Madi Yerlanov

Preprint · March 26, 2026 In populations with community structure, the formation of consensus requires both alignment within and diffusion of beliefs across groups, processes that evolve on distinct time scales. How do modularity, asymmetry, and polarization shape this process? We ... Link to item Cite

A study of general reaction-advection-diffusion equations describing dynamics between target, partaker, and guardian

Preprint · October 17, 2025 This paper introduces a reaction-advection-diffusion system that models interactions among three actors: a target, a partaker, and a guardian. The framework is versatile, capturing phenomena ranging from the emergence and movement of crime hotspots in urba ... Link to item Cite

Global Bifurcations and Pattern Formation in Target-Offender-Guardian Crime Models

Preprint · September 15, 2025 We study a reaction-advection-diffusion model of a target-offender-guardian system designed to capture interactions between urban crime and policing. Using Crandall-Rabinowitz bifurcation theory and spectral analysis, we establish rigorous conditions for b ... Link to item Cite

Algebraic sets defined by the commutator matrix

Preprint · June 24, 2020 In this paper we study algebraic sets of pairs of matrices defined by the vanishing of either the diagonal of their commutator matrix or its anti-diagonal. We find a system of parameters for the coordinate rings of these two sets and their intersection and ... Link to item Cite