7 papers
Below-threshold Bistability and Implementation Lag in a Simplex Model of Radical Vote-Share Dynamics
Alexander Omelchenko
We study a nonautonomous compartmental model on the probability simplex for radical vote-share dynamics under delayed policy implementation. The model distinguishes a target regime…
Affine weighted Motzkin paths and the differential kernel method
Alexander Omelchenko
We study Motzkin paths whose up-, level-, and down-step weights are affine functions of the height: alpha_k = A k + alpha_0, gamma_k = B k + gamma_0, beta_k = C k + beta_0. Let w_{…
Mean Time to Remediate Is Not a Fielding Model: A Cadence Audit for Enterprise Vulnerability Management
Alexander Omelchenko
Enterprise security teams commonly summarize remediation through mean time to remediate (MTTR), SLA compliance, dwell time, or detection delay. These metrics are useful, but they c…
Same Mean Lag, Different Stability: Periodic Implementation in Adaptive Competition
Alexander Omelchenko
Can two implementation processes with the same mean lag give opposite stability predictions for adaptive competition? We show that they can, and quantify the discrepancy. The motiv…
Crisis, Disengagement, and Structural Realignment: A Threshold Model of Radical-Party Support
Alexander Omelchenko
When does a crisis-induced surge in radical-party support fade away, and when does it become a durable realignment? We address this in a mathematical sociology threshold model on a…
Threshold-Safe Shock Absorption in a Compartmental Voter-Flow Model:\ A Conservative Impulse-Control Benchmark
Alexander Omelchenko
We formulate a deterministic threshold-safety problem for a reduced compartmental voter-flow model. An exogenous load enters an alienation reservoir; between releases the reservoir…
Balanced affine Motzkin paths: Pearson geometry and global endpoint asymptotics
Alexander Omelchenko
We study endpoint distributions of balanced affine weighted Motzkin paths. In the balanced case, the generating-function equation has Pearson-type characteristic geometry. We show…