web geometry which is a branch of the dierential geometry. Assome results have already shown, the concepts of this discipline can be adopted successfully to characterizethe associativity of totally ordered monoids and triangular norms in a very intuitive visual way. Thus, thereis a good motivation to continue this research and to exploit its potential. The aim of the project is ageometric investigation of questions of structural characterization of associative structures, in particular,totally ordered monoids which play an important role in MTL algebras. These algebras represent semanticsof the monoidal t-norm based logic which is a prototypical many-valued logic studied intensively nowadaysby many researches. As the outcome of the project, it is expected not only a deeper understanding ofassociative structures but also a generalization of web geometry to a more general case.

01. 01. 2012 - 31. 12. 2014

Integrated Verification and Falsification of Hybrid Systems of Industrial Size

A large part of the development costs of complex systems with a deep integration of software and physical components (e.g. cars. trains, airplanes) goes into the stage of testing the correctness of the system design. The notion of a hybrid system is a formalism to model such systems. The results of this project will, for the first time, allow techniques for formal verification of hybrid systems to handle systems of industrial size. This will be achieved by integrating techniques for formal verification and automated falsification/testing. Since new results in hybrid systems falsification allow the handling of huge systems already now, and since, in the case of software, a corresponding integration of verification and falsification has resulted in huge speedups, we are convinced that this approach will result in a corresponding break-through also in the field of hybrid systems.

01. 01. 2012 - 31. 12. 2014

Iterative Methods in Computational Mathematics: Analysis, Preconditioning, and Applications

The project deals with iterative methods for several important problems of numerical linear algebra. It includes their analysis,preconditioning, solving ill-posed problems as well as real-world applications. We focus on Krylov subspace methods, openquestions related to their convergence, associated matrix approximation problems, error estimation and stopping criteria. Wewill study various preconditioning techniques including new algorithms based on incomplete factorizations andorthogonalization schemes, and block saddle-point preconditioning. We intend to analyze regularization methods for solvingill-posed problems in image and signal processing, open problems in total least squares and Golub-Kahan bidiagonalization. Aninseparable part of our work are broad international collaboration and selected real-world applications such as theapproximation of scattering amplitude and nuclear magnetic resonance.

01. 02. 2013 - 31. 01. 2018

Klimatické sítě: Rozmanitost měřítek dynamiky a interakcí v atmosféře Země

01. 04. 2014 - 31. 12. 2016

Large-scale dynamics and critical transitions in neuronal networks and their role in limbic seizure genesis

Transition to epileptic seizure represents sudden and abrupt shift between distinct dynamic regimes of the brain. In simplified brainpreparations we have demonstrated that seizures are preceded by detectable changes in neuronal behaviour which marked progressivedecrease in neuronal network resilience and proximity to transition to seizure. These processes correspond to phenomenon of “critical slowingdown” described in dynamics of complex systems, innovative and rapidly emerging field of modern physics. In the proposed work we aim toelucidate mechanisms responsible for transition to seizure in intact brain and examine whether this process displays features of criticaltransition. We will apply integrative approach which will combine advanced techniques of large-scale recording, methods of active probing,computational modelling and analyses of complex systems. Demonstrating that dynamics of epileptic networks is governed by similarprinciples to other dynamical systems will open new ways to design innovative and more efficient therapies to abort or reverse transition toseizure

01. 01. 2014 - 31. 12. 2016

Mathematical Fuzzy Logic in Computer Science

Mathematical fuzzy logic is a symbolic (mathematical) logic with a graded notion of truth, to be distinguished from fuzzy logic in broad sense which is a highly applied domain using the notion of fuzzy sets. Mathematical propositional and predicate logics have exact notions of formulas, axioms, proofs, semantics (standard with the real unit interval as the set of truth values and general algebraic semantics). Since Hajek's 1998 monograph, mathematical logic has been under intensive international development, in which our Czech group has played a very important role. The present project will continue this development and international cooperation, stressing the purely theoretical logical study as well as its application in computer science. In particular, the following topics will be investigated: proof theory and model theory of fuzzy logic, its relation to other logical systems, comutational and arithmetical complexity, fuzzy logic in the semantic web (description logic) and several other logics of importance for compter science (epistemic, deontic, dynamic, etc.).

01. 01. 2010 - 31. 12. 2014

Modeling of Complex Systems by Soft-Computing Methods

The goal of the project is theoretical analysis of properties of softcomputing computational models suitable for processing of high-dimensional complex data from point of view of minimization of model complexity, efectivity of learning and capability of generalization.Further goal is application of theoretical results to design of hybrid algorithms of methalearning with adaptive choices of models and their parameters and implementation of these algorithms as Java and MATLAB software tools and their testing on real data.

21. 03. 2013 - 31. 05. 2016

Nanostructures with transition metals: Towards ab-initio material design

Development of new functional nanomaterials requires understanding nanoscale rules and mechanisms. Our aim is to elucidate the interdependence between magnetism and structure in nanostructures which contain transition metals with unfilled 3d and 4d orbitals. To achieve this we will perform ab-initio calculations of selected properties of nanostructures and observe how these properties change if the shape, size and composition of the nanostructure is varied. Our approach is based on combining calculations performed within the Green's function formalism with calculations performed by means of the finite elements method (FEM). As a by-product, this will also result in further improvemets of FEM so that it could be used in ab-initio materials science more widely. Our work will facilitate experimental and technological research aimed at practical use of nanomaterials, especially in data storage devices.

01. 01. 2011 - 31. 12. 2015

NoSCoM: Non-Standard Computational Models and Their Applications in Complexity, Linguistics, and Learning

NoSCoM is a basic research project combining several complementary subfields of theoretical computer science in order to deepen aur knowledge of important specialized non-standard models of computation. Its aim is to characterize the computational power and efficiency of these models and to explore their ability to model problems from selected application domains such as complexity theory, linguistics, and machine learning. Our multi-model approach will also include the analysis of new resources or measures of effective computation which are introduced in the respective non-standard computational models. In particular, the research will focus mainly on non-uniform amofphous computing systems modeling mobile sensory nets, nano-scale machines, formal models of practical neurocomputing in AI, specialized unbounded automata and grammars with important applications in linguistics (e.g. word-order freedom measures), branching programs for studying space-complexity aspects of computing, models for approximating distributions of empirical data such as random forests.

01. 01. 2010 - 31. 12. 2014

Personality and spntaneous brain activity during rest and movie watching: relation and structural determinants

Current psychological theory provides complex description of mental functions and personality.It is generally accepted that mental functions have brain as their substrate, suggesting that personality differences should bereflected in brain structure and function. However, the specific relation remains elusive.A rapidly developing area of brain research is the study of spontaneous brain activity with functional magnetic resonanceimaging, allowing simultaneous characterization of a plethora of brain networks.We suggest that psychological characteristics are likely to be strongly related to endogenous patterns of brain activity.We seek to further improve the detectability of this relation by robustifying the patterns by measuring the brain during naturalviewing, a rich quasi-realistic stimulation.The combined psychometrical and neuroimaging study will allow relating specific features of functional brain networks andpersonality. The findings will be put in context by investigation of structural determinants of this relation through data-drivenanalysis and theoretical models.

01. 02. 2013 - 31. 01. 2016

History of grants
(end year - alphabetical order)

2014

  • 100 vědců do středních škol

2013

  • Application of artificial neural networks in systems for person
  • Interactions, information transfer and complex structures in the dynamics of changing climate
  • Learning of functional relationships from high-dimensional data
  • Number theory and its applications

2012

  • Applications of Methods of Knowledge Engineering in Data Mining
  • Decompositions of matrices with binary and ordinal data: theory, algorithms, and complexity
  • Efficient Handling Non-linear Numerical Constraints Arising in Automated Reasoning about Rich Models of Computer Systems
  • Greenhouse gases emission reduction using information technologies
  • Interoperability of Future Web Services in the Web of Linked Data
  • Logical Foundations of Semantics
  • Logic-based fuzzy mathematics
  • Model-Driven Evaluation of Design Desicion Impacts in Software Engineering
  • Preconditioning and iterative solution of saddle-point problems
  • Res Informatica
  • Social Network of IT Specialists in Regions of Czech Republic
  • Theory of Krylov subspace methods and its relationship to other mathematical disciplines
  • Towards deeper understanding of Krylov subspace methods
  • Web Semantization

2011

  • Analysis of negative impacts on driver attention
  • BrainSync - Large Scale Interactions in Brain Networks and Their Breakdown in Brain Diseases
  • Development of Methods for Solving Large Scale Nonlinear Programming and Nonsmooth Optimization Problems
  • Extraterrestrial effects on atmospheric circulation in mid and high latitudes
  • Logical Models of Reasoning with Vague Information
  • Methods of Artificial Inteligence in GIS
  • Úloha folátů v etiopathogenesi metabolického syndromu
  • Universe of informatics

2010

  • Complexity of perceptron and dernel networks
  • Decentralized control and communication
  • Dynamic Formal Systems
  • Intelligent Middle Agents for Mediation of Semantic Web Services
  • Model complexity of large fuzzy rule-based systems and neural networks
  • Neural Networks Learning Algorithms Based on Regularization Theory
  • Verification of Hybrid Systems - Exploiting the Synergy with Underlying Constraint Solving Technology

2009

  • Advanced Remedial Technologies and Processes
  • Algebraic, analytic and combinatorial number theory
  • Centre of Biomedical Informatics
  • Complexity of t-norm based logics - algebraic and proof-theroetical approach
  • Dynamics of system aliances
  • Institute for Theoretical Computer Science
  • Interactive Information Portal for Algorithmic Mathematic
  • Mathematical Foundation of Inference and Decision under Uncertainty
  • Mathematical Modelling of Natural Gas Consumption for Small and Middle Clients
  • Methods for Intelligent Systems and Their Applications in Datamining and Natural Language
  • Realistic Application of Formal Methods in Component Systems
  • Solution of large, sparse and nonsymmetric linear systems with Krylov subspace methods.

2008

  • A new approach to knowledge representation and exchange in concept and sensor networks
  • Application of quantum informatics on PKI (Public Key Infrastructure)
  • BRACCIA - Brain, Respiration and Cardiac Causalities in Anaesthesia
  • Collegium Informaticum
  • Development of numerical methods for solving large scale nonlinear programming problems
  • Development of software system for solving large-scale problems of nonlinear and nonsmooth optimization
  • Information technologies for development of continuous shared health care
  • Intelligent methods for incresing of reliability of electrical networks
  • Intelligent Models, Algorithms, Methods and Tools for the Semantic Web (realization)
  • Mathematical modelling of air quality with applications in management of emergencies
  • Modelling and simulation of complex technical problems: effective numerical algorithms and parallel implementation using new information technology
  • Scientific-information gate for informatics and cybernetics.

2007

  • Approximation and Learning of Multivariable Functions by Neural Networks and Kernel Methods
  • Complex investigation of biomechanical coditions of the artificial skeletal replacements applications, evaluatin of their failure reasons and proposal of conditions for increasing their stability in t
  • Formal Concept Analysis of Indeterminate and Large Data: Theory, Methods and Applications
  • Formal Theories of Mathematical Structures with Vagueness
  • New Methods and Tools for Knowledge Discovery in Databases
  • New Trends in Research and Application of Voice Technology

2006

  • Automated model building for fuzzy logic
  • Methods of number theory
  • New results in testing the goodness-of-fit based in Pearson-type statistics
  • Quantification of cardiovascular interactions in health and disease

2005

  • Analysis of system aliances function reliability
  • Autonomous computational agents
  • Consortial Approach to the Development of Experimental Models
  • COSTRetional Structures in Data Mining nad Discovery Science
  • Krylov subspace methods - mathematical theory, stopping criteria and behaviour in finite precision arithmetic
  • Special classes of matrices

2004

  • Air Quality Data Assimilation in Regional Chemistry Transport Models
  • BARRANDE - E-Learning a E-Business: Auto-Adapting Web Sites via Neural Networks
  • Center for Applied Cybernetics
  • International cooperation in ATLAS Detector in CERN
  • Mathematical foundations of inference under vagueness uncertainty
  • Mathematical Theory of Iterative Processes with Applications
  • Modeling the rainfall-runoff relationships by artificial intelligence methods
  • Nonlinear Approximation with Variable Basis and Neural Networks
  • Specialized Computational Models in Contemporary Computer Science
  • Study of Dynamical Models of Pain During the Development
  • Voice Technologies a Support of Information Society

2003

  • Algebraic, analytic and combinatorial methods of number theory
  • General Asymptotic Theory of M-estimators
  • Learning Algorithms for Local Unit Neural Networks
  • Linear Optimization Problems with Inexact Data
  • Research of Neural Networks Capability to Provide Nonlinear Boolean Factor Analysis
  • Scalable Sparse Linear Algebraic Solvers: Analysis, Development, Implementation and Application

2002

  • Alternative learning procedures for feedforward neural networks
  • Alternative mathematical models for uncertainty quantification and processing
  • Analysis of reliability of large hybrid technical and biological systems
  • NEUROINFORMATICS: Computational Theory of Neural Networks
  • Parallelization of computer processing
  • Polynomial and structured matrices
  • Prediction of epileptic seizures: Extracting information with predictive power from scalp EEG by using nonlinear dynamical methods
  • SOFA - Software Appliances
  • SOFT COMPUTING: Theoretical Foundations and Experiments
  • Toxic oxygen products and antioxidant eye protextion. Conditions leading to the exidative eye damage, its prevention or healing
  • 2000 ADBIS-DASFAA Symposium on Advances in Databases and Information Systems

2001

  • MGT - Medical Guideline Technology: representing, interpreting and sharing cost-effective standards
  • Nonlinear approximation by neural networks
  • Parameter spaces and learning complexity of neural networks
  • Study of behaviour of neurons in normal states and in the pain by methods of chaodynamics - experimental and theoretical approach

2000

  • Computational Models and Complexity of Computation
  • The structure and dynamics of relationship between the psychological profile and embodiment of students of medicine

1999

  • Analysis of Informational and Dynamical Capatibilities of Recurrent Neural Networks
  • Extensions of linear-algebraic problems
  • Inconsistency resolution methods in the integration of data and knowledge bases
  • Preconditioned Iterative Methods for Linear Algebraic

1998

  • Application of Neural Nets for Triggering of Events in Elementary Particle Physics, principal investigator
  • Approximation of functions and neural networks learning algorithms
  • Complexity of Continuous Models of Neurocomputing
  • Development of the psychological method of newborn behavior assessment
  • Information Technologies Education and Training IT EDUCTA
  • Mathematical foundations of inference under vagueness and uncertainty
  • Mathematical modelling of the transport and the reactions of the chemical substances in the contaminated underground water
  • Research in application of the object paradigm in distributed systems

1997

  • New methods of prediction and optimization for applications in electric power network of the Czech republic

1996

  • Analysis of Informational Capabilities of a Class of Artificial Neural Networks to Optimize their Structure
  • Application of modern mathematical methods in economic information processing
  • Design of Modular Artificial Neural Networks
  • Information Retrieval from Textual Databases Bsed on AT and NN Methodology
  • New Approaches to Neural Networks in Digital Signal Processing for Applications to System Identification and Modelling
  • Numerical Methods for Linear Algebraic Systems with Application to Nonlinear Problems
  • Structured matrices

1995

  • Approximation of functions and architectures of neural networks
  • Construction of methods for data analysis in epidemiological studies, detection of risk factors and disease risk modelling
  • Hadron interaction in TeV region and their fast triggering for the quark-physics
  • Research of optimization methods and develop of an interactiove system for universal functional optimization

1994

  • Non-numerical uncerianty quantification and processing in computer-aided systems for conclution drawing and decision making
  • Research of optimization methods and developmentof an interactive system for univerzal functional optimization
  • The approximation capabilities of multilayer neural networks

1993

  • Convergence and stability of conjugate gradient type methods for solving linear systems and computing eigenvalues in finite precision arithmetic
  • Model search techniques
  • The analysis and applications of new neural networks architectures

1992

  • Mathematical foundations of inference in expert systems
  • Neural Nets with Neurons of Limited Number of Synapses
  • The Analysis of the Generalization Abilities of Layered Neural Networks Used for Signal Processing
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