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Introduction to graph theory | 1. Linear graphs: L(N) and L(N,S) 2. Reptation: SAW and RW 3. Minimal spanning tree 4. Bond percolation |
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Examples of complex networks | 1. Self-similarity, 2. Tress, 3. Mountains, rough surfaces, 4. Sierpinski triangle: fractal dimension, 5. Fractal Silica, 6. Tree-like structures in Biology, 7. DNA, 8. Percolation, 9. Finance, 10. Internet |
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Mobile networks | 1. Human mobile networks: crouds, 2. Mobile networks in Nature, 3. MST: the Dijkstra algorithm, 4. Examples of MST, 5. Further applications of mobile networks, 6. Forest fires. |
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DNA | 1. DNA, 2. Chromosomes, 3. Transcription of DNA, 4. DNA Nanotechnology, 5. DNA in the nucleus of cell, 6. RNA secondary strcutures, 7. Translation: Proteins formation, 8. Models of proteins. |
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DNA | 1. DNA, 2. Chromosomes, 3. Transcription of DNA, 4. DNA Nanotechnology, 5. DNA in the nucleus of cell, 6. RNA secondary strcutures, 7. Translation: Proteins formation, 8. Models of proteins. |
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Exercises discussion. Protein models | 1. Lattice dynamics for protein folding, 2. Lattice protein models, 3. Clusjatering coefficient, 4. Betweenness. |
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Theory of networks | 1. Random graphs, 2. Node degree distribution, 3. Scale-free networks. 4. Examples. |
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Scale-free network models | 1. Modeling scale-free networks with a given exponent, 2. Random models with given degree distribution, 3. Optimization algorithms. |
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Fractal dimension and convergence networks. | 1. Regular and fractal structures, 2. Random trees fractal dimensions, 3. Scale-free networks and clustering coefficients. 4. Networks on regular lattices: percolation. 5. Scale-free networks in biology. 6. Modules, 7. Human eye, 8. Alveoli. |
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Student projects discussion | 1. Network feature dependency, 2. Graph theory for anomalous traffic detection, 3. Protein-protein networks, 4. Mobility patterns in human networks, 5. Improved routing algorithm for random sensors, 6. Complex networks for Software engineering, 7. Graph theory for cancer therapy. |
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Generic model of scale-free networks | 1. Barabasi model: analytical solution, 2. Random nodes in space: optimization model, 3. Shrotest paths structures. 4. Continuum percolation: Theory and models. |
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Stochastic processes and Levy flights. | 1. Random walks and time series, 2. Central limit theorem, 3. Levy distribution, 4. Memory: short and long range. 5. Correlations: Hurst exponent. |
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Levy flights statistics | 1. Modeling Levy walks, 2. Distribution functions, 3. Correlations and stationarity, 4. Air temperature correlations in the atmosphere, 5. Correlation function and Hurst exponent. |
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Fractal landscapes and profiles | 1. Self-similarity and self-affinity, 2. Fractal decomposition for self-affine profiles, 3. Random fractal surfaces, 4. Temperature fluctuations and correlations, 5. Wavelets. |
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Fractional derivates | 1. Concept of fractional derivative, 2. Fractional random walks: Hurst exponent, 3. Distribution functions |
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Student projects discussion: Mid-term presentation. | (see also 9) | ![]() |
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Stochastic models with long range memory | 1. Autoregressive models, 2. Power-law distributions, 3. Financial time series: modeling stock markets, 4. Non-stationarity issues, 5. Fractional random walk model for stocks. 6. Handwriting process: long range memory versus short range behavior. |
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Complex random networks | 1. Complex system of chemical reactions, 2. Image denoising method based on wavelets, 3. Polymers in solution and attachment on a surface, 4. Glass sponges and multifunctional hybrid materials. |
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