-
March Madness Without Monte Carlo
The incidence matrix of an NCAA bracket Petri net connects ODE, Monte Carlo, and analytical methods — and makes simulation redundant. A closed-form formula derived from the bracket topology replaces 150,000 stochastic transitions with 256 exact configurations.
-
Paper: Incidence Reduction via Petri Net ODE Equilibrium
A draft paper formalizing incidence reduction — extracting exact strategic values from game topologies — validated on tic-tac-toe, poker, Connect Four, and Hex.
-
The Incidence Reduction
ODE steady-state values with uniform rates reveal integer structure — incidence degrees to terminal transitions — giving a reverse-engineering technique for rate constants.
-
Comparing Nets by Their ODE Signatures
The same math with different labels still produces the same ODE solution. In tic-tac-toe, we see it directly — each board position is a place, and the heatmap is the solution projected onto the grid.
-
Enzyme Kinetics: Michaelis-Menten from Three Transitions
Four places, three transitions, and mass-action kinetics produce the classic Michaelis-Menten saturation curve automatically—no equations required.
-
Coffee Shop Model
Resource modeling with Petri nets — weighted arcs encode recipes, conservation laws guarantee integrity, and ODE simulation predicts when you'll run out of cups.
-
Sudoku Petri-Net Model
Modeling Sudoku as a Petri net with ODE simulation—constraint satisfaction through token flow.
-
Declarative Differential Models (DDM)
A modeling approach where system behavior is described declaratively and encoded directly in differential equations.
-
Knapsack Model
Using Declarative Differential Models (DDM) to explore the knapsack problem with Petri nets and ODEs.