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On human-centred security: A new systems model based on modes and mode transitions

Edwin J Beggs, John V Tucker, Victoria Wang

TL;DR

The paper presents a human-centred security framework built on modes and mode transitions, formalised with abstract and concrete simplicial complexes to enable geometric visualisation of system beliefs and decisions. It formalises how monitoring data, objectives, and capabilities generate beliefs that drive mode transitions, offering a continuous, explainable view of system behavior via $\Delta_{\mathcal{C}}$ constructions and belief functions. The framework is demonstrated through triage, cyber architectures, and multi-agency critical incident responses such as the UK Gold-Silver-Bronze structure, illustrating benefits like concurrency, independence, continuity, and transparency. This approach advances security analysis and design in human contexts and points toward software tools and rigorous scenario theory as future directions, with broad potential for scenario-based planning across domains.

Abstract

We propose an abstract conceptual framework for analysing complex security systems using a new notion of modes and mode transitions. A mode is an independent component of a system with its own objectives, monitoring data, algorithms, and scope and limits. The behaviour of a mode, including its transitions to other modes, is determined by interpretations of the mode's monitoring data in the light of its objectives and capabilities -- these interpretations we call beliefs. We formalise the conceptual framework mathematically and, by quantifying and visualising beliefs in higher-dimensional geometric spaces, we argue our models may help both design, analyse and explain systems. The mathematical models are based on simplicial complexes.

On human-centred security: A new systems model based on modes and mode transitions

TL;DR

The paper presents a human-centred security framework built on modes and mode transitions, formalised with abstract and concrete simplicial complexes to enable geometric visualisation of system beliefs and decisions. It formalises how monitoring data, objectives, and capabilities generate beliefs that drive mode transitions, offering a continuous, explainable view of system behavior via constructions and belief functions. The framework is demonstrated through triage, cyber architectures, and multi-agency critical incident responses such as the UK Gold-Silver-Bronze structure, illustrating benefits like concurrency, independence, continuity, and transparency. This approach advances security analysis and design in human contexts and points toward software tools and rigorous scenario theory as future directions, with broad potential for scenario-based planning across domains.

Abstract

We propose an abstract conceptual framework for analysing complex security systems using a new notion of modes and mode transitions. A mode is an independent component of a system with its own objectives, monitoring data, algorithms, and scope and limits. The behaviour of a mode, including its transitions to other modes, is determined by interpretations of the mode's monitoring data in the light of its objectives and capabilities -- these interpretations we call beliefs. We formalise the conceptual framework mathematically and, by quantifying and visualising beliefs in higher-dimensional geometric spaces, we argue our models may help both design, analyse and explain systems. The mathematical models are based on simplicial complexes.
Paper Structure (25 sections, 2 theorems, 12 equations, 9 figures)

This paper contains 25 sections, 2 theorems, 12 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Tools for thinking about security systems
  3. Structure of this paper
  4. Acknowledgments
  5. Human-centred security systems
  6. Responding to security incidents
  7. Critical incidents and the Gold-Silver-Bronze command structure of the UK
  8. Modes and their visualisation
  9. What is a mode?
  10. Principles for designing modes
  11. Simple security examples
  12. Geometric intuitions
  13. Illustrative security scenarios and systems
  14. Triage: Persons of interest
  15. Cyber architectures and ecosystems
  16. ...and 10 more sections

Key Result

Proposition 6

To every abstract simplicial complex $(\mathcal{M},\mathcal{C})$ (as in Definition absc) is associated its standard realisation $\Delta_\mathcal{C} \subset \mathbb{R}^\mathcal{M}$, as a simplicial complex. The simplex spanned by $X\in \mathcal{C}$ is Further, a map of abstract simplicial complexes $\Psi:(\mathcal{M},\mathcal{C})\to (\mathcal{M}',\mathcal{C}')$ can be extended to a map of their re

Figures (9)

  • Figure 1: Visualising a mode transition for a trigger mechanism and triage for emergency services
  • Figure 2: Initial assessment for potential security risks
  • Figure 3: The axes for the space of evidence for the investigation
  • Figure 4: The subsets for neither, concern, opportunity and begin respectively
  • Figure 5: Adding a shadow mode $\alpha'$
  • ...and 4 more figures

Theorems & Definitions (10)

  • definition 1
  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Proposition 6
  • Definition 7
  • definition 2
  • lemma 1