Committee:

Topics:

1. Astronomical observations in the visible band. Photometry and photometric systems in astrophysics. Types of telescopes, their construction, and mounts.
2. Spectroscopy in astrophysics. Observations in the non-visible spectral bands. Space observatories and their most important results.
3. Stellar physics: the Lane-Emden equation and the polytrope model. The energy production in stars (the p-p chain and the CNO cycle). The HR diagram. The stellar evolution on the HR diagram.
4. The endpoints of stellar evolution: nuclear burning in high mass stars, stellar nucleosynthesis, supernovae.
5. Types and classification of galaxies. The structure of the various types of galaxies and their components. The spiral structure of galaxies.
6. Galaxy clusters and superclusters in the Universe. The Abell and the Zwicky catalogues.
7. The large scale structure of the Universe. Observations and surveys aimed at exploring the large scale structure (CfA slice, pencil beam observations, SDSS) and their results: the statistical description of the large scale structure.
8. The hierarchical model of galaxy formation and evolution. The physics of quasars, observational results.
9. Fundamentals of cosmology: Friedmann equations, the expanding universe, Big Bang, and the cosmological parameters.
10. Observational pillars supporting the standard Big Bang theory, questions left open by the model, and cosmic inflation as a possible solution.
11. Precision cosmological measurements and their results: the power spectrum of CMB fluctuations, the large-scale structure of the Universe, and SNIa experiments.
12. Active galactic nuclei (AGN) and the unification model: the properties of the different AGN classes (Seyfert galaxies, quasars, blazars, radiogalaxies), the evidence for supermassive black holes, the unification model.
13. Gamma-ray bursts (GRBs): the detection of various kinds of GRBs, the fireball model, GRB afterglows.
14. The astrophysics of the hot intra-cluster medium (ICM): the properties of the ICM, cooling flows and AGN feedback, the observational techniques of the ICM (X-ray spectroscopy and the Sunyaev-Zeldovich effect)
15. The mathematics and physics of general relativity.
16. Correspondence principle, Einstein equations, their solutions, the conservation laws from the point of view of general relativity.
17. Observations and experiments that provide the foundations and support for general relativity.
18. The theory of gravitational waves: general relativistic background, the production of GWs, GW interaction with an interferometer.
19. The detection of gravitational waves: principles of interferometric detection, noise sources, detections with multiple detectors.
20. Gravitational waves in astrophysics: types of GWs, fundamentals of signal searches, detections achieved, multi-messenger astronomy.

Committee:

Topics A:

1. The principles of the quantum mechanical many-body problem (approximate methods: variational principles and methods, perturbation theory; identical particles, Pauli principle, Slater determinants; spin wave functions, Coulomb- and exchange integrals)
2. Hartree-Fock approximation and electron correlation (mean-field, closed and open shell systems, Koopmans-theorem: ionization an electron affinity, Roothan method, electron correlation, configuration interaction, electron pair methods)
3. Atoms with several electrons (Helium, screening, periodic system, spin-orbit interaction, Hund’s rules, multiplets and configurations, coarse, fine and hyperfine level structures, Grotrian diagram)
4. Theoretical descriptions of molecules (Born-Oppenheimer approximation, potential energy surface (PES): bindings, oscillations, dissociation, predissociation, virial theorem, Hellmann-Feynman theorem, hydrogen molecule ion, hydrogen molecule, VB method, MO method)
5. Diatomic and polyatomic molecules (diatomic molecules: homonuclear and heteronuclear diatomics, symmetries, configurations, number of bonds, para-magnetism, oxygen molecule, correlations diagram, rule of avoided level crossings; polyatomic molecules: symmetries, water molecule, carbon dioxide, localized and delocalized molecular orbits, hybridization, single pair, planar molecules, s- and p-bonds, benzene molecule)
6. Interactions of atoms, interactions of molecules, interactions with external electric and magnetic fields (Lennard-Jones interaction, van der Waals interactions, dipol interaction, hydrogen bond, the structure of the water molecule, Stark-effect, normal and anomalous Zeeman-effects, electric polarization, magnetic susceptibility, diamagnetic shielding, g-factor, magnetic resonance)
7. Principles of atomic and molecular spectroscopy (electron transitions in atoms and molecules, symmetries, selection rules, UV-VIS spectroscopy, charge transfer, chromophore, ORD-CD, fluorescence, phosphorescence, Franck-Condon principle, photoelectron spectroscopy)
8. Experimental methods for atomic and molecular structures (UV, VIS, IR and microwave spectroscopies, Raman-, resonant Raman-spectroscopy, ORD-CD, NMR, ESR, Mössbauer-spectroscopy, mass-spectroscopy, photoelectron spectroscopy, X-ray, electron microscopy, STM, AFM)

Topics B:

1. Calculations of electron structures for atoms and molecules (traditional quantum chemistry, density functinal theory, ab initio and semi-empirical methods, occupation number representation, one and two particle operators)
2. Macromolecules (structures and statistical properties of flexible polymers with chains, polymers with conjugated carbon chains, linear chain: one dimensional instabilities, effects of doping on the electric, magnetic and optical properties, biological macromolecules: non-informational (e.g., polysaccharide) and informational (e.g., protein) macromolecules, secondary and tertiary structure, DNS, genetic code)
3. Complex molecules (theory of atomic spectra, spin-orbit interaction, hyperfine interaction, crystal field theory, ligand field theory, vibronic interactions, Jahn-Teller instability)
4. Carbon nanostructures (the discovery of C60, historical overview, isolated cage like molecules, fullerenes in liquid and solid phases, doped fullerenes, fullerites, transport properties, optical properties, polymers, endohedral compounds, carbon nanotubes)
5. Semiclassical dynamics (WKB approximation, Bohr-Sommerfeld quantization, Maslov index, Berry-Tabor conjecture, Gutzwiller’s trace formula, Poisson and Wigner level spacing statistics)
6. Principles of mesoscopic systems (2D electrongas, open and closed channels, the role of magnetic field, Landauer-Büttiker formula, relationship between S-matrix and Green’s function, Aharonov-Bohm effect, weak localization, universal conductivity fluctuation)
7. Many-body theory at zero temperature (Green’s functions, physical quantities that can be expressed by Green’s function, Feynman diagrams, elementary excitations, applications, the method of canonical transformations for Bose-gas and superconductors)
8. Many-body theory at finite temperature (Green’s functions, the thermodynamic potential expressed by the Green’s function, Matsubara frequencies, Feynman-diagrams, applications)
9. New experiments in quantum mechanics (neutron interference, ion- and atom traps, micromaser, atomoptics, two-photon interference)
10. Quantum phenomena (decoherence, quantum jumps, quantum Zenon-effect, quantum non-demolition, Berry-phases)
11. Statistical quantum optics (quantum theory of electro-magnetic fields, quasi-probability distribution functions, non-classical states of light, photon statistics, optical parametric processes, quantum theory of damping: Langevin-equation, atom-field interaction: Jaynes-Cummings model, methods of quantum information transfer: discrete and continuous teleportation.)
12. Trapped atomic systems (non-interacting bosons in harmonic potentials, finite size effects in non-interacting systems, Gross-Pitaevskii equation, collapse for bosons with negative scattering length, Thomas-Fermi approximation for bosons, elementary excitations, Bogoliubov-equations, hydrodynamical approach, fermions in traps, BCS-BEC crossover)

Committee:

Topics:

1. Ground-state properties, and electromagnetic and weak interactions of nuclei
2. Nuclear forces (nucleon-nucleon interaction, phase shift analysis, three-body forces)
3. Nuclear models (liquid drop model, Fermi gas model, shell model, unified model)
4. Nuclear scattering theory (two- and three-body scattering, multichannel scattering, polology, scattering-theoretic description of nuclear reactions)
5. Bound and resonant states in few-nucleon systems, effective interaction
6. Nuclear reactions (medium-energy neutron capture reactions, astrophysically important reactions)
7. Production and reactions of radioactive nuclear beams
8. The quark-quark interaction potential in perturbation theory and beyond (asymptotic freedom, bag model of quark confinement)
9. Field-theoretic descriptions of nuclear matter and its equation of state (Johnson-Teller model, Walecka model of symmetric- and neutron matter)
10. Effective theories of chiral symmetry and its spontaneous breaking (Nambu--Jona-Lasinio, Gell-Mann--Levy and the nonlinear sigma model)
11. Phases of nuclear matter, phase transitions, and the signatures of the quark-gluon plasma
12. Modelling methods of medium-energy heavy-ion reactions (VUU, BUU, (r)QMD, hydro, initial states, fragmentation)
13. Mechanisms of particle production in heavy-ion reactions (resonances, mesons, subthreshold production, direct reactions)
14. The basic principles of particle detection (interaction of particles and matter, tracking of charged particles, calorimetry)
15. Complex detector systems (types of particle detectors, event reconstruction, particle identification, the structure of a modern high-energy detector system, neutrino experiments)
16. Particle accelerators and beams (fixed target, colliding beams, generation of electron-, proton-, antiproton-, pion-, muon-, and neutrino beams, the LHC accelerator complex)

Committee:

Information for the defense: 15 minutes are available for the defense of the dissertation, as well as an additional 5 minutes for answering the questions of the committee and the audience. Using a projectable presentation (PowerPoint, PDF) is recommended, which can be uploaded to the notebook provided for the presentation in advance.

Topics:

1. The cell as a basic unit of living system (IB)
2. Fundamentals and biological aspects of thermodynamics and statistical physics (BP, SPB)
3. Structure and function of proteins (BP, BET, MM, IB)
4. Structure and function of DNA (RNA), the genetic code, transcription, translation (BP, IB)
5. Gene technology (BP, IB)
6. Classical and molecular genetics (IB)
7. Biological membranes (BP, MM, IB)
8. Bioenergetics: anaerobic and aerobic processes, chemiosmosis (BP, IB)
9. Bioenergetics: photosynthesis (BP)
10. Membrane potential, ion transport (BP, IB)
11. Neurons and synapses, nerve signalling, Hodgkin-Huxley theory (BP, IB)
12. Spectroscopic methods in biology (BET, IB)
13. Biophysical experimental methods (BP, BET, IB)
14. Biophysics of perception (BP, IB)
15. Cell communication, signal transduction, cell movement (QM, IB)
16. Collective behavior (synchronization, networks, motion) (BP, SPB)

The topics are based on the following subjects*:

BP:  Biophysics I. and II.
BET: Biophysical Experimental Techniques
QM:  Quantitative Models in Cell and Developmental Biology
SFB: Statistical Physics of Biological Systems
MM:  Macromolecules
IB:  Introduction to Biology 1., 2., 3.

* Those who have not taken any of these subjects, please inform the committee before the exam.

Committee:

Topics:

1. Bonding in solid states (van der Walls, ionic, covalent, and  metallic bonding)
2. Crystalline structures, experimental determination of crystalline structures (basic structures, symmetry properties, direct and reciprocal lattice, X-ray-, electron-, and neutron-diffraction)
3. Disordered systems ( alloys, amorphous materials, liquid crystals, quasicrystals)
4. Lattice vibrations (classic and quantum description, acoustic and optic  banches, expeeimental determination of phonon spectra)
5. Thermal properties of crystalline materials (heat capacity of phonon gas, anharmonicity, thermal expansion, heat conductivity by phonons), Superfluidity.
6. Electron states in periodic systems (Bloch and Wannier functions, band structure and its relation to the symmetry of the crystal, experimental determination of band structure, metals, semiconductors, insulators)
7. Pure and doped semiconductors,  (Fermi energy, donor and acceptor levels,  excitons). Schottky barrier, p-n transition, transistor.
8. Semiclassical description of the dynamic of electrons. Exp erimental determination of Fermi surface (motion of electron in electric and magnetic fields, cyclotron resonance, size effects, magneto-acoustic effect)
9. Electron is strong magnetic field (Landau levels, de Haas-van Alphen effect, quantum Hall effect)
10. Electron-phonon interaction, (limits of adiabatic decoupling, obtaining the electron- phonon interaction, polaron, Kohn anomaly).
11. Theory of conduction (Boltzmann equation, relaxation time approximation and its limitations, transport coefficients in metals and semiconductor, scattering of impurities,  phonons and electrons, scattering of electron on magnetic impurities, Kondo effect).
12. Interaction of solid materials with photons and neutrons (optical properties, Brillouin and Raman scattering, neutron scattering). Experimental methods for studying the properties of solid materials (Mössbauer effect, NMR, ESR, positron annihilation). 
13. The phenomenological theory of superconductivity (thermodynamics of superconductors, I. II. type superconductors, Ginzburg-Landau theory, superconducting vortex)
14. BCS theory of superconductivity, tunnel effect, Josephson effect
15. Many electron systems, electron-electron interaction (Hartree-Fock approximation, correlations, dielectric constant, screening, plasmons, density function theory).      
16. Basic properties of magnetism (Hund’s rules, splitting of atomic levels in magnetic field,  dia and  paramagnetism, paramagnetic resonance, Pauli paramagnetism, exchange interaction,  direct exchange, super exchange, RKKY exchange)
17. Ordered magnetic materials (ferro and antiferromagnets, mean field theory, spin waves, magnetic anisotropy, magnetic domains) disordered magnets (spin glasses)
18. Low-dimensional systems (magnetic models in 1 and 2D, super-lattice,   magnetic coupling through and non-magnetic layer, 1D electron system, Luttinger liquid)  
19. Defects in crystals, and their role in material properties, Point defects (equilibrium concentration, mixing and formation entropy and enthalpy, evolution of point defects), dislocations (topological properties, continuum description, force acting on a dislocation, partial dislocations), internal surfaces (grain boundary, phase boundary, energy of the boundaries, nanostructural materials).
20. Diffusion in solid states (macroscopic and microscopic descriptions, concentration dependence of diffusion constant, Kirkendall-effect, Darken equations)
21. Mechanical properties (plasticity, work hardening, hardening by solid solution and precipitates)
22. Solid solutions (thermodynamic of multicomponent systems, quasi chemical theory,  ideal and ordered solid solutions, factors determining the solubility limit)
23. Phase diagram (equilibrium and non equilibrium phase diagrams, calculating the phase diagram from free energy), solidification (homogeneous and heterogeneous   nucleation, crystal growing, cleaning by zone melting, non equilibrium solidification)
24. Phase transformations in solid phase (precipitation, spinodal decomposition, phase transformations without diffusion, martensitic transformation)
25. Ceramics and composite materials (chemical structure of ceramics, properties, properties of composites, how to select materials for composites)

Vizsgabizottság:

Információ a védéshez: A diplomamunka védésére 15 perc áll rendelkezésre, valamint további 5 perc a bizottság és a hallgatóság kérdéseinek megválaszolására. A védéshez javasoljuk kivetíthető prezentáció (PowerPoint, PDF) használatát, melyet érdemes a védések megkezdése előtt feltölteni a vetítésre biztosított notebookra.

Tételsor:

A kötelezően választható tárgyak közül a hallgató csak azokból kap kérdést, amelyeket a tanulmányai során elvégzett.

Anatómia

1. Az emberi szív szerkezete és fejlődési rendellenességei
2. Az emberi légzőszervrendszer morfológiai felépítése
3. Az ember vázizomrendszerének általános jellemzői, a törzs (mellkas, a has és a hát) izmai és működésük

Élettan

4. Testfolyadékok és homeosztázis
5. A szív és a keringés működése
6. Idegi működések

Sugárvédelem

7. A sugárvédelem hármas alapelve
8. Dózisfogalmak, a lakossági- és foglalkozási korlátok
9. A három legnagyobb, ember által okozott nukleáris szennyezés

MR-Fizika I.

10. Mágneses rezonancia képalkotás (mágneses momentumok mágneses térben, kvantummechanikai és klasszikus leírás)
11. Rezonancia, gerjesztés, MR jel
12. Jelakvizíciós eljárások (FID, echo, spektroszkópia, képalkotó eljárások, Fourier, back-projection)

MR-Fizika II.

13. Szekvenciák (Spin echo, Fast spin echo, Gradiens echo 2D, -3D, EPI)
14. RF gerjesztések, akvizíciós technikák (Phased Array, Parallel Imaging)
15. Kontraszt-mechanizmusok és alkalmazásaik, fiziológiai folyamatok detektálása (áramlás, diffúzió, perfúzió)

Ionizáló sugárzások a gyógyításban

16. Teleterápia (folyamata, gyorsítók, kobaltágyú, RTG-terápia, dózis-profilok, mélydózis-görbék, kollimáció, besugárzási mezők, ékek, verifikáció)
17. Sugárterápiás besugárzás-tervezés (ICRU ajánlások, 2D/3D-s tervezés, céltérfogat, védendő szervek, DVH, minőségi indexek, konformális besugárzási technika)
18. Brachyterápia (folyamata, típusai, izotópok, besugárzó készülékek, dózis-teljesítmény, dózis-előírási technikák, optimalizálási módszerek, különböző lokalizációk besugárzása, IGABT)

Sugárterápiás fizika

19. Speciális teleterápiás eljárások és technikák, sugárvédelem és biztonság
20. Brachyterápiás besugárzástervezés és képvezérlés (dozimetriai rendszerek, 2-, 3- és 4D-s BT, TG-43 dózisszámítási formalizmus és modell-alapú algoritmusok, optimalizálás és kiértékelés)
21. Sugárbiológia, prosztata, nőgyógyászati, emlő és egyéb daganatok brachyterápiája

Kvantitatív modellek a sejt- és fejlődésbiológiában

22. Sztochasztikus reakciókinetika (Gillespie-algoritmus)
23. Transzkripciós regulációt leíró egyenletek: transzkripció, transzláció, visszacsatolások
24. Többsejtű szerveződés biofizikai modelljei (felületi feszültség analógia, sejtmozgás, mint pozitívan visszacsatolt sztochasztikus rendszer)

Sejtszignalizációs hálózatok kvantitatív analízise

25. Jelátviteli hálózatok matematikai modellezése. Kinázok, foszfatázok, transzkripciós faktorok, mRNS-ek és promóterállapotok leírása reakcióegyenlet rendszerekkel. Fixpont analízis, Gillespie-féle stochasztikus szimuláció
26. Robosztusság és visszacsatolások. Baktériumok kemotaxis rendszere és molekuláris kapcsolók. PID szabályzók

Fejlődésbiológiai mechanizmusok kvantitatív modelljei

27. Többsejtű rendszerek matematikai modelljei. Sokrészecske, Potts és folytonos modellek.
28. Diffúzív morfogén faktorok vezérelte mintázatképződés: Turing mechanizmus, gerjeszthető közegek

Preklinikai modellek a daganatkutatásban

29. A főbb ellenanyag alapú vizsgálati módszerek (immunoblot, IP, IF, IHC, ELISA, FACS) egy-egy konkrét daganatkutatási példával
30. Egy-egy konkrét in vivo modellt, amely alkalmas (I) a klasszikus kemoterápia, (II) a célzott terápia és (III) az immunterápia kísérletes vizsgálatára
31. A xenograft tumormodellekben használható képalkotási módszerek összehasonlítása

Committee:

Topics:

1. Basic principles of particle detection, tracking, calorimetry.
2. Accelerators and beams (fix target, colliding-beam, e, p beams).
3. Complex detector systems, hardware, software, presentation of a modern detector system. 
4. Description of some important experiments (P, CP, J/Ψ).
5. Geometrical symmetry groups; rotation group, Poincaré group, reflection symmetries.
6. The quantum field theory of free fields, symmetries.
7. S matrix in quantum field theory, functional integrals, Feynman graphs.
8. Gauge theories.
9. The renormalization of QED and QCD.
10. Electron-photon interaction (processes)
11. The interaction of electromagnetic and ionizing radiation with condensed matter, penetrating power and particle showers.
12. The basics of the strong interaction: conserved quantities, properties of particles and resonances.
13. Internal symmetry groups: SU(2), SU(3) and the particle multiplets, the basics of the quark model.
14. The dynamics of the strong interactions, the basics of QCD.
15. The dynamics of strong interactions at low energies, chiral symmetry breaking and the effective Lagrangian based description.
16. Basics of high energy physics, renormalization group equations and their application, running coupling constant, deep inelastic scattering, jet physics.
17. Classification of the weak processes, conserved quantum numbers and selection rules, the theory of β decay, V-A coupling.
18. Elements of current algebra: conserved vector current, PCAC, Cabbibo theory, GIM mechanism.
19. Fundamentals of the electroweak theory: spontaneous symmetry breaking, Goldstone bosons, Higgs mechanism, masses and couplings of the W ans Z bosons, lepton and quark multiplets.

General relativity branch

The above first 4 topics are replaced by:

1. Topological and metric properties of spacetime, Einstein equations and their action principle derivation.
2. Exact solutions (Minkowski, De Sitter, Robertson-Walker), cosmological models (Schwarzschild, Reisner-Nordström, Kerr, Gödel, Taub-Nut), Penrose diagrams.
3. Causal structure, space and time orientability, causal curves, achronal boundaries, Cauchy surfaces, causal boundary of spacetime.
4. Gravitational collapse, black holes, Schwarzschild black hole, remnant black holes, Hawking radiation, thermodynamics, final state, experimental data.

Committee:

Topics:

1. Foundation of statistical physics and thermodynamics.
2. Ideal Fermi and Bose gases, occupation number representation.
3. Manybody problem, perturbation calculus, Feynman diagrams.
4. Interacting fermion and boson systems.
5. Elementary excitations. Superfluidity.
6. Transport processes.
7. First-order and continuous phase transitions.
8. Critical phenomena, scale hypothesis and renormalization.
9. Response and correlation functions, fluctuation-dissipation theorem.
10. Fundamentals of statistical physical simulations.
11. Non-equilibrium and stochastic processes.
12. Fractal geometry, fractal measures and fractal growth.
13. Transport in nanosystems.
14. Structure and dynamics of complex networks.

Committee:

Topics: 

1. Many-body systems (molecular dynamics, Hartree-Fock, collision integral Vlasov / Boltzmann equation, Vlasov (Boltzmann) -Uhling-Uhlenberg equation)
2. Transport processes (Boltzmann equation, diffusion, thermal conductivity)
3. Generation of random graphs, properties (small-world, clustering, robustness)
4. First order and continuous phase transitions (eg. Ising model)
5. Response and correlation functions, fluctuation-dissipation theorem
6. Stochastic processes (Kauffman network, spin glasses, Markov chain)
7. Fundamentals of statistical physical simulations and the Monte Carlo method
8. Dynamic systems, chaotic behavior (based on Complex and Adaptive Dynamical Systems).
9. Data analysis: linear and nonlinear regression (demonstrated on a model)
10. Data analysis: bootstrap models
11. Operation of TCP networks
12. Data analysis: ARCH, GARCH processes
13. Numerical methods ((adaptive) Runge-Kutta, relaxation, etc.)
14. Visualization methods

Vizsgabizottság: 

Tételsor:

1. Az akusztika alapjai (a hullámegyenlet általánosságban, eredete különböző mechanikai rendszerekben, megoldásai 1 és 3 dimenzióban, transzverzális és longitudinális hullámok, vízfelszíni hullámok sekély és mély folyadékokban, a hang fizikája)
2. Elektromágneses hullámok környezetünkben (fizikai alapok, elektromágneses spektrum, a Napból érkező sugárzás, elektroszmog)
3. A Coriolis-erő és környezeti jelentősége (definíció, megjelenése a lokális koordinátarendszerben, béta-hatás, Eötvös-effektus, Rossby-szám)
4. A geosztrofikus áramlás tulajdonságai (dinamikai egyensúly, homogén folyadék belsejében, sekély folyadék felszínén, rétegzett folyadék belsejében)
5. Laboratóriumi jelenségek rétegzett folyadékokban (lineáris hullámok kétrétegű folyadék belsejében, Kelvin–Helmholtz-instabilitás, holt víz effektus, baroklin instabilitás)
6. Radioaktív izotópok a környezetünkben (uránsor, tóriumsor, cézium szennyezések, radioaktív egyensúly, gamma spektroszkópia)
7. Radon mozgása a környezetünkben (a radon forrása, radonexhaláció, radon eljutása az emberhez, egészségügyi hatásai, radon detektorok)
8. Ismertesse a megújuló energiák felhasználásának alapjait! Elemezze a) energia előállítás gazdaságossága b) környezeti hatás szempontjából!
9. Ismertesse a nukleáris fűtőanyagciklust és térjen ki azoknak az aggályoknak a fizikai hátterére, amelyeket a társadalom aggályosnak tarthat!
10. Populációdinamika korcsoportstruktúrával (Leslie mátrix karakterisztikus egyenlete). A domináns sajátérték közelítő megoldása (ha a növekedési ráta közel 1, a stabil koreloszlás alakja, reproduktív érték, demográfiai paraméterek és jelenlétük)
11. Kétfajos préda-predátor típusú ökológiai modellek (a klasszikus Lotka–Volterra-modell dinamikai viselkedése, globális és lokális analízis), a Holling II. és a Holling III funkcionális válasz, préda-predátor modell dinamikája Holling II funkcionális válasszal. Hiszterézis jelenség a predációs nyomás változásával (túllengetés és fázisátmenet)
12. Környezeti fényszennyezés (alapfogalmak, poláros fényszennyezés, detektálásának alapfogalmai, kísérleti bizonyítékok, ökológiai következmények, a táplálkozási láncban bekövetkező hatások, fényszennyezés megelőzése)

Committee:

Topics:

1. Measurement data and measurement error - Errors and noise, their sources. Statistical and systematic error. Stochastic modelling of error. Data modelling - The basic problem of function fitting. Kernel function estimation.
2. Bootstrap methods. The maximum likelihood method. Hypothesis testing. Extreme statistics. Post hoc analysis. Regression. Independence test. Exact tests. Bayesian methods.
3. Random number generation. Numerical integration, Newton-type formulas, Gauss-type formulas. Monte-Carlo method, Markov chain Monte-Carlo. Hierarchical Bayesian networks.
4. Simulation of thermodynamic systems, Ising model, Metropolis algorithm. 
5. Fractal dimension, self-similar mathematical fractals, naturally occurring fractals, cellular automata. 
6. Numerical analysis of differential equations, Euler's method, Runge-Kutta method, stability, partial differential equations. 
7. Chaotic behaviour of dynamical systems. Population dynamics models, Strange attractor. Chaotic mappings, bifurcation, Lyapunov exponent. Quantum chaotic systems, distributions associated with eigenvalues of random matrices. 
8. Molecular dynamics, Verlet and velocity-Verlet algorithms. Determination of thermodynamic quantities and relaxation.
9. Signal processing and time series analysis - Fourier methods, FFT, spectra and spectrogram, transfer and window functions, Wiener filter. Correlation functions, Wiener-Hinchin theorem and power spectrum. Convolution and deconvolution. 
10. Machine learning - Prediction and classification methods. Supervised and unsupervised learning. The training set, validation and overfitting. K-means, Support Vector Machine, Random Forest, k-NN method.
11. Neural networks - fully connected neural nets, convolutional neural nets, backpropagation, optimizers (SGD, Adam), batch normalisation, autoencoders, word2vec.
12. Dimensionality reduction methods - Statistical properties of high dimensional data. 
13. Relational databases - the relational data model, logical and physical operators (seek, scan and variants of joins, aggregation), data storage models (row store, column store), indexes (clustered index, non-clustered index), the B-tree, keys and constraints, transactions. Query optimization. Data loading process. 
14. Multidimensional data, representation of geographic and spatial data. Basic search problems: interval search, spatial search, nearest neighbours. Spatial indices, spatial filling curves (Z-index, Peano-Hilbert-index), kD-tree, R-tree, role of bit coding. Spatial celling methods: Delaunay triangulation, Voronoi tessellation.
15. Image processing - Digital representation of images, colour models. Interpolation, convolution and deconvolution methods, homomorphic filtering. Edge, corner and speckle detection. Morphological analysis, feature extraction. Perspective correction, noise filtering methods.
16. Visualisation - Techniques for two and three dimensional visualisation of scientific data, representation of scalar, vector and tensor data. Use of colours, notation, Gestalt laws, Static and interactive visualisation techniques, Spatial data visualisation, Volumetric and level surface visualisation.