Current journal publications on the topic, especially those related to the descriptional complexity of automata.
J.E. Hopcroft, R.Motwani, J.D. Ullman: Introduction to automata theory, languages, and computation, Addison-Wesley, 2001.
J. Shallit: A second course in formal languages and automata theory, Cambridge University press, 2009.
M. Sipser: Introduction to the theory of computation, Thomson Course Technology, 2006.
D.P.Bovet, P.Crescenzi: Introduction to the theory of complexity, Prentice Hall, 1994.
J.van Leeuwen (ed.): Handbook of theoretical science, North-Holland, 1990.
G.Brassard, P.Bradley: Fundamentals of algorithmics, Prentice Hall, 1996.
Written test combined with an oral examinationi.
Slovak or English
Content prerequisites: Basic knowledge in the area of automata, formal languages, set theory, and graph theory.
Chomsky hierachy of languages and grammars. Finite state automata and its variants: deterministic, nondeterministic, alternating, probabilistic, quantum ... one-way, two-way, reversal bounded. Regular expressions and grammars. Unary regular languages and their properties. Connection between finite state automata and complexity theory. Pushdown automata, time and space complexity for recognition of context-free languages. Closure properties of contex-free, context-sensitive, and recursively enumerable languages.
To obtain background about efficient representation of regular languages and finite state automata, as well as about connection between automata and complexity theory.
Moore, J.: Oxford Academic Vocabulary Practice. OUP, 2017.
Kolaříková, Z., Petruňová, H., Timková, R.: Angličtina v akademickom prostredí – cvičebnica. Košice, Vydavateľstvo ŠafárikPress, 2021.
Tomaščíková, S., Rozenfeld, J. Developing Academic English in Speaking and Writing. Vydavateľstvo ŠafárikPress, 2021.
McCarthy, M., O´Dell, F.: Academic Vocabulary in Use. CUP, 2008.
Štepánek, L., J. De Haff a kol.: Academic English-Akademická angličtina. Grada Publishing, a.s., 2011.
Armer, T.: Cambridge English for Scientists. CUP, 2011.
lms.upjs.sk
Completion of e-course English for PhD Students (lms.upjs.sk), consultations (1-3).
Written assignments - Professional/Academic CV, Short Academic Biography.
English, level B2 according to CEFR
Specific aspects of academic and professional English with focus on correct pronunciation, vocabulary development (noun and verb collocations, phrasal verbs, prepositional phrases, word-formation, formal/informal language, etc.), selected aspects of English grammar (prepositions, grammar tenses, passive voice, etc.), academic writing (professional/academic CV, Short Academic Biography).
The development of students´ language skills - reading, writing, listening, speaking; improvement of their linguistic competence - students acquire knowledge of selected phonological, lexical and syntactic aspects; development of pragmatic competence - students acquire skills for effective and purposeful communication, with focus on Academic English and English for specific/professional purposes, level B2.
Moore, J.: Oxford Academic Vocabulary Practice. OUP, 2017.
Kolaříková, Z., Petruňová, H., Timková, R.: Angličtina v akademickom prostredí (cvičebnica). UPJŠ Košice, 2021.
Tomaščíková, S., Rozenfeld, J. Developing Academic English in Speaking and Writing. Vydavateľstvo ŠafárikPress, 2021.
McCarthy, M., O´Dell, F.: Academic Vocabulary in Use. CUP, 2008.
Štepánek, L., J. De Haff a kol.: Academic English-Akademická angličtina. Grada Publishing, a.s., 2011.
Armer, T.: Cambridge English for Scientists. CUP, 2011.
Test, oral exam in accordance with the exam requirements (available at the web-site of the LTC and in MS TEAMS)
B2 level according to CEFR
Academic communication (self-presentation, presenting at scientific meetings and conferences). Specific aspects of academic and professional English with focus on vocabulary development (formality, academic word-list), English grammar (passive voice, nominalisatio), language functions (expressing opinion, cause/effect, presenting arguments, giving examples, describing graphs/charts/schemes, etc.). Cross-language interference.
The development of students´ language skills - reading, writing, listening, speaking, improvement of their linguistic competence - students acquire knowledge of selected phonological, lexical and syntactic aspects, development of pragmatic competence - students can efectively use the language for a given purpose, with focus on Academic English and English for specific/professional purposes, level B2.
Citation in a national scientific journal
Obtaining a citation demonstrates broad and very well-founded scientific knowledge in the researched field, based on the ability to formulate research questions, to reflect on a scientific problem in such a way that generates new knowledge. At the same time, a citation in an indexed source demonstrates the competence to communicate new knowledge, which is a significant contribution to scientific knowledge, at the highest expert level.
Obtained citation registered in SCI or Scopus.
Obtaining a citation demonstrates broad and very well-founded scientific knowledge in the researched field, based on the ability to formulate research questions, to reflect on a scientific problem in such a way that generates new knowledge. At the same time, a citation in an indexed source demonstrates the competence to communicate new knowledge, which is a significant contribution to scientific knowledge, at the highest expert level.
Completion of a certified professional/training course.
The PhD student acquires up-to-date scientific knowledge, develops the capabilities of scientific work and familiarizes himself with the methodologies of making scientific knowledge available. He confronts his own knowledge and skills with other course participants, develops the abilities of peer discussion in the given scientific field.
Obtained citation in a foreign scientific journal
Obtaining a citation demonstrates broad and very well-founded scientific knowledge in the researched field, based on the ability to formulate research questions, to reflect on a scientific problem in such a way that generates new knowledge. At the same time, a citation in an indexed source demonstrates the competence to communicate new knowledge, which is a significant contribution to scientific knowledge, at the highest expert level.
Publication accepted in a national journal as author/co-author.
By publishing in a national journal as an author/co-author, the PhD student demonstrates a high level of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas.
Active participation in the home conference
By actively participating in the national scientific conference, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology in his scientific field. He demonstrates the ability to reflect on a specific scientific problem by using the latest approaches and applying them critically. Demonstrates competence in using existing theories and concepts in an innovative way, as well as generating new original scientific knowledge and communicating research results to a wider audience using adequate means and through the Slovak language.
Active participation in a national conference with foreign participation.
By actively participating in a scientific conference, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology in his scientific field. He demonstrates the ability to reflect on a specific scientific problem by using the latest approaches and applying them critically. Demonstrates competence to use existing theories and concepts in an innovative way, as well as generate new original scientific knowledge and communicate research results to a wider audience by adequate means and through Slovak or a foreign language.
1. BĚLOHLÁVEK, Radim. Fuzzy relational systems: foundations and principles. New York: Kluwer Academic/Plenum Publishers, [2002]. International federation for systems research. ISBN 0-306-46777-1.
2. GANTER B, WILLE R.: Formal Concept Analysis: Foundations and Applications, Lecture Notes in Artificial Intelligence, no. 3626, Springer-Verlag, ISBN 3-540-27891-5, 2005
During consultations during the semester.
Independent and creative mastery of theoretical and practical aspects of the issue and an overview of the current state of research and further direction, in the form of an oral exam, are evaluated.
Slovak or English
Prerequisites: Logic
Basic theorem on conceptual lattices.
Fuzzifications of concept lattices.
Formal conceptual analysis in terms of category theory.
Relationship of formal concept analysis to other data-mining methods.
Applications of formal concept analysis.
The aim of the course is to understand the basic features of formal conceptual analysis as one of the methods of relational-data analysis and its relationship to other data-mining methods.
[1] HAZZAN, Orit, Tami LAPIDOT and Noa RAGONIS, 2011. Guide to teaching computer science: an activity-based approach. New York: Springer. ISBN 9780857294425.
[2] LAU, William, 2017. Teaching Computing in Secondary Schools: A Practical Handbook [online]. Taylor & Francis Group, 211 p. [cited 2021-7-10]. ISBN 9781315298191. Available from: https://ebookcentral.proquest.com/lib/upjs-ebooks/detail.action?docID=5056529
[3] COMPUTER SCIENCE EDUCATION RESEARCH GROUP AT THE UNIVERSITY OF CANTERBURY, NEW ZEALAND. Computer Science Field Guide: An online interactive resource for high school students learning about computer science [online]. [cited 2021-7-10]. Available from: https://www.csfieldguide.org.nz/en/
[4] COMPUTER SCIENCE EDUCATION RESEARCH GROUP AT THE UNIVERSITY OF CANTERBURY, NEW ZEALAND. Computer Science without a computer [online]. [cited 2021-7-10]. Available from: https://csunplugged.org/en/
[5] QUEEN MARY, UNIVERSITY OF LONDON. Computer Science For Fun: A magazine where the digital world meets the real world [online]. [cited 2021-7-10]. Available from: http:// www.cs4fn.org/
[6] GUNIŠ, Ján and Ľubomír ŠNAJDER, 2009. Ďalšie vzdelávanie učiteľov základných škôl a stredných škôl v predmete informatika: Tvorba úloh a hodnotenie žiakov v predmete informatika. Bratislava: Štátny pedagogický ústav, 40 p. ISBN 978-80-8118-012-5. Also available from: https://www.statpedu.sk/files/sk/o-organizacii/projekty/projekt-dvui/publikacie/ tvorba_uloh_a_hodnotenie.pdf
[7] GUNIŠ, Ján and Ľubomír ŠNAJDER, 2010. Ďalšie vzdelávanie učiteľov základných škôl a stredných škôl v predmete informatika: Metodika výučby tematickej oblasti Informácie okolo nás. Bratislava: Štátny pedagogický ústav, 40 p. ISBN 978-80-8118-030-9. Also available from: https://www.statpedu.sk/files/sk/o-organizacii/projekty/projekt-dvui/publikacie/ metodika_informacie_okolo_nas.pdf
[8] GUNIŠ, Ján and Ľubomír ŠNAJDER, 2010. Ďalšie vzdelávanie učiteľov základných škôl a stredných škôl v predmete informatika: Metodika výučby tematickej oblasti Komunikácia prostredníctvom IKT. Bratislava: Štátny pedagogický ústav, 32 p. ISBN 978–80–8118–036-1. Also available from: https://www.statpedu.sk/files/sk/o-organizacii/projekty/projekt-dvui/ publikacie/metodika_komunikacia_prostrednictvom_ikt.pdf
[9] GUNIŠ, Ján and Ľubomír ŠNAJDER. Ďalšie vzdelávanie učiteľov základných škôl a stredných škôl v predmete informatika: Metodika výučby oblastí Princípy fungovania IKT a Informačná spoločnosť. Bratislava: Štátny pedagogický ústav, 32 p. ISBN 978–80–8118–045-3. Also available from: https://www.statpedu.sk/files/sk/o-organizacii/projekty/projekt-dvui/publikacie/ metodika_informacna_spolocnost.pdf
[10] ČAPEK, Robert, 2015. Moderní didaktika: lexikon výukových a hodnoticích metod. Praha: Grada. Pedagogika (Grada). ISBN 978-80-247-3450-7.
[11] LUKÁČ, Stanislav, Ľubomír ŠNAJDER, Ján GUNIŠ and Zuzana JEŠKOVÁ, 2016. Bádateľsky orientované vyučovanie matematiky a informatiky na stredných školách [online]. Košice: Prírodovedecká fakulta UPJŠ v Košiciach [cited 2021-7-10]. ISBN 978-80-8152-471-4. Available from: https://unibook.upjs.sk/img/cms/2016/pf/bov.pdf
[12] SPENDLOVE, David, 2015. 100 Ideas for Secondary Teachers: Assessment for Learning [online]. Bloomsbury Publishing, 129 p. [cited 2021-7-9]. ISBN 9781472911018. Available from:: https://ebookcentral.proquest.com/lib/upjs-ebooks/detail.action?docID=1990785 GANAJOVÁ, Mária, Beáta BRESTENSKÁ, Ján GUNIŠ, et al., 2021. Formatívne hodnotenie vo výučbe prírodných vied, matematiky a informatiky. Košice: Univerzita Pavla Jozefa Šafárika v Košiciach. ISBN 978-80-8152-973-3.
[13] GUNIŠ, Ján, Miloslava SUDOLSKÁ and Ľubomír ŠNAJDER, 2009. Ďalšie vzdelávanie učiteľov základných a stredných škôl v predmete informatika: Aktivizujúce metódy vo výučbe školskej informatiky. Bratislava: Štátny pedagogický ústav, 40 p. ISBN 978-80-89225-96-5. Also available from: https://www.statpedu.sk/files/sk/o-organizacii/projekty/projekt-dvui/publikacie/ aktivizujuce_metody.pdf
- Conditions for ongoing evaluation:
1. Microteaching with a sample solution of an algorithmic problem.
2. Assessment of administered didactic test.
3. Proposal for the preparation of a lesson with a 5E inquiry cycle.
4. Creation of an interactive educational aid.
- Conditions for the final evaluation:
1. Creation of a graded system of tasks for teaching selected topic of school informatics.
Conditions for successful completion of the course:
- Obtaining at least 50% of points for ongoing and final assignments.
slovak
1. Maturita on informatics. Logical structure of the curriculum, conceptual mapping. Determination of specific educational objectives and creation of a concept map for a selected topic of school informatics.
2. Educational task, its forms, and parameters. A graded system of tasks.
3. Creation of a graded system of tasks for teaching a selected topic of school informatics.
4. Activating methods of teaching school informatics (problem-based learning, discussion, situational and staging methods).
5. Activating methods of teaching school informatics (project-based learning, flipped learning, educational games, scientific humor).
6. Inquiry-based learning, inquiry cycle, inquiry skills, levels of inquiry, 5E learning cycle.
7. Formative assessment, cognitive and metacognitive tools. Creating a worksheet with selected formative assessment tools.
8. Assessment of students' learning outcomes in school informatics. Didactic tests.
9. Assessment of student projects. Student portfolio.
10. Conceptual process in school informatics. Informatics concepts in informatics competitions (iBobor). Informatics concepts in activities outside the computer (Computer Science Unplugged).
11. Methodology of teaching selected informatics topics (coding, encryption, compression)
12. Methodology of teaching selected informatics topics (specifics of computer floaiting point arithmetics).
13. Methodology of teaching selected informatics topics (mathematical modelling and simulation).
After completing this course, students are able to:
- acquire an overview of the objectives, content, modern methods and aids for teaching school informatics,
- create conceptual map, cognitive objectives and graded tasks collection for selected topic of school informatics,
- create a inquiry-based methodology of teaching a selected topic of school informatics.
- select and explain essential concepts for a selected topic of school informatics,
- create and present an assignment and a sample solution to an algorithmic problem,
- analyze and assess students' assignments and identify their misconceptions,
- design and discuss the methodology of teaching a selected topic of school informatics, which includes its own interactive teaching aid.
Proceedings of the Spring School of Doctoral Students.
Active participation in the Spring School of PhD students of UPJŠ.
1. Interdisciplinary lectures from the fields of medicine, natural sciences, law, public affairs, humanities. Lecturers - top foreign or national experts from the mentioned fields.
2. Scientific lectures in sections created within related disciplines. Lecturers - top experts from UPJŠ from the mentioned fields.
3. Scientific contributions of PhD students in sections of related fields.
4. Panel discussions on the issue of PhD studies and current trends in the development of scientific disciplines at UPJŠ.
By actively participating in the Spring School of PhD Students of UPJŠ, the PhD student demonstrates a high level of ability to process the issues of his dissertation for a multidisciplinary audience with an emphasis on clarifying the motivation, scientific problem, processing methodology and own contribution to the solution of the selected topic. The PhD student demonstrates the ability to professionally discuss various research topics, present his own positions and accept a plurality of opinions. Demonstrates the ability to communicate research results to a wider professional audience with adequate means and through the Slovak language.
1. ROSEN, K. H.: Elementary Number Theory and Its Applications, Addison Wesley, 2000
2. STINSON, D. R. : Cryptography. Theory and Practie, CRC Press, 2002
3. MEZENES, A.,. van Oorschot, P., Vanstone, S.: Handbook of Applied Cryptography, CRC Press, 1996
4. BLAKE, I. F., Seroussi, G., Smart, N.P.: Elliptic Curves in Cryptography, CUP 1999
Witten and oral exam.
Slovak or English
Special parts of computational algebra - rings of polynoms, cyclic groups, factorization of big numbers, arithmetic of eliptic curves. Actual problems of symmetric and nonsymmetric cryptography and cryptoanalysis.
To learn theoretical background and standard methods of computer algebra and know how they can be used in cryptographic systems and cryptoanalytic methods. To know current trends of research in this area of computer science.
1. GRUSKA, J. Quantum Computing. McGraw-Hill, 1999.
2. HIRVENSALO, M. Quantum Computing, Springer, 2004.
3. KITAEV, A.Y., SHEN, A.H., VYVALYI, M.N. Classical and Quantum Computation. American Mathematical Society, 2002.
4. NIELSEN, M.A., CHUANG, I.L. Quantum Computation and Quantum Information. Cambridge University Press, 2000.
5. STEEB, W. H., HARDY, Y. Problems And Solutions in Quantum Computing And Quantum Information. World Scientific Publishing Company, 2006.
oral exam
Slovak or English
Content prerequisities: Linear algebra. Hillbert space. Introduction to quantum mechanics. Computational complexity.
Quantum information. Principles and power of quantum computing. Fast factorisation. Qunatum search algorithm anf ther application for NP-hard problems. The class BQNP - an analogy of the class NP. Quantum coding. Quantum kryptography.
To learn how quantum algorithms can be used for solving hard problems, in coding theory and in cryptology.
Final thesis consultant.
By consulting the final thesis, the PhD student demonstrates broad and scientifically based knowledge in the field of study, as well as knowledge of a wide range of methods and approaches. Demonstrates the ability to critically assess a professional problem and its proposed solution, as well as to evaluate it and possibly propose another solution. He applies knowledge and skills from the field of pedagogical sciences to his own field.
1. GOLDSTERN, M., JUDAH H.: The Incompleteness Phenomenon, A New Course in Mathematical Logic, A K Peters, Wellesley, Massachusetts, 1995
2. ABITEBOUL, S. HULL, R., VIANU, V.: Foundations of databases, Addison-Wesley Publishing Co, 1995
Satisfiable understanding of basic concepts.
Slovak or English
Predicate logic – logic language, syntax and semantics, term, formula.
Axioms, proof, provability.
Interpretation, truth, model.
Correctness of the predicate logic.
Boolean algebras.
Syntactic model, completeness of predicate logic.
Inductive structures in general.
Aplications of logic in database systems.
Understanding of basic notions of mathematical logic (logic language, term, formula, axioms, proof, provability, truth, model, syntax and semantics, soundness, completeness) and ability to formalize concisely.
1. RYAN, P. Y. A., SCHNEIDER, S.A.: Modelling and Analysis of Security Protocols, Addison Wesley, 2001
2. HUTH, M., RYAN, M.: Logic in Computer Science - Modelling and Reasoning about Systems, CUP, 1999
3. MENEZES, A., van OORSCHOT, P., VANSTONE, S.: Handbook of Applied Cryptography, CRC Press, 1996
Written and oral exam.
Slovak or English
Authentication and certification schemes, key distribution and maintenance. Formal description of cryptographic protocols and methods for their analysis. Algebraic and logic methods for attack modelling, utilisation of dynamic logical systems. Datalog for automatic security verification.
To learn essential properties of the used cryptographic authentication and certification schemes and standard methods of attacks to them. To understand the theoretical background of a design of formal models and know how it is possible to utilise them in practise. To know the actual problems concerning the analysis of the security of cryptographic protocols.
Active participation in an international conference abroad.
By actively participating in an international scientific conference abroad, the phD student demonstrates a high level of ability to identify, evaluate, and apply correct scientific methods or research methodology in his scientific field. He demonstrates the ability to reflect on a specific scientific problem by using the latest approaches and applying them critically. Demonstrates competence to use existing theories and concepts in an innovative way, as well as generate new original scientific knowledge and communicate research results to a wider audience by adequate means and through a foreign language.
1. PEARL J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan – Kaufmann, San Francisco, CA, 1988
2. JENSEN, F. V.: An Introduction to Bayesian networks, UCL Press, 1996
3. DUBOIS, D., Prade, H.: Possibility Theory. Plenum Press, N.York, 1988
4. PARIS, J. B.: The uncertain Reasoners Companion. Cambridge University Press, 1994
During consultations during the semester.
Independent and creative mastery of theoretical and practical aspects of the issue, an overview of the current state of research and open problems and further direction, in the form of a written and oral exam, are evaluated.
Slovak or English
prerequisites: Logic
Belief and probability, Dempster-Shaferova belief. Necessity and possibility. Uncertainty in artificial intelligence.
Fuzzy sets, constructions of fuzzy sets from statistic data.
Uncertainty in artificial intelligence, Markov and Bayesian networks, belief updating, belief revision.
To give the students basic techniques in systems processing imperfect information to be able read and write scientific papers in the area.
Co-author of a monograph in a renowned publishing house.
By publishing a monograph in a renowned publishing house, the PhD student demonstrates a high level of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The doctoral student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas.
Co-author of the monograph.
By publishing a monograph, the PhD student demonstrates a high level of ability to identify, evaluate, and apply correct scientific methods or research methodology. It demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The doctoral student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas.
1. M. Anthony, N. Biggs: Computational Learning Theory, Cambridge University Press, 1991, 1997.
2. Lectures CS224n: Natural Language Processing with Deep Learning, Stanford University, 2019
3. A. P. Engelbrecht: Computational Intelligence, John Wiley & Sons, Ltd, 2005,
4. V. Kecman: Learning and Soft Computing, MIT Press, 2001
5. V. Mařík, a kol.: Umělá inteligence 4, Academia, Praha, 2003
6. P. Baldi, S. Brunak: Bioinformatics, MIT Press, 2001
The realization of a project focused on methods of computational learning and artificial intelligence.
Successful completion of the written and oral part of the exam focused on computational learning and artificial intelligence.
Slovak or English
1. Concepts, hypotheses, learning algorithms, Boolean formulae and representations
2. Probabilistic Learning
3. Efficient algorithms I
4. Efficient Algorithms II
5. VC dimension
6. CS224N: Introduction and word vectors
7. CS224N: Word vectors and word senses Word window classification, NN, PyTorch, RNN and language models
8. CS224N: RNN and language models Matrix calculus and BP, Linguistic structure dependency
9. CS224N: Machine translation Seq2Seq and attention (L8)
10. CS224N: Convolutional Networks for NLP (L11)
11. CS224N: Subword models (L12)
12. CS224N: Contextual word embeddings (L13): BERT
13. CS224N: Modeling contexts of use: Contextual representations and pretraining. ELMo, BERT
14. CS224N: Natural language generation
The knowledge about methods used to solve issues in the following two areas:
1. Learning from experimental data - examples, samples, measurements, records, or observations.
2. Inclusion of existing structured human knowledge in the created systems - experience, expert activity, heuristics
1. Poeppel D., Mangun G., Gazzaniga M. (ed.): The Cognitive Neurosciences. 6th ed. MIT Press.
2020. ISBN-13: 978-0262043250
2. Dayan P and LF Abbott: Theoretical Neuroscience - Computational and Mathematical
Modeling of Neural Systems. MIT Press, 2005 ISBN-13: 978-0262541855
3. Thagard P: Mind: Introduction to Cognitive Science, 2nd Edition. Bradford Books. ISBN-13 :
978-0262701099
4. KANDEL, E. R., SCHWARTZ, J. H. and JESSELL, T.M.: Principles of Neural Science.
McGraw-Hill, 2021 ISBN-13: 978-1259642234
5. HERTZ, J., KROGH, A. and PALMER R. G.: Introduction to the theory of neural
computation. Addison-Wesley 1991 ISBN-13: 978-0201515602
Midterm exam. Project
Final exam consisting of written and/or oral part.
English
Content prerequisities: programming, mathematics, basics of neurobiology and cognitive psychology
1. Cognitive Science
2. Neuron, synaptic transmission, CNS, experimental methods
3. Hearing and speech: general intro
4. Spatial hearing
5. Auditory scene analysis, "Cocktail party effect", informational masking.
6. Vision: Intro - pathways, perception, illusions.
7. Binocular and spatial vision.
8. Visual motion perception.
9. Sensory and motor system.
10. Memory.
11. Attention.
12. Emotions, motivation,conditioning and reinforcement learning
Skills in quantitative analysis and modeling of neural data. Overview of cognitive functions and their neural basis in the human brain.
1. Lewis Tunstall, Leandro von Werra, Thomas Wolf: Natural Language Processing with Transformers, ISBN 978-1098136796, O'Reilly Media, 2022
2. Yoav Goldberg: A Primer on Neural Network Models for Natural Language Processing, available online: <https://u.cs.biu.ac.il/~yogo/nnlp.pdf>
3. Dan Jurafsky, James H. Martin: Speech and Language Processing, available online: <https://web.stanford.edu/~jurafsky/slp3/>
Evaluation of individual work in the study of theoretical issues of natural language processing. Oral examination based on selected area od NLP.
slovak, english
1. words, tokens, n-grams, embeddings
2. transformers
3. large language models
4. training of language models
5. Information retrieval and RAG
6. Extracting information from texts
7. Agent systems and knowledge graphs
Understanding the principles of methods used in natural language processing. Practical solution of selected tasks on real data.
A publication published in a non-reviewed foreign or national journal as an author/co-author.
By publishing in a non-reviewed foreign or national journal as an author/co-author, the PhD student demonstrates the ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The phD student demonstrates the ability to finalize his own thoughts in a written speech.
The recommended literature is determined individually in accordance with the topic of the dissertation thesis.
The dissertation thesis is the result of the student's own scientific research. It must not show elements of academic fraud and must meet the criteria of good research practice defined in the Rector's Decision no. 21/2021, which lays down the rules for assessing plagiarism at Pavol Jozef Šafárik University in Košice and its components. Fulfillment of the criteria is verified mainly in the process of supervision and in the process of thesis defense. Failure to do so is reason for disciplinary action.
Slovak or English
1. Elaboration of the dissertation thesis in accordance with the instructions of the supervisor.
2, Presentation of the results of the dissertation thesis before the examination commission.
3. Answering questions from oponents and questions related to the topic of the dissertation thesis within the discussion.
The dissertation thesis has the character of a scientific work and the student demonstrates extensive mastery of the theory and professional terminology of the field of study, acquisition of knowledge, skills and competencies in accordance with the declared profile of the graduate of the study program, as well as the ability to apply them creatively in solving selected scientific problem. The student demonstrates the ability of independent scientific work in terms of content, formal and ethical. Further details on the dissetation thesis are determined by Directive no. 1/2011 on the basic requirements of final theses and the Study Regulations of UPJŠ in Košice for doctoral studies.
1. HROMKOVIČ, J.: Design and analysis of ranodmized algorithms. Springer-Verlag, 2005. ISBN 3-540-23949-9.
2. MOTWANI, R. and RAGHAVAN, P.: Randomized Algorithms. Cambridge University Press 1995. ISBN 0-521-47465-5
3. MITZEMANCHER, M. and UPFAL, E.: Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press 2005. ISBN 0-521-83540 2
4. HROMKOVIČ, J.: Communication Protocols - An Exemplary Study of the Power of Randomness. In: Handbook on Randomized Computing, P.Pardalos, S.Rajasekaran, J.Reif, J.Rolim, Eds., Kluwer Publ., 2001.
Written test combined with an oral examination.
Slovak or English
Content prerequisities: Basic knowlegde of in the area of probability theory, computational complexity, and programming.
1. Elementary probability theory. Basic probabilistic computational models.
2. Las Vegas algorithms, One-sided error Monte Carlo algorithms.
3. Two-sided error Monte Carlo algorithms, with bounded and unbounded-error.
4. Probabilistic classes with polynomial time.
5. Foiling the adversary
6. Hashing.
7. Fingerprinting.
Providing en extended backgroung in the area of probabilistic and approximation algorithms, with respect to their classification, efficiency, and probability of error.
Oosterhof, N. N., Connolly, A. C., and Haxby, J. V. CoSMoMVPA: multi-modal multivariate pattern analysis of neuroimaging data in Matlab / GNU Octave. Frontiers in Neuroinformatics, 2016. doi:10.3389/fninf.2016.00027.
Connolly, A. C., Guntupalli, J. S., Gors, J., Hanke, M., Halchenko, Y. O., Wu, Y. C., Abdi, H., and Haxby, J. V. The Representation of Biological Classes in the Human Brain. Journal of Neuroscience, 32(8):2608–2618, February 2012.
Haxby, J. V., Gobbini, M. I., Furey, M. L., Ishai, A., Schouten, J. L., and Pietrini, P. Distributed and overlapping representations of faces and objects in ventral temporal cortex. Science, 293(5539):2425–2430, September 2001.
Midterm exam. Project Final exam consisting of written and/or oral part.
English
1. Advanced GLM modeling
2. Intro to machine learning
3. Multi-voxel Pattern Analysis: A neuroscientific perspective
4. Multi-voxel pattern analysis v/s Univariate
5. CosmoMVPA toolset
6. Split half correlation analysis
7. Search Light analysis
8. SVM and other classifiers
Skills necessary for application of advanced computational tools to fMRI data analysis.
Active involvement in the popularization of science.
Demonstrated ability to present science to the lay public, use interactive methods of scientific communication, identify the target group and adapt the communication language to the level of professional knowledge. A PhD student is able to arouse interest and motivate specific target groups in the field of his scientific work, but also in the wider context of science.
Work in the organizing committee of the conference
By working in the organizing committee of the conference, the PhD student demonstrates the abilities and competences to organize a scientific or professional event independently or in a team, to manage the implementation in terms of time and content, to communicate effectively verbally and in writing using various technical means as needed, including in a foreign language at a professional level with various types of people, if necessary, correctly recommend solutions or make independent decisions.
Direct teaching activity 1 semester hour
Through pedagogical activity, the PhD student demonstrates the ability to transfer and integrate knowledge from his own field of study into education. He is able to select and apply the right techniques and strategies of study group management, higher education and evaluation of learning outcomes. He is capable of designing and implementing part of the educational process in accordance with current trends in higher education and the requirements placed on the level of communication and digital competencies.
Direct teaching activity 2 semester hours
Through pedagogical activity, the PhD student demonstrates the ability to transfer and integrate knowledge from his own field of study into education. He is able to select and apply the right techniques and strategies of study group management, higher education and evaluation of learning outcomes. He is capable of designing and implementing part of the educational process in accordance with current trends in higher education and the requirements placed on the level of communication and digital competencies.
Direct teaching activity 3 semester hours
Through pedagogical activity, the PhD student demonstrates the ability to transfer and integrate knowledge from his own field of study into education. He is able to select and apply the right techniques and strategies of study group management, higher education and evaluation of learning outcomes. He is capable of designing and implementing part of the educational process in accordance with current trends in higher education and the requirements placed on the level of communication and digital competencies.
Direct teaching activity 4 semester hours
Through pedagogical activity, the PhD student demonstrates the ability to transfer and integrate knowledge from his own field of study into education. He is able to select and apply the right techniques and strategies of study group management, higher education and evaluation of learning outcomes. He is capable of designing and implementing part of the educational process in accordance with current trends in higher education and the requirements placed on the level of communication and digital competencies.
Patent filed, invention, software product created.
The PhD student demonstrates the ability to create an innovative product in a given scientific field, or with impact on an interdisciplinary scale or in technical practice
Publication accepted in a journal of category Q1 as co-author.
By publishing in a journal of category Q1 as a co-author, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas.
Publication accepted in a journal of category Q1 as first or corresponding author.
By publishing in a journal of category Q1 as the first or corresponding author, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas.
Publication accepted in a journal of category Q2 as co-author.
By publishing in a journal of category Q2 as a co-author, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas
Publication accepted in a journal of category Q2 as first or corresponding author.
By publishing in a journal of category Q2 as the first or corresponding author, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas.
Publication accepted in a journal of category Q3 as co-author
By publishing in a journal of category Q3 as a co-author, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas
Publication accepted in a journal of category Q3 as first or corresponding author
By publishing in a journal of category Q3 as the first or corresponding author, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas.
Publication accepted in a journal of category Q4 as co-author.
By publishing in a journal of category Q4 as a co-author, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas.
Publication accepted in a journal of category Q4 as first or corresponding author.
By publishing in a journal of category Q4 as the first or corresponding author, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas.
A publication published in a peer-reviewed foreign or national proceedings as an author/co-author.
By publishing in a peer-reviewed foreign or national journal as an author/co-author, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas
Obtained citation registered in SCI or Scopus.
Obtaining a citation demonstrates broad and very well-founded scientific knowledge in the researched field, based on the ability to formulate research questions, to reflect on a scientific problem in such a way that generates new knowledge. At the same time, a citation in an indexed source demonstrates the competence to communicate new knowledge, which is a significant contribution to scientific knowledge, at the highest expert level.
Co-investigator of the domestic project
The PhD student demonstrates the ability to participate in teamwork, to bring his own contribution to the solution of the project objective and to take responsibility for the assigned tasks. By solving the domestic project, he acquires the ability to implement the project intention according to the established procedure, to follow the project schedule, to coordinate his own activities with colleagues, to participate in the creation of outputs. The PhD student gains valuable experience from the practical course of the grant project.
R.P. Dobrow, Introduction to Stochastic Processes with R, Wiley, 2016, ISBN 978-1-118-74065-1
R.H. Shumway, D.S. Stoffer, Time Series Analysis and Its Applications, Examples with R, Springer, 2017, ISBN 978-3-319-52452-8
Ch. J. Geyer, Bayesian Inference via Markov Chain Monte Carlo (MCMC), 2021, https://www.stat.umn.edu/geyer/3701/notes/mcmc-bayes.html
G.P. Nason, Wavelet Methods in Statistics with R, Springer, 2011, ISBN: 978-0-387-75960-9
Ch. K. Chui, G. Chen, Kalman Filtering, Springer, ISBN 978-3-319-47610-0, 2017
Cs. Török, H.-P. Bernhard, Wavelet Shrinkage and Mutual Information, Communications of JINR, Dubna, Russia, 1999
Nonparametric Regression Smoothers in R, http://users.stat.umn.edu/~helwig/notes/smooth-notes.html#simple-smoothers-in-r
J. S. Simonoff, Smoothing Methods in Statistics, Springer, ISBN-13: 978-0387947167, 1996
The ability to formulate a problem in the acquired terminology and solve it within a project.
Project.
Oral exam.
Slovak or English
1. Random processes and time series, Moving average, ARIMA processes.
2. Markov chains, Markov Chains Monte Carlo - MCMC.
3. Stationary processes and correlation function.
4. Martingales, Wiener process and SDE.
5. Fourier transformation, FFT, Fourier series.
6. Wavelet analysis.
7. Filtration, Kalman filter.
8. Modeling, Goodness of fit tests; Likelihood and Bayesian principle.
9. Mutual information, Fisher information, Akaike criterion.
10. Nonparametric estimation and approximation: Nadaraya-Watson kernel, Loess(locally estimated scatterplot smoothing).
11. Smoothing Spline and penalization, Multivariate adaptive regression spline (MARS), Generalized additive model (GAM).
During the completion of the course, the doctoral student will master the most relevant methods of signal processing and corresponding software. He will be able to explain the differences between the types of stochastic data models and thus analyze and simulate data, determine the scheme or dependence between attributes and obtain information.
Co-worker of project supported by internal grant schemes (VVGS)
The PhD student demonstrates the ability to participate in teamwork, to bring his own contribution to the solution of the project objective within the internal grant system at UPJŠ. By solving the internal VVGS grant, he acquires the ability to implement the project plan according to the established procedure, adhere to the project schedule, coordinate his own activities with colleagues, and participate in the creation of outputs. The PhD student gains valuable experience from the practical course of the grant project.
Membership in the research team of an international project.
Current professional and scientific literature in the field of dissertation topic or related field.
The condition for passing the course is a summary presentation of the student's results in the field of research and a presentation of studied professional and scientific texts.
Slovak or English
1. Independent study of professional and scientific texts focused on issues related to the topic of the dissertation,
2. Presentation of newly acquired knowledge,
3. Summary presentation of research activities.
The result of the education is the student's guidance to independent and creative extraction of the latest knowledge focused on issues related to the topic of the student's dissertation and continuous verification of his ability to present the newly acquired knowledge.
Current professional and scientific literature in the field of dissertation topic or related field.
The condition for passing the course is a summary presentation of the student's results in the field of research and a presentation of studied professional and scientific texts.
Slovak or English
1. Independent study of professional and scientific texts focused on issues related to the topic of the dissertation,
2. Presentation of newly acquired knowledge,
3. Summary presentation of research activities.
The result of the education is the student's guidance to independent and creative extraction of the latest knowledge focused on issues related to the topic of the student's dissertation and continuous verification of his ability to present the newly acquired knowledge.
Current professional and scientific literature in the field of dissertation topic or related field.
The condition for passing the course is a summary presentation of the student's results in the field of research and a presentation of studied professional and scientific texts.
Slovak or English
1. Independent study of professional and scientific texts focused on issues related to the topic of the dissertation,
2. Presentation of newly acquired knowledge,
3. Summary presentation of research activities.
The result of the education is the student's guidance to independent and creative extraction of the latest knowledge focused on issues related to the topic of the student's dissertation and continuous verification of his ability to present the newly acquired knowledge.
Current professional and scientific literature in the field of dissertation topic or related field.
The condition for passing the course is a summary presentation of the student's results in the field of research and a presentation of studied professional and scientific texts.
Slovak or English
1. Independent study of professional and scientific texts focused on issues related to the topic of the dissertation,
2. Presentation of newly acquired knowledge,
3. Summary presentation of research activities.
The result of the education is the student's guidance to independent and creative extraction of the latest knowledge focused on issues related to the topic of the student's dissertation and continuous verification of his ability to present the newly acquired knowledge.
Current professional and scientific literature in the field of dissertation topic or related field.
The condition for passing the course is a summary presentation of the student's results in the field of research and a presentation of studied professional and scientific texts.
Slovak or English
1. Independent study of professional and scientific texts focused on issues related to the topic of the dissertation,
2. Presentation of newly acquired knowledge,
3. Summary presentation of research activities.
The result of the education is the student's guidance to independent and creative extraction of the latest knowledge focused on issues related to the topic of the student's dissertation and continuous verification of his ability to present the newly acquired knowledge.
Current professional and scientific literature in the field of dissertation topic or related field.
The condition for passing the course is a summary presentation of the student's results in the field of research and a presentation of studied professional and scientific texts.
Slovak or English
1. Independent study of professional and scientific texts focused on issues related to the topic of the dissertation,
2. Presentation of newly acquired knowledge,
3. Summary presentation of research activities.
The result of the education is the student's guidance to independent and creative extraction of the latest knowledge focused on issues related to the topic of the student's dissertation and continuous verification of his ability to present the newly acquired knowledge.
Current professional and scientific literature in the field of dissertation topic or related field.
The condition for passing the course is a summary presentation of the student's results in the field of research and a presentation of studied professional and scientific texts.
Slovak or English
1. Independent study of professional and scientific texts focused on issues related to the topic of the dissertation,
2. Presentation of newly acquired knowledge,
3. Summary presentation of research activities.
The result of the education is the student's guidance to independent and creative extraction of the latest knowledge focused on issues related to the topic of the student's dissertation and continuous verification of his ability to present the newly acquired knowledge.
Current professional and scientific literature in the field of dissertation topic or related field.
The condition for passing the course is a summary presentation of the student's results in the field of research and a presentation of studied professional and scientific texts.
Slovak or English
1. Independent study of professional and scientific texts focused on issues related to the topic of the dissertation,
2. Presentation of newly acquired knowledge,
3. Summary presentation of research activities.
The result of the education is the student's guidance to independent and creative extraction of the latest knowledge focused on issues related to the topic of the student's dissertation and continuous verification of his ability to present the newly acquired knowledge.
Co-investigator of the applied research project
The PhD student demonstrates the ability to participate in teamwork, to bring his own contribution to the solution of the project objective of applied research and to take responsibility for assigned tasks. By solving an applied research project, he acquires the ability to implement the project objective according to the established procedure, to follow the project schedule, to coordinate his own activities with colleagues, to participate in the creation of applied research outputs. The PhD student gains valuable experience from the practical course of a grant project with a focus on applied research.
1. GOODFELLOW Ian, BENGIO Yoshua a Aaron COURVILLE. Deep Learning. MIT Press, 2016. ISBN: 9780262035613.
2. HERTZ, John, Anders KROGH a Richard G. PALMER. Introduction to the theory of neural computation. Redwood City: CRC Press, [1991]. Santa Fe Institute studies in the sciences of complexity. ISBN 0-201-51560-1.
3. KVASNIČKA, Vladimír. Úvod do teórie neurónových sietí. [Slovenská republika]: IRIS, 1997. ISBN 80-88778-30-1.
4. ŠÍMA, Jiří a Roman NERUDA. Teoretické otázky neuronových sítí. Praha: MATFYZPRESS, 1996. ISBN 80-85863-18-9.
5. HASSOUN, M. H.: Fundamentals of artificial neural networks, The MIT Press, 1995.
6. HAYKIN, S.: Neural Networks, A comprehensive foundation, Prentice-Hall, second edition 1999.
Evaluation of individual work in the study of theoretical issues of neural networks - advanced methods of neural networks. Oral examination based on selected type of neural network.
Slovak or English
1.-3. Computational complexity of neural networks.
4.-6. Probabilistic neural networks.
7.-9. Computational capability of neural networks, a transformation of neural networks to Turing machines, and Turing machines to neural networks.
10.-12. Approximation of functions using neural networks.
13. Kolmogorov theorem and its proof, theorems connected to Kolmogorov theorem.
To understand mathematical principles of neural networks and to know their capabilities. To be able to construct models of neural networks to solve some problems.
Poldrack R.: Handbook of Functional MRI Data Analysis. Cambridge University Press. 2011. ISBN-13: 978-0521517669
Midterm exam. Project
Final exam consisting of written and/or oral part.
English
1. Design methods for stimulus-driven and task-driven fMRI experiments.
2. Design methods for resting-state fMRI experiments and other types.
3. Workflows for model-based analysis methods.
4. Workflows for data-driven analysis methods.
5. Analysis methods using MVPA.
6. Analysis using ICA and graph theory.
7. Computational modeling.
8. Parametric and non-parametric statistics.
9. Integrating functional MRI with PET / EEG / MEG.
10. Tools: FreeSurfer, FSL.
11. diffusion MRI data, connectomics.
12. large-scale neuroimaging initiatives, Big Data analysis, and machine learning.
This course provides the background necessary for designing, conducting, and interpreting fMRI studies. Lectures are formatted as advanced seminars, combined with hands-on labs. The course will also introduce basic neuroscience concepts necessary.
E. Süli, D.F. Mayers, An Introduction to Numerical Analysis, Cambridge University Press, 2003, ISBN 0 521 81026 4
V.A. Bloomfield, Using R for Numerical Analysis in Science and Engineering, Chapman & Hall, 2014, 978-1-4398-8449-2
S. Sheather, A Modern Approach to Regression with R, Springer, 2009, 978-0-387-09607-0
R.I. Kabacoff, R in Action, Data analysis and graphics with R, 3rd edition, Manning, 2021, ISBN-13: 978-1617296055
J. Andel, Matematická statistika, SNTL/ALFA, 1985
T. Hastie, R. Tibshurani, J.H. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Spinger, 2017, 978-0387848570
O. Jones, R. Maillardet, A. Robinson, Introduction to Scientific Programming and Simulation Using R, Chapman & Hall, 2nd Edition, 2014, 978-1-4665-7001-6
The ability to formulate a problem in the acquired terminology and solve it within a project.
Project.
Oral exam.
Slovak or English
1. Solving Systems of Equations, QR, SVD and eigenfaces
2. Orthogonalization
3. Splines of class C2, B-splines, Uniform and non-uniform splines
4. Interpolation splines; 2D and 3D splines
5. Parametric Data approximation and smoothing
6. Piecewise approximation with automatic node detection and penalization
7. Chebyshev nodes and CHEBFUN
8. Logistic regression
9. Multidimensional methods, Principal components
10. Factor analysis, Discriminant analysis
11. Cluster analysis
Upon completion of the course, the doctoral student, when solving a new type of problem, is able to choose a suitable method based on the analysis of requirements and principles of the considered numerical method and algorithm. The student will master suitable software for data processing and information gain.
Supervision of Student's Scientific Activity
By guiding a student within the SOČ or ŠVOČ, the PhD student demonstrates broad and scientifically based knowledge in the field of study, as well as knowledge of a wide range of methods and approaches. Demonstrates the ability to critically assess a professional problem and its proposed solution, as well as to evaluate it and possibly propose another solution. He applies knowledge and skills from the field of pedagogical sciences to his own field.
Scientific work after being sent to the editorial office as an author/co-author.
By sending a manuscript to the editors of a scientific journal as an author/co-author, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to formulate his own ideas in a structured form.
Elaboration of reviewer report
The PhD student demonstrates broad and scientifically based knowledge in the field of study, as well as knowledge of a wide range of methods and approaches. Demonstrates the ability to critically assess a professional problem and its proposed solution, as well as to evaluate it and possibly recommend another solution. He applies knowledge and skills from the field of pedagogical sciences to his own field.
J.E. Hopcroft, R.Motwani, J.D. Ullman: Introduction to automata theory, languages, and computation, Addison-Wesley, 2007.
M. Sipser: Introduction to the Theory of Computation, Thomson, 2nd edition, 2006.
S. Arora, B. Barak: Computational Complexity: A Modern Approach, Cambridge Univ. Pess, 2009.
C. Calude and J. Hromkovič: Complexity: A Language-Theoretic Point of View, in G. Rozenberg and A. Salomaa, Handbook of Formal Languages II, Springer, 1997.
G.Brassard, P.Bradley: Fundamentals of algorithmics, Prentice Hall, 1996.
Ch. H. Papadimitriou: Computational Complexity, Addison-Wesley, 1994.
D.P.Bovet, P.Crescenzi: Introduction to the theory of complexity, Prentice Hall, 1994.
Written test combined with an oral examination.
Slovak or english
Content prerequisity: Basic knowlegde in the area of formal languages, automata theory, and programming.
1. Measuring time and space complexity, basic computational models: single- and multi-tape Turing machines, RAM and RASP models, unit and logarithmic costs.
2. Basic complexity classes: L, NL, P, NP, PSPACE, NPSPACE, EXPTIME, NEXPTIME, EXPSPACE.
3. P versus NP, L versus NL. Examples of complete problems in these classes.
4. Polynomial time and logarithmic space reducibilities, definition and basic properties of complete problems.
5. NP-completenss of the Boolean formula satisfiability (SAT).
6. Variants of SAT, problems related to graph coloring.
7. Other NP-complete problems: vertex cover, Hamiltionian paths, subset sum, balancing, traveling salesman problem.
8. Subexponential deterministic solutions for selected NP-complete problems: planar 3-colorability, balancing. Restricted variants with more efficient solutions.
9. Space complexity classes: Savitch theorem, inductive counting.
10. Problems complete for NL, P, and PSPACE: graph accessibily (GAP), circuit-value, quantified Boolean formulas (QBF).
11. Hierarchy and translation theorems for time and space.
12. Relativized complexity classes.
13. Alternating complexity classes.
14. Polynomial time hierarchy.
15. Alternating logarithmic space hierarchy.
Providing an extended backgroung in the area of efficient computations, computational complexity of algorithms, fundamental time and space complexity classes, hardest complete problems, and about reducibility among problems.
Presentation at the seminar
By actively participating in the seminar, the PhD student demonstrates the ability to identify, evaluate, and apply correct scientific methods or research methodology in his field of study. He demonstrates the ability to reflect on a specific scientific problem by using the latest approaches and applying them critically. Demonstrates competence in using existing theories and concepts in an innovative way, as well as generating new original scientific knowledge and communicating research results by adequate means and through Slovak or a foreign language.
Supervisor of the final thesis.
By supervising the final thesis, the PhD student demonstrates broad and scientifically based knowledge in the field of study, as well as knowledge of a wide range of methods and approaches. Demonstrates the ability to critically assess a professional problem and its proposed solution, as well as to evaluate it and possibly propose another solution. He applies knowledge and skills from the field of pedagogical sciences to his own field.
Publication accepted in a foreign journal as an author/co-author.
By publishing in a foreign journal as an author/co-author, the PhD student demonstrates a high level of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas.
Principal investigator of an internal grant (VVGS)
The PhD student demonstrates the ability to process a successful application for his own research problem within the internal grant system at UPJŠ. Acquires skills with the design of research stages, their time schedule, measurable outputs and adequate distribution of funds. The very solution of the internal VVGS grant acquires the ability to implement the project intention according to the established procedure, to be responsible for achieving the set outputs. As a responsible researcher, the PhD student acquires competencies in project management, its administration, and presentation of results.
Completion of a foreign study stay lasting less than 30 days.
By completing a shorter study stay, the PhD student demonstrates the ability to reflect on research problems and work critically with sources at an expert level and in an interdisciplinary context, while being able to generate new knowledge. He is able to actively communicate at an expert level in more than one language. He acts as a responsible independent scientist, works independently and in a group with the aim of pushing the boundaries of knowledge and transferring them to other areas of research, to practice and to the wider public. He can competently argue and explain his ideas.
Completion of a foreign study stay lasting more than 30 days.
By completing the study stay, the PhD student demonstrates the ability to reflect on research problems and work critically with sources at an expert level and in an interdisciplinary context, while being able to generate new knowledge. He is able to actively communicate at an expert level in more than one language. He acts as a responsible independent scientist, works independently and in a group with the aim of pushing the boundaries of knowledge and transferring them to other areas of research, to practice and to the wider public. He can competently argue and explain his ideas.