Graph rewriting and causality for rule-based modeling
## Graph rewriting and causality for rule-based modeling

The class will present the recent technique of 'rule-based modeling', with emphasis on its use in modeling of intra-cellular signaling pathways, including a thorough treatment of the mathematical foundations of the approach in terms of graph rewriting.
Rule-based modeling is a recent development that allows for compact description of complex systems -- most notably for (bio-)chemical reactions -- as collections of rewriting rules that describe how the system may evolve over time. Unlike traditional reaction-based descriptions, rules do not necessarily act upon fully-specified molecules, instead referring only to those aspects pertinent to the reaction mechanisms at play. In addition to providing more generic, compact descriptions, this also enables completely new analysis techniques based on notions of causality familiar from concurrency theory.

### Pre-requisites

There are no formal pre-requisites although an acquantaince with very basic probability theory would be a help, as would a passing familiarity with transition systems and rewriting. I will use Python for my programming examples.
### TPs

There will be some practical classes with programming and/or modeling exercises. These would require a laptop computer with Python (or your language of choice) installed. We will use the rule-based modeling language Kappa which can be used online or installed locally.
### Evaluation

Evaluation will be based on a programming exercise, a modeling project and a written exam.
### Outline

In a little more detail, the class will include:
- an introduction to (stochastic) chemical kinetics: Markov jump processes and stochastic simulation
- the rule-based approach: the Kappa language
- the rule-based approach: mathematical formulation and implicit state simulation
- causal analysis of rule-based models
- hierarchical and higher-order graph rewriting
- graph-based knowledge representation for rule-based models