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Lecture
Response Theory and Phase Transitions
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Signals and Systems: Introduction
Introduces the fundamental concepts of Signals and Systems course, emphasizing practical applications of system behavior analysis.
Stochastic Calculus: Lecture 1
Covers the essentials of probability, algebras, and conditional probability, including the Borel o-algebra and Poisson processes.
Linear Response and Complex Diffusivity
Explores martingale-based linear response, complex diffusivity, and Nyquist relation in stochastic systems with time-dependent perturbation.
State-space Modeling
Introduces the state-space approach to modeling dynamical systems and its utility for high-speed solution of differential equations and computer algorithms.
Stability of Collisionless Systems
Explores the stability of collisionless systems, covering entropy, weak perturbations, Jeans instability, and Landau damping.
Linear Systems in Sinusoidal Regime
Explores linear systems in sinusoidal regime, discussing frequency response, transfer functions, stability, quadripoles, and Bode diagrams.
Stability Analysis: Linear Systems
Explores stability analysis in linear systems, emphasizing eigenvalues, eigenvectors, and stable manifolds.
Multivariable Control: Gaussian Processes and Linear Systems
Explores Gaussian processes, linear systems, transformations, and noise properties in multivariable control applications.
Nonlinear Dynamics: Homoclinic Orbits and Bifurcations
Delves into homoclinic orbits, bifurcations, and limit cycles in nonlinear dynamics.
Parameter Estimation of SDEs with Linear Response Theory
Explores parameter estimation of SDEs using Linear Response Theory and covers challenges, examples, algorithms, and convergence.