The surprisal equals the sum over the constraints and is a measure of the deviation from the balanced state. These deviations are ranked on the degree of deviation from the balance state and ordered on the most to least influential to the system. This ranking is provided through the use of Lagrange multipliers. The most important constraint and usually the constraint sufficient to characterize a system exhibit the largest Lagrange multiplier. The multiplier for constraint α α is denoted above as λ λ α α ; larger multipliers identify more influential constraints. The event variable G α α ( n ) is the value of the constraint α α for the event n . Using the method of Lagrange multipliers requires that the prior probability P 0 ( n ) and the nature of the constraints be experimentally identified. A numerical algorithm for determining Lagrange multipliers has been introduced by Agmon et al. Recently, singular value decomposition and principal component analysis of the surprisal was utilized to identify constraints on biological systems, extending surprisal analysis to better understanding biological dynamics as shown in the figure.