Stochastic Dynamics in Systems Biology Lecture Notes

Lecture Notes on Logical Theory & Completeness

This course has studied a number of logics, first-order logic FOL in Lecture 2, differential dynamic logic dL [Pla08, Pla10a, Pla12c, Pla12b] in Lecture 3 and Lecture 4 and following, differential temporal dynamic logic dTL [Pla07, Pla10a, Chapter 4] in Lecture 16 and 17, as well as differential game logic dGL [Pla13] since Lecture 22. There are other logics for cyber-physical systems that have...

Evolutionary game theory and population dynamics

We begin these lecture notes by a crash course in game theory. In particular, we introduce a fundamental notion of a Nash equilibrium. To address the problem of the equilibrium selection in games with multiple equilibria, we review basic properties of the deterministic replicator dynamics and stochastic dynamics of finite populations. We show the almost global asymptotic stability of an efficie...

Polynomial Dynamical Systems in Systems Biology

Research in systems biology focuses on the prediction and control of the behavior of biochemical networks through the use of mathematical models that accurately capture the responses of the network to certain types of perturbations. The construction of models based on the observations of these responses, referred to as reverse engineering, is an important step in discovering the structure and d...

Rare Events and Heavy Tails in Stochastic Systems

This is a set of lecture notes on large deviations and heavy tails in stochastic systems. After an introduction, a short and biased review on heavy-tailed distribution is given. Applications are mostly concerned with stochastic networks, and cover single-server queues, regenerative processes, and fluid models.

Lecture Notes on Stochastic Hybrid Systems