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STABLE AND UNSTABLE ARMS
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age-grade system arms race assumptions average number axioms behavior Chapter column compute constant constraints convex set critical point curve defined definition denote derivative determine deterministic model differential equation dual problem dx/dt dy/dt elements entries epidemic example Exercise expected value expenditures experiment feasibility set feasible solution formulation function gamble given graph increase inequality infectives initial integration linear programming linear programming problem logistic logistic curve Lotka Markov chain Markov process mathematical model measure negative nonnegative object obtain operating room optimal orbit outcomes pair plane possible Pr(X predator-prey predictions prefers primal problem probabilistic model probability procedure Proof of Theorem random variable real numbers real-world recovery room relation result Richardson model satisfy sciences Show simple simplex method simulation social solve species stability step stochastic stochastic matrix stochastic process student subset Suppose surgical tableau theory tion transition matrix utility vector voting mechanism winning zero