State doctoral exam topics

Artificial Intelligence and Biocybernetics

Common topics

  1. Sets. Matrix theory. Linear equations.
  2. Fundamentals of mathematical analysis. Approximation of functions. Least-squares fitting. Applications of model fitting to real data.
  3. Static optimization. Linear programming. Gradient methods. Problem of convergence to local extremes.
  4. Fundamentals of statistics, experiments and statistical hypotheses testing, maximum likelihood.
  5. Graph theory. Combinatorial algorithms and their complexity. Asymptotic measures of complexity, P and NP classes.
  6. Linear integral transforms, the Fourier transform. FFT. Non-linear filtration.
  7. Information theory, information measure, entropy, mutual information, maximum entropy principle.
  8. Mathematical model of an object. Identification of a structure and estimation of parameters of a model.
  9. Propositional logic. First-order logic. Formal system, theories, their consistency and completeness. Proof theory. Resolution principle. Limitations of formal systems.
  10. Problem solving. State space, state space search methods.
  11. Formulation of statistical decision making and recognition tasks. Bayes decision rule as risk minimization. Non-Bayesian recognition tasks.
  12. Formulation of a learning task. Induction, deduction, abduction. Learning (training) and parameter estimation. Supervised and unsupervised learning. Basic approaches. Training and testing sets, and their sizes.
  13. The notion of knowledge, its representation and application in artificial intelligence tasks.
  14. Knowledge systems and their practical applications.
  15. Main tasks of artificial intelligence and methods for their solving: symbolic manipulation, connectionism, distributed systems.

Specialization topics for the branch "Artificial intelligence"

  1. Programming languages for AI. Declarative and procedural programming paradigmas, their differences and possible interconnections including implementation issues.
  2. Natural language processing, challenges. Issues of natural language understanding, principles, methods, and tools. Employment in contemporary applications of AI.
  3. Fuzzy reasoning. Models of complex systems and their design. Qualitative simulation.
  4. Design and implementation of knowledge systems. Decision making under uncertainty and its exploitation in expert systems. Fundamentals of game theory.
  5. Knowledge discovery in data (KDD)and artificial intelligence techniques for KDD.
  6. Learning with extensive apriori knowledge. Inductive logic programming and relational learning.
  7. Reinforcement learning. Neural networks and their applications.
  8. Evolutionary computing principles and their applications.
  9. Multi-agent systems. Modelling of social agents. Behaviour of agent societies.
  10. Planning and scheduling. Knowledge in a dynamic environment, frame problem.
  11. Robotics. Models of the environment and knowledge fusion.
  12. Artificial life.

Specialization topics for the branch "Machine perception"

  1. Statistical learning theory according to Vapnik and Cervonenkis.
  2. Unsupervised statistical learning. EM algorithm.
  3. Linear discriminative function. The Perceptron. SVM (Support Vector Machine). Multilayer Perceptron and its learning by back propagation.
  4. Syntactic pattern recognition tasks. Exact and approximate matching tasks. Recognition using Markov chains.
  5. Tasks of computer vision. Measurement of shape, navigation, tracking, following, recognition.
  6. Image formation. Image structure. Relation between surface properties and luminance function.
  7. Projective and affine geometry.
  8. Multi-camera geometry.
  9. Motion analysis. Correspondence problem.
  10. Shape from X. Stereovision. Photometric stereo. Shape from shading.

Specialization topics for the branch "Biocybernetics"

  1. Modelling and simulation in biocybernetics. Design and implementation of models. Applications.
  2. Physiology of nervous system and neural networks.
  3. Cognitive processes and implementation of their computer models.
  4. Information systems for medicine and hospitals. Requirements on information systems from the medical viewpoint.
  5. Exploitation of knowledge systems in medical diagnostics and therapy planning.
  6. Man-machine systems. Models of human behaviour. Man-machine interface. Simulations in training of pilots and operators.
  7. Types of biological data and signals. Signal pre-processing. Identifying dependency between values. Specific issues of biological data processing.
  8. Methods for decision making under uncertainty and their employment in medical diagnostics.
  9. Deployment of machine learning methods in processing of medical data. Practical applications.
  10. Use of statistical methods in evaluation of medical data. Sensitivity, specificity, ROC curve (receiver operating characteristic), ROC surface.
  11. Data warehouses and data mining in medical applications.
  12. Perception methods, basic principles in machine vision and audio processing.
Responsible person: RNDr. Patrik Mottl, Ph.D.