Lectures related to Probabilistic Description of Turbulence

Introduces data science topics, evaluation methods, and course organization for the semester.

Probability Distributions in Environmental Studies

Explores probability distributions for random variables in air pollution and climate change studies, covering descriptive and inferential statistics.

Dynamics of Simple Pendulum and Lorenz Equations

Explores the dynamics of a simple pendulum and the intriguing Lorenz equations, highlighting sensitivity to initial conditions and the transition to chaos.

Coordinate Systems: Applications and Transformations

Explores coordinate systems, including polar and curvilinear coordinates, and their transformations.

Block Pulled by a Spring

Explores the dynamics of a block pulled by a spring under various conditions.

Maximum Likelihood: Inference and Model Comparison

Explores maximum likelihood inference, model selection, and comparing models using likelihood ratios.

Random Walks: Return Probabilities in Lattice Dimensions

Covers random walks on a lattice, focusing on return probabilities and their dependence on dimensionality.

Maximum Likelihood Inference

Explores maximum likelihood inference, comparing models based on likelihood ratios and demonstrating with a coin example.

Logistic Regression: Probability Modeling and Optimization

Explores logistic regression for binary classification, covering probability modeling, optimization methods, and regularization techniques.

Natural Language Generation: Decoding Techniques and Training Challenges

Covers decoding methods and training challenges in natural language generation.

Random Variables: Expected Value

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

Statistical Thermodynamics: Phase Space and Probability Distributions

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

Diffusion Models in Generative Modeling

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

Characterization of Stochastic Processes: Theory and Applications

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

Nonlinear Dynamics: Homoclinic Orbits and Bifurcations

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

Air Pollution Analysis

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

Hydrologic and Hydraulic Design

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

Vertical Metronome: Equilibrium and Stability

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

Sampling a Probability Distribution

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

Conditional Entropy and Information Theory Concepts

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