Lectures related to Modeling Gene Expression

Covers the convergence of fixed point methods for nonlinear equations, including global and local convergence theorems and the order of convergence.

Explores stability properties and fixed points in discrete time solutions.

Explores scaling and renormalization in statistical mechanics, emphasizing critical points and invariant properties.

Covers the Picard method for solving nonlinear equations using fixed point iteration.

Covers the basics of information theory, entropy, and fixed points in graph colorings and the Ising model.

Explores the Banach Fixed Point Theorem, showing the uniqueness of fixed points in contraction mappings.

Explores the convergence of fixed point methods and the implications of different convergence rates.

Explores the numerical analysis of nonlinear equations, focusing on convergence criteria and methods like bisection and fixed-point iteration.

Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.

Explores the Newton method for non-linear equations, discussing convergence criteria and stopping conditions.

Covers the topic of nonlinear equations and the fixed point method.

Explores bistability in gene regulation, analyzing fixed points, bifurcation diagrams, and hysteresis behavior in gene expression.

Focuses on fixed points in graph theory and their implications in algorithms and analysis.

Covers rotations around fixed points and spherical coordinates, discussing cinematic moments and angular velocity.

Explores bistability in genetic networks, analyzing fixed points and stability, phase portraits, and experimental implementation.

Explores growth models for populations and gene regulation analysis.

Covers the movement of a grinding wheel on a non-slip bearing and the physics of a rotating thin disc.

Covers the stability of discrete time periodic solutions and their properties.

Covers the Newton method for finding zeros of functions using data interpolation.

Explores nonlinear systems through phase portraits in 2D, focusing on vector fields, isoclines, and trajectories.