Lectures related to Linear Response: Self-Consistent Transfer Operators

Fluctuation-dissipation relations for reversible diffusions

Covers linear response, steady states, Girsanov transforms, and covariance limits in reversible diffusions.

Linear Request Problem: Rigorous Results

Delves into the linear request problem, infinitesimal perturbations, transport plans, and the main theorem from 2018.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.

Mapping Functions and Surjections

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Linear Response in High-Dimensional Systems

Explores linear response in high-dimensional systems, covering theory, practice, and implications of non-hyperbolicity and inhomogeneous subsystems.

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Analog Filters: General

Explores analog filters, linear phase filters, rational transfer functions, and filter design compromises.

Markov Chain Monte Carlo

Covers the Markov Chain Monte Carlo method and the Metropolis-Hastings algorithm for generating samples from a target probability distribution.

Fluctuation Dissipation Theorem

Explores the Fluctuation Dissipation Theorem, covering topics like the Langevin equation and force correlations in high-temperature equilibrium.

Modeling Dynamic Systems: Definitions and Examples

Covers the modeling of dynamic systems, including definitions, examples, and linearization processes for easier analysis.

RIF Filters: Characteristics and Synthesis

Explores the characteristics and synthesis of RIF filters, including windowing operations and linear phase filters.

Signals & Systems II: Discrete Linear Systems

Explores categorization of signals, linear systems, LID, convolution, and impulse response.

Optimal Linear Response: Stochastic Dynamical Systems

Explores optimal linear response for stochastic dynamical systems, addressing perturbations and mixing rate optimization.

Dynamical Response Functions in Neuroscience

By Tatjana Tchumatchenko explores dynamical response functions in neuroscience, emphasizing the role of linear response functions in understanding neural activity.

Ridge Regression: Penalised Least Squares

Explores Ridge Regression for handling multicollinearity and the LASSO method for model selection.

Complex Fourier Space Analysis

Covers the analysis of instability in complex Fourier space and its application to mixing layers.

Kelvin's Wake and Instability Theory

Explores Kelvin's wake, instability theory, and fluid dynamics analysis in various flow scenarios.

Theoreus Chain Role: Lipschitz Sit

Covers the Theoreus Chain Role for Lipschitz functions and its practical applications.

Signals & Systems I: Filter Equations and Poles

Explores rational transfer functions, filter equations, poles, zeros, and impulse response in signal processing.

Dynamics on homogeneous spaces and interactions with number theory

Explores dynamics on homogeneous spaces, Khintchine theorem, Sullivan's logarithm law, and interactions with number theory.