Advanced Process Control
Comprehensive exploration of advanced process control techniques, covering linearization, modeling, stability analysis, stochastic processes, and control design methods for complex industrial systems.
Risk Modelling and Survival Analysis - Actuarial Science
Explore stochastic processes, Markov chains, risk modeling, and survival analysis in actuarial science. Learn key concepts and tackle past exam questions using R for practical applications.
Set-Valued Martingales and Backward Stochastic Differential Equations - Lecture
Explore set-valued backward stochastic differential equations and martingale representation, connecting dynamic risk measures to advanced probability theory concepts.
Why Are Cell Populations Maintained via Multiple Intermediate Compartments?
Explore the efficiency of multiple intermediate compartments in maintaining cell populations, minimizing clonality, and optimizing division rounds from progenitors to product cells.
The Laws of Life, Time and Chance
Explore the intersection of physics and biology, uncovering mathematical frameworks for understanding life, time, and probability. Discover how chance governs cellular behavior and impacts complex biological phenomena.
Stochastic Learning Dynamics and Generalization in Neural Networks
Explore stochastic learning dynamics and generalization in neural networks, uncovering key insights into their behavior and performance in various applications.
Financial Derivatives and Risk Management
Comprehensive exploration of financial derivatives, risk management, and option pricing, covering forwards, futures, hedging strategies, portfolio theory, interest rates, and stochastic processes.
Advanced Probability Theory
The course introduces the concept of probability through Kolmogorov’s Axioms. It develops the concept of probability density function, cumulative distribution function, and introduces the concept of a random variable.
From Ronald Ross to ChatGPT: The Birth and Strange Life of the Random Walk
Explore the fascinating history of random walks in mathematics, from mosquito control to AI, and their impact on various fields including physics, finance, and theology.
Dependent Stopping Times and Application to Credit Risk Theory - BQE Lecture Series
Explore dependent stopping times in credit risk theory, covering Cox construction, instantaneous default, and systemic risk measures in financial markets.
Signals and Systems II
Comprehensive exploration of advanced signal processing concepts, including probability theory, random variables, stochastic processes, and spectral analysis for electrical engineering applications.
Continuum Limit of Moran Birth-Death and Death-Birth Process - Fisher-Waves Speeds
Explore the continuum limit of Moran birth-death and death-birth processes, focusing on Fisher-wave speeds in this 28-minute lecture by Kamran Kaveh from Harvard University. Delve into advanced concepts in mathematical oncology and computational medicine…
Mathematical Modeling of Blood Cancer and Premalignancy
Explore a 33-minute lecture on mathematical modeling of blood cancer and premalignancy presented by Morten Andersen and Jordan Snyder from Roskilde University. Delivered on October 3, 2024, as part of the Ecology and Evolution of Cancer series and the Th…
Estimating Clonal Dynamics Using Coalescent Theory and Branching Processes
Explore a 39-minute lecture on estimating clonal dynamics through coalescent theory and branching processes, delivered by Kit Curtius from the University of California, San Diego. Delve into the intersection of mathematics and oncology as part of the Fie…
Entropy and Curvature of Markov Chains on Metric Spaces
Explore the Peres-Tetali conjecture and its implications for Markov chains in this 57-minute lecture by Justin Salez from the Hausdorff Center for Mathematics. Delve into the relationship between contraction in Wasserstein distance and relative entropy f…
Genetic Composition of Supercritical Branching Populations Under Power Law Mutation Rate
Explore genetic composition in supercritical branching populations, focusing on power law mutation rates and their implications for evolutionary dynamics.
Branching Processes for Cascades on Networks
Explore branching processes and their application to network cascades, gaining insights into complex system dynamics and interdisciplinary physics concepts.
Conditioned Exit Measures of Non-Local Branching Processes
Explore conditioned exit measures of non-local branching processes in this mathematical conference talk by Emma Horton at CIRM.
Accessibility Percolation for the Rough Mount Fuji Model
Explore accessibility percolation in the rough Mount Fuji model through a mathematical conference talk by Matt Roberts at CIRM.
On the Extinction Time and Maximal Displacement of Critical Branching Killed Levy Processes
Explore critical branching killed Levy processes, focusing on extinction time and maximal displacement in this mathematical analysis.
Geometric Representations of Far Future Predictions in Deep Neural Networks - Next-Token Training
Explore universal geometric representations of far-future beliefs in deep neural networks trained on next-token prediction, uncovering fractal and quantum-like structures embedded in network activations.