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BSc. Topic: Productivity of Geniuses (Kárný)

Type of Work: 
bachelor
Affiliation/Phone: 
ÚTIA AV ČR, v.v.i., oddělení AS, 266052274
Supervisor: 
Kárný

Even highly creative people (scientists, artists, influencers...) are able to create a limited number of significant outputs in life. Predicting the extent to which their creative capacity is exhausted is important for making decisions affecting their careers. The work is focused on the creation and data-driven personalization of the personal creative productivity drawing model.

Tasks: 

1. Learn about Bayesian parameter estimation.
2. Familiarize yourself with productivity modeling and choose a simple parametric model.
3. Get to know the numerical indicators of the productivity of scientists (or artists).
4. Choose an indicator available from public sources and collect the corresponding data.
5. Implement the proposed estimator in MATLAB and evaluate the quality your estimation and the resulting prediction.

Bibliography: 

Doporučená literatura (části vybrané po dohodě se školitelem)

1. V. Peterka, Bayesian System Identification, in P. Eykhoff "Trends and Progress in System Identification", Pergamon Press, Oxford, 239-304, 1981.
2. C. Marchetti. Action curves and clockwork geniuses. Technical report, IASA, Laxenburg, Vienna, 1984.
3. T. Braun, W. Ganzel, and A. Schubert. Scientometric indicators. World Scientific, (1985).
4. J. Mingers and L. Leydesdor_. A review of theory and practice in scientometrics. European Journal of Operational Research, 246 (2015),1-19.

2022-09-15 10:15

BSc./Mgr. Téma: Inverzní modelování zdroje při radiačním úniku do atmosféry (Tichý)

Type of Work: 
bachelor
diploma
Affiliation/Phone: 
ÚTIA AV ČR, v.v.i., oddělení AS, 266052570
Supervisor: 
Tichý
Keywords: 
Bayesovské modelování a odhadování, inverzní problém, atmosférické modelování

Při detekci radioaktivity v ovzduší je zásadním úkolem určení lokace úniku a jeho časového průběhu. Zatímco lokace bývá velmi často známa, časový průběh a celkové množství uniklé látky bývá většinou známo jen jako hrubý odhad nebo vůbec. Hlavním úkolem navrhované práce je určení časového průběhu úniku z dostupných terénních měření. Toho lze dosáhnout optimalizací mezi naměřenými hodnotami a mezi numerickými výsledky atmosférického modelu šíření.

Bibliography: 

1. M. Hutchinson, H. Oh, W. Chen, A review of source term estimation methods for atmospheric dispersion events using static or mobile sensors. Information Fusion 36, 2017, 130-148.
2. P. Seibert and A. Frank, Source-receptor matrix calculation with a Lagrangian particle dispersion model in backward mode. Atmospheric Chemistry and Physics 4(1), 2004, 51–63.
3. V. Šmídl, A. Quinn, The Variational Bayes Method in Signal Processing. Springer, 2006.
4. O. Tichý, V. Šmídl, R. Hofman, K. Šindelářová, M. Hýža, A. Stohl, Bayesian inverse modeling and source location of an unintended I-131 release in Europe in the fall of 2011, Atmospheric Chemistry and Physics 17(20), 2017, 12677-12696.
5. O. Tichý, V. Šmídl, N. Evangeliou, Source term determination with elastic plume bias correction, Journal of Hazardous Materials vol.425 (2022), 127776.

2022-09-15 10:16

BSc. Topic: Approximate Recursive Bayesian Estimation with Forgetting (Kárný)

Type of Work: 
bachelor
Affiliation/Phone: 
ÚTIA AV ČR, v.v.i., oddělení AS, 266052274
Supervisor: 
Kárný

Recursive estimation of model parameters is a key part of adaptive systems predicting or influencing their complex random environment. Mostly, the models do not allow the desired exact Bayesian estimation and therefore it is necessary to implement them approximately. In this case, it is necessary to forget the invalid knowledge, because otherwise the behavior of the estimated model and the modeled environment often diverge from each other. The choice of data-dependent forgetting rate is still an open problem despite decades of ongoing research on this issue.

Tasks: 

1. Learn about Bayesian parameter estimation.
2. Learn about the principle of minimum expected relative entropy.
3. Propose an approximate Bayesian model parameter estimation based on the Taylor expansion of the logarithm of the model.
4. Use Bayesian predictors using a priori and posterior probabilities of parameters to estimate confidence in them. This will serve for the design of a new a priori distribution using the principle of minimum expected entropy.
5. Program the result and, in case of logistic regression, compare its quality with a suitable standard.

Bibliography: 

Recommended literature (parts selected after agreement with the supervisor)

1. V. Peterka, Bayesian System Identification, in P. Eykhoff "Trends and Progress in System Identification", Pergamon Press, Oxford, 239-304, 1981.
2. R. Kulhavy, M.B. Zarrop, On a General Concept of Forgetting, International Journal of Control 58(4), 905-924, 1993.
3. M. Kárný, Minimum Expected Relative Entropy Principle, Proc. of the 18th European Control Conference, 35-40, 2020.
4. M. Kárný, Approximate Bayesian recursive estimation, Inf. Sciences 285(1), 100-111 2014.

2022-09-15 10:16

BSc. Topic: Sequential Monte-Carlo Estimation Seen as Learning on Variable Grid (Kárný)

Type of Work: 
bachelor
Affiliation/Phone: 
ÚTIA AV ČR, v.v.i., oddělení AS, 266052274
Supervisor: 
Kárný

Recursive estimation of model parameters is a key part of adaptive systems predicting or influencing their complex random environment. Most models do not allow us to use the desired exact Bayesian estimation. Therefore it is necessary to implement them approximately. Monte Carlo procedures allow this, but their efficiency is not great.

Tasks: 

1. Learn about Bayesian parameter estimation.
2. Familiarize yourself with the concept of recursive Bayesian estimation.
3. Learn about assigning a priori probability to hypotheses.
4. Design an estimation algorithm that at each step: i) generates a new sample of parameters; ii) assigns a priori probability to all samples; iii) correct those probabilities with the Bayes relation; iv) excludes the least suitable parameter sample.
5. Program the result for a simple useful model and compare the quality of your algorithm with a suitable standard.

Bibliography: 

Recommended literature (parts selected after agreement with the supervisor)

1. V. Peterka, Bayesian System Identification, in P. Eykhoff "Trends and Progress in System Identification", Pergamon Press, Oxford, 239-304, 1981.
2. A. Doucet, V.B. Tadic, Parameter estimation in general state-space models using particle methods, Annals of the institute of Statistical Mathematics,55(2),409-422,2003.
3. A. Doucet, M. Johansen, A tutorial on particle filtering and smoothing: 15 years later, In: Handbook of Nonlinear Filtering, Oxford Univ. Press, UK, 2011.
4. M. Kárný, On Assigning Probabilities to New Hypotheses, Pattern Recognition Letters, 150(1), 170-175, 2021.

2022-09-15 10:16

BSc./Mgr. Topic: Numerical methods in the design of control of industrial robots (Belda)

Type of Work: 
bachelor
diploma
Affiliation/Phone: 
UTIA CAS, dept. of AS, 26605 2310
Supervisor: 
Belda
Keywords: 
Model predictive control, numerical integration methods, industrial robots, nonlinear dynamic models

The topic of the bachelor/diploma thesis is focused on the selection and implementation of a suitable numerical method for the predictive control algorithm, which uses a default physical nonlinear model describing the robot's dynamics. Numerical methods should be used in the construction of prediction equations that express the dependence of future planned outputs on unknown calculated inputs (control actions) and also for control using internal simulation in its design. Algorithms will be created in the MATLAB language with a connection to the C language.

Bibliography: 

[1] Rektorys, K. et al.: Survey of Applied Mathematics, Available Edition.
[2] Belda, K.: Nonlinear Model Predictive Control Algorithms for Industrial Articulated Robots. Informatics in Control, Automation and Robotics. Lecture Notes in Electrical Engin., 613. Springer, 2020, pp. 230-251.
[3] Belda, K., Záda, V.: Predictive Control for Offset-Free Motion of Industrial Articulated Robots. Proc. 22nd IEEE Int. Conf. Methods and Models in Automation and Robotics. West Pomeranian University of Technology, Szczecin, Poland, 2017, pp. 688-693.
[4] Other literature according to the specific focus of the thesis.

Note: 
The topic is suitable for FNSPE CTU, by agreement for FEE, FME CTU and other universities.
2022-09-15 10:17

BSc./Mgr. Topic: Mathematical modelling of motion of industrial robots (Belda)

Type of Work: 
bachelor
diploma
Affiliation/Phone: 
UTIA CAS, dept. of AS, 26605 2310
Supervisor: 
Belda
Keywords: 
Parametric models, analytic geometry, time parameterisation, industrial robots, kinematic quantities

The theme of the bachelor/diploma thesis is focused on the motion modelling of industrial articulated robots. Modelling will deal with the investigation of parametric models of both planar and spatial curves containing the so-called geometric parameter. This parameter determining the position on the given curve will be used in the design of a suitable time parameterization of the robot's motion. Its output will be the time dependencies of partial coordinates of a specific coordinate system and their respective derivatives.

Bibliography: 

[1] Rektorys, K. et al.: Survey of Applied Mathematics, Available Edition.
[2] Belda, K.: Smoothing and Time Parametrization of Motion Trajectories for Industrial Machining and Motion Control. Proc. of the 16th Int. Conf. on Informatics in Control, Automation and Robotics. ICINCO 2019. Prague, The Czech Republic 2019, Vol. 2, pp. 229-236.
[3] Záda, V., Belda, K.: Structure Design and Solution of Kinematics of Robot Manipulator for 3D Concrete Printing. IEEE Trans. Automation Science and Engineering. IEEE, New York, 2022, 1-12 pp.
[4] Other literature according to the specific focus of the thesis.

Note: 
The topic is suitable for FNSPE CTU, by agreement for FEE, FME CTU and other universities.
2022-09-15 10:17

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