Title: Nonlinear Perception in Usability: A Threshold-Based Framework for Cybersecurity HMIs

Presented by Oliver MacDonald, Computing PhD student, Computational Math Science and Engineering emphasis

Abstract

As cybersecurity systems grow increasingly complex, the usability of human-machine interfaces (HMIs) becomes essential to operational security. Despite advances in visualization and automation, there remains no quantitative model describing how cognitive and perceptual thresholds shape HMI usability. This paper presents two mathematically defined metrics (I_L and Xi) that quantify cognitive complexity and perceptual stability.

A Python-based evaluation system validated these metrics in an empirical study (24 participants, 590 balance and 186 cognitive-load trials). Results revealed nonlinear perceptual behaviors consistent with cognitive thresholds, with inflection points near Xi ~ 0.14-0.29 and I_L ~ 0.43-0.45 that mark distinct perceptual zones (balanced->transitional->unbalanced and manageable->overloaded). These findings indicate that usability behaves not as a smooth continuum but as a system of discrete perceptual regions, where small design changes can cause abrupt shifts in workload and stability. By formalizing usability through quantitative, threshold-based metrics, this framework bridges heuristic and computational evaluation, advancing the design of cybersecurity HMIs that align with human perceptual limits and the human-centered vision of Industry 5.0.

Advisor: Dr. Hoda Mehrpouyan

Committee Members: Dr. Max Taylor, Dr. Sindhu Reddy Kalathur Gopal

External Examiner: Dr. Arvin Farid