Probabilistic Description of Turbulence

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Covers advanced probability concepts, including random variables and expected value calculation.

Covers phase space, ensembles of particles, probability distributions, and probability density functions.

Explores diffusion models in generative modeling, covering probability estimation, data generation, and model evaluation.

Covers the characterization of stochastic processes, focusing on their mathematical foundations and real-world applications.

Delves into homoclinic orbits, bifurcations, and limit cycles in nonlinear dynamics.

Explores air pollution analysis using wind data, probability distributions, and trajectory models for air quality assessment.

Explores the design of engineering works for floods, focusing on 100-year flood determination and the collapse of levees during extreme events.

Explores equilibrium and stability of a vertical metronome system with springs.

Explores sampling a probability distribution and structure functions in statistical analysis.

Discusses conditional entropy and its role in information theory and data compression.