5 papers
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…
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_{…
Exhaustive Generation of Genus-One Knot and Link Diagrams via Maps on the Torus
Alexander Omelchenko
We present an algorithmic framework for the exhaustive generation and tabulation of knot and link diagrams on the thickened torus T^2 x I, based on the theory of maps on surfaces.…
Threshold Dynamics of Voter Radicalization on the Probability Simplex
Alexander Omelchenko
We analyse two coupled ODE models of political competition on invariant probability simplices with a conserved electorate. The baseline three-group model tracks left-radical, centr…
Unsensed enumeration of cubic unicellular maps on orientable and non-orientable surfaces
Alexander Omelchenko, Igor Labutin
We enumerate cubic (3-regular) unicellular maps on closed surfaces up to all homeomorphisms. Using the orbifold approach, we reduce the unsensed enumeration to explicit counts of q…