• Study for the weekly research seminar
• Mar. 2, 2021 ~ Feb. 1, 2022

• Neural Networks, Logistic Regression, Gradient Descent

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• Lengyel-Epstein model (1D, 2D)

| Presentation | Code |

• Convex optimization, Newton-method, Lagrange multiplier
• Rosenbrock function

| Presentation | Code |

• Wavelet Transform and Windowed Fourier transform, Orthonormal wavelet bases : Multiresolution analysis
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• Hilbert Space and Fourier Analysis
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• Continuous windowed FT, operators, and Mathematical theorem related to wavelet transformation
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[1] Daubechies, Ingrid. Ten lectures on wavelets. Society for industrial and applied mathematics, 1992.
[2] Harris, Terri Joan. "HILBERT SPACES AND FOURIER SERIES." (2015).

• Markov chain Monte-Carlo (MCMC), MCMC Analysis of Diffusion model, Kinetic/Dynamic Monte-Carlo

| Presentation | Code |

• Mini-batch gradient descent, exponentially weighted averages, bias correction, momentum, RMSprop, Adam

| Presentation | Code |

• Correlation coefficient, Minimal spanning tree (MST), Subdominant ultrametric distance matrix

| Presentation | Code |

• MST, four moments, central vertex, vertex degree, power law, multi-step survival ratio

| Presentation | Code |