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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
Artificial Intelligence reached maturity in many of its subareas and the most recent trend is re-integration of developed techniques to tackle hard real-life problems such as driverless cars, deep-space and ocean explorers, drones etc. The project deals with developing autonomousagents (robots) that can build and refine their internal models and do their own decisions. The focus is on internal knowledge model of autonomous agents that is appropriate for planning their behavior and that can be obtained and refined in a (semi-) automated way rather than being manually encoded. The model will be a core part of a modular architecture and it will be developed by integrating research results from areas of robotics, planning, uncertainty reasoning, knowledge representation, nature-inspired computation, and linguistics. In addition totheoretical formal results (models, algorithms), the important output will be verification of the developed techniques on real robots. The aim is to bridge different research areas and bring their results closer to practical applicability.
01. 01. 2015 - 31. 12. 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
Project aims to describe the current status of admission process to Czech colleges and universities and to prepare a methodology for development of standardized admission tests. Project covers the whole cycle of test development – from defining objectives, blueprinting, item writing, reviewing and pretesting, to assembling the test and its validation. Special attention is given to psychometric tools needed for student scoring, item calibration, detection of improper items, estimation of reliability and validity in complex design and student scoring and item selection in automatized adaptive testing. Theoretical results are implemented and demonstrated on real data from admission test to a medical school.
01. 01. 2015 - 31. 12. 2017
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
The project will contribute to development of theoretical foundations of neurocomputing. The goal of the research is to obtain new knowledge in terms of mathematical results describing capabilities and limitations of multilayer networks. Relationships between networks with varioustypes of computational units (perceptrons, radial, and kernel), various parameters of these units will be described. Estimates of model complexities of networks will be derived in dependence on input dimensions, types of units and network architectures. Properties of highdimensional tasks which can be represented or approximated by networks of reasonable sizes will be characterized. Optimal solutions of learning tasks from point of view of generalization and model complexity will be analyzed.
01. 01. 2015 - 31. 12. 2017
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
Vague quantifiers like `many', `few', or `about a half' present a major problem in natural language processing. Designing a satisfactory theory of vague quantifiers requires to construct formal models and evaluate them with regard to linguistic adequateness, automated deduction, and embeddability in logical frameworks. This constitutes a serious research challenge involving computer science, logic, linguistics, and analytic philosophy. The fuzzy logic paradigm, based on the notion of degrees of truth, provides a mathematical apparatus for dealing with several aspects of vagueness. The applications of fuzzy methods to vague quantifiers have so far largely neglected the potential of deductive systems studied by mathematical fuzzy logic. The aim of the project is to deepen and extend the mathematical foundations for adequate modeling of vague quantifiers by employing formalisms and results of mathematical fuzzy logic, including modal logics with two-level syntax, game-theoretic semantics, and automated reasoning techniques.
01. 01. 2015 - 31. 12. 2017
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
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
One of the most important objects used in the field of formal verification are invariants. An invariant is a set of states of a given system such that the system will always stay in this set of states. Recently, there has been a lot of progress on the constraint-based computation of invariants, that reduces invariant computation to a constraint solving problem in a decidable theory. However, this approach cannot be applied in cases where the corresponding logical theory is not decidable, or where the available constraint solvers are not efficient enough to solve problems of interesting size. The proposal concerns computation of invariants of hybrid dynamical systems, that is, dynamical systems thathave partially discrete, partially continuous states and behavior. In order to circumvent the mentioned problems of undecidability and efficiency limitations of constraint solvers, we use a radically different approach that exploits robustness and simulations.
01. 01. 2015 - 31. 12. 2017
The subject of the project is an investigation of the variety of lattice-ordered monoids with a special focus on the subclass of totally ordered ones. As the known methods investigate this problem seem to become exhausted, the project intends to take a benefit of newly introducedmethods of geometric nature to attack this task, whose nature is algebraic, in a new way. The new tools include the approach of web geometry, a branch of the differential geometry introduced by Blaschke and Bol, and the representation by Cayley monoids; both these approaches allow to display algebraic properties of structures in an appealing visual way.
01. 01. 2015 - 31. 12. 2017