# Topological Run-time Monitoring for Complex Systems

## TL;DR

This paper presents a novel data-driven run-time monitoring system using Topological Data Analysis to analyze complex systems' behavior, exemplified by a simulated human immune system, enabling real-time property verification.

## Contribution

Introduces Persistent Entropy Automaton (PEA), a topological data analysis-based monitor for complex systems, capable of real-time invariant mining and temporal property verification.

## Key findings

- Successfully analyzed simulated immune system data
- Revealed temporal properties related to immunization memory
- Demonstrated feasibility of topological monitoring approach

## Abstract

In this paper we introduce a new data-driven run-time monitoring system for analysing the behaviour of time evolving complex systems. The monitor controls the evolution of the whole system but it is mined from the data produced by its single interacting components. Relevant behavioural changes happening at the component level and that are responsible for global system evolution are captured by the monitor. Topological Data Analysis is used for shaping and analysing the data for mining an automaton mimicking the global system dynamics, the so-called Persistent Entropy Automaton (PEA). A slight augmented PEA, the monitor, can be used to run current or past executions of the system to mine temporal invariants, for instance through statistical reasoning. Such invariants can be formulated as properties of a temporal logic, e.g. bounded LTL, that can be run-time model-checked. We have performed a feasibility assessment of the PEA and the associated monitoring system by analysing a simulated biological complex system, namely the human immune system. The application of the monitor to simulated traces reveals temporal properties that should be satisfied in order to reach immunization memory.