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Cílem projektu je pomoci vědcům ke komunikaci se středoškolskými studenty a pedagogy. Vzájemně se propojit s cílem zlepšit výuku matematiky a obecně vědy na středních školách a vytvořit větší vlnu inovativních studentů se zájmem uskutečnit nápady pomocí samostatných projektů a později se stát vědcem.Dalším cílem je pomoci středoškolským studentům a učitelům motivačně usktečňovat samostatné projekty synergicky s účastí na přehlídce nejlepších projektů maldých středoškolských vědců EUCYS (European Union Contest for Young Scientists) a nejlepším z nich potom na ISEF v USA (International Scientific and Engineering Fair) a účastnit se tam odborného programu.
01. 06. 2012 - 31. 05. 2014
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
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
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
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 (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
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
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
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
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
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
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
01. 04. 2014 - 31. 12. 2016
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 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
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
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 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
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
