State doctoral exam topics
Artificial Intelligence and Biocybernetics
Common topics
- Sets. Matrix theory. Linear equations.
- Fundamentals of mathematical analysis. Approximation of functions. Least-squares fitting. Applications of model fitting to real data.
- Static optimization. Linear programming. Gradient methods. Problem of convergence to local extremes.
- Fundamentals of statistics, experiments and statistical hypotheses testing, maximum likelihood.
- Graph theory. Combinatorial algorithms and their complexity. Asymptotic measures of complexity, P and NP classes.
- Linear integral transforms, the Fourier transform. FFT. Non-linear filtration.
- Information theory, information measure, entropy, mutual information, maximum entropy principle.
- Mathematical model of an object. Identification of a structure and estimation of parameters of a model.
- Propositional logic. First-order logic. Formal system, theories, their consistency and completeness. Proof theory. Resolution principle. Limitations of formal systems.
- Problem solving. State space, state space search methods.
- Formulation of statistical decision making and recognition tasks. Bayes decision rule as risk minimization. Non-Bayesian recognition tasks.
- 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.
- The notion of knowledge, its representation and application in artificial intelligence tasks.
- Knowledge systems and their practical applications.
- Main tasks of artificial intelligence and methods for their solving: symbolic manipulation, connectionism, distributed systems.
Specialization topics for the branch "Artificial intelligence"
- Programming languages for AI. Declarative and procedural programming paradigmas, their differences and possible interconnections including implementation issues.
- Natural language processing, challenges. Issues of natural language understanding, principles, methods, and tools. Employment in contemporary applications of AI.
- Fuzzy reasoning. Models of complex systems and their design. Qualitative simulation.
- Design and implementation of knowledge systems. Decision making under uncertainty and its exploitation in expert systems. Fundamentals of game theory.
- Knowledge discovery in data (KDD)and artificial intelligence techniques for KDD.
- Learning with extensive apriori knowledge. Inductive logic programming and relational learning.
- Reinforcement learning. Neural networks and their applications.
- Evolutionary computing principles and their applications.
- Multi-agent systems. Modelling of social agents. Behaviour of agent societies.
- Planning and scheduling. Knowledge in a dynamic environment, frame problem.
- Robotics. Models of the environment and knowledge fusion.
- Artificial life.
Specialization topics for the branch "Machine perception"
- Statistical learning theory according to Vapnik and Cervonenkis.
- Unsupervised statistical learning. EM algorithm.
- Linear discriminative function. The Perceptron. SVM (Support Vector Machine). Multilayer Perceptron and its learning by back propagation.
- Syntactic pattern recognition tasks. Exact and approximate matching tasks. Recognition using Markov chains.
- Tasks of computer vision. Measurement of shape, navigation, tracking, following, recognition.
- Image formation. Image structure. Relation between surface properties and luminance function.
- Projective and affine geometry.
- Multi-camera geometry.
- Motion analysis. Correspondence problem.
- Shape from X. Stereovision. Photometric stereo. Shape from shading.
Specialization topics for the branch "Biocybernetics"
- Modelling and simulation in biocybernetics. Design and implementation of models. Applications.
- Physiology of nervous system and neural networks.
- Cognitive processes and implementation of their computer models.
- Information systems for medicine and hospitals. Requirements on information systems from the medical viewpoint.
- Exploitation of knowledge systems in medical diagnostics and therapy planning.
- Man-machine systems. Models of human behaviour. Man-machine interface. Simulations in training of pilots and operators.
- Types of biological data and signals. Signal pre-processing. Identifying dependency between values. Specific issues of biological data processing.
- Methods for decision making under uncertainty and their employment in medical diagnostics.
- Deployment of machine learning methods in processing of medical data. Practical applications.
- Use of statistical methods in evaluation of medical data. Sensitivity, specificity, ROC curve (receiver operating characteristic), ROC surface.
- Data warehouses and data mining in medical applications.
- Perception methods, basic principles in machine vision and audio processing.