Phase Transitions in a Particle Model for the Self-Adaptive Response to Cancer Dynamics

TL;DR

This paper provides a rigorous probabilistic analysis of a particle model describing the immune system's adaptive response to cancer, confirming phase transitions and quantifying information gain over time.

Contribution

It confirms the predicted phase transition in immune learning and introduces a method to compute information acquisition in the model.

Findings

Confirmed sharp phase transition in immune response.

Quantified information gained by immune system.

Used time-reversal techniques for analysis.

Abstract

In this paper, we present a probabilistic analysis of a dynamical particle model for the self-adaptive immune response to cancer, as proposed by the first author in a previous work. The model is motivated by the interplay between immune surveillance and cancer evolution. We rigorously confirm the sharp phase transition in immune system learning predicted in the original work. Additionally, we compute the expected amount of information acquired by the immune system about cancer cells over time. Our analysis relies on time-reversal techniques.