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…
Implementation Filters and Delay-Budget Instability in Coupled Replicator--Mutator Dynamics
Alexander Omelchenko
We model an adaptive contest in which two antagonistically coupled populations continually reallocate effort among competing methods, but decisions are not fielded instantly. Each…
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…