The Thinker
Formula: Nash Equilibrium
Equation: uᵢ(sᵢ*, s₋ᵢ*) ≥ uᵢ(sᵢ, s₋ᵢ*)
The Mediator
Formula: Shannon Entropy
Equation: H(X) = -∑ p(x) log<0xE1><0xB5><0x87> p(x)
The Architect
Formula: Fourier Transform
Equation: f̂(ξ) = ∫ f(x) e^(-i2πξx) dx
The Commander
Formula: PID Controller
Equation: u(t) = Kₚe(t) + Kᵢ∫e(τ)dτ + K<0xE1><0xB5><0xAB>de(t)/dt
The Debater
Formula: Q-Learning Update Rule
Equation: Q(s,a) ← Q(s,a) + α[r + γmax<0xE2><0x82><0x90>Q(s′,a′) - Q(s,a)]
The Advocate
Formula: Kalman Filter
Predict: x̂<0xE2><0x82><0x96|k−1> = F<0xE2><0x82><0x96>x̂<0xE2><0x82><0x96−1|k−1>
Update: x̂<0xE2><0x82><0x96|k> = x̂<0xE2><0x82><0x96|k−1> + K<0xE2><0x82><0x96>(z<0xE2><0x82><0x96> - H<0xE2><0x82><0x96>x̂<0xE2><0x82><0x96|k−1>)
The Giver
Formula: Prospect Theory
Equation: V = ∑ π(pᵢ) v(xᵢ)
The Champion
Formula: Kuramoto Model
Equation: dθᵢ/dt = ωᵢ + (K/N) ∑ sin(θ<0xE2><0x82><0x9F> - θᵢ)
The Inspector
Formula: Bayes' Theorem
Equation: P(A|B) = [P(B|A)P(A)] / P(B)
The Protector
Formula: Hooke's Law
Equation: F = -kx
The Director
Formula: Simple Linear Regression
Equation: Y = β₀ + β₁X + ϵ
The Caregiver
Formula: PID Controller (Integral)
Equation: Kᵢ ∫ e(τ) dτ
The Crafter
Formula: PID Controller (Derivative)
Equation: K<0xE1><0xB5><0xAB> de(t)/dt
The Artist
Formula: Wavelet Transform
Equation: ψ<0xE2><0x82><0x90>,<0xE2><0x82><0x85>(t) = (1/√|a|) ψ((t-b)/a)
The Persuader
Formula: Signal Detection (d')
Equation: d′ = z(Hit Rate) - z(False Alarm Rate)
The Performer
Formula: Signal Detection (c)
Equation: c = -0.5 * [z(Hit Rate) + z(False Alarm Rate)]