Long-range Correlations in Polymer Science

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Linear Regression: Estimation and Inference

Explores linear regression estimation, linearity assumptions, and statistical tests in the context of model comparison.

Quantifying Statistical Dependence: Covariance and Correlation

Explores covariance, correlation, and mutual information in quantifying statistical dependence between random variables.

Propagation of Uncertainty: Estimation and Distribution

Discusses estimation and propagation of uncertainty in random variables and the importance of managing uncertainty in statistical analysis.

Probability and Stochastic Processes: Fundamentals and Applications

Discusses the fundamentals of probability and stochastic processes, focusing on random variables, their properties, and applications in statistical signal processing.

Flory Approximation

Explores the Flory approximation for analyzing polymer chain behavior and the impact of excluded volume on chain conformation.

Statistical Independence and Correlation: Understanding Gauss Functions

Explores statistical independence, correlation, Gauss functions, likelihood estimation, and Gaussian Mixture Models for clustering.

Signal Processing Fundamentals

Explores signal processing fundamentals, including discrete time signals, spectral factorization, and stochastic processes.

Graphs and Probabilities

Explores the connection between graphs and probabilities, emphasizing modular and super modular probabilities and correlation properties.

Polymer Models: Basic Observables

Introduces basic observables and simple models in polymer science, emphasizing the importance of reproducible measurements and discussing the concept of one-dimensional polymers.

Elements of Statistics: Estimation & Distributions

Covers fundamental statistics concepts, including estimation theory, distributions, and the law of large numbers, with practical examples.