Rényi entropy 1961 H_α = (1/(1-α))·log₂(Σp_i^α) bit. Shannon Hartley collision min-entropy. SISSA Trieste, IIT Genoa,...
Kullback-Leibler 1951 divergence calc D_KL(P||Q)=Σp·log₂(p/q) bit. Cross-entropy ML, VAE, t-SNE. SISSA Trieste 1978, ...
Calculate Lyapunov exponent lambda logistic map x_n+1 = r*x_n*(1-x_n) chaos theory + bifurcation cascade + Feigenbaum...
Calculate lognormal distribution PDF, CDF, mean, median, mode, variance, skewness. ln X ~ N(mu, sigma^2). Galton-McAl...
Compute Hill equation Y=L^n/(Kd^n+L^n) cooperative binding ligand-receptor. Archibald Hill 1910 Cambridge Nobel 1922....
Compute Monod bacterial growth kinetics mu=mu_max*S/(Ks+S). Jacques Monod Pasteur Paris 1941 Nobel Medicine 1965. mu_...
Compute Kermack-McKendrick SIR epidemic model 1927: dS/dt=-βSI/N, dI/dt=βSI/N-γI, dR/dt=γI. R0 basic reproduction. He...
Compute Lotka-Volterra predator-prey equation dx/dt=αx-βxy, dy/dt=δxy-γy. Equilibrium x*=γ/δ y*=α/β. Period T=2π/√(αγ...
Compute Benford's law P(d)=log10(1+1/d) leading significant digit. P(1)=30.10%, P(9)=4.58%. History Newcomb 1881 Benf...
Compute birthday paradox probability n people sharing same birthday. Exact formula P=1-prod((365-i)/365). Approximati...
Compute Easter date Gregorian and Orthodox Julian with Gauss 1800 algorithm. Formula a=Y mod 19, b=Y mod 4, c=Y mod 7...
Compute Julian Day Number JDN MJD J2000.0 from Gregorian or Julian date. Scaliger 1583 formula: JDN = D + floor((153m...