Matrix exponentiation is an integration method for all kinetic schemes with any degree of complexity.It can be used for the integration of kinetic schemes that are irreversible, reversible, second order, and reactions of such complexity that algebraic integration is impossible.It is naturally suited to the integration of sets of differential equations that characterize first- and pseudo-first-order chem. reaction networks since it assumes exact exponential functions as the results.The results of the application of a second-order fit to the data suggest the method is also capable of integrating second-order processes.The results show that matrix exponentiation is more than precise enough for such integrations.This is in marked contrast to numerical integration methods such as Runge-Kutta or Gear where the function is approximated.Last but not least, the demonstrated mechanism selectivity is a powerful tool in discrimination among various mechanisms.The simplicity, elegance, precision, and mechanism discrimination of matrix exponentiation make it the method of choice for the integration sets of differential equations sets for diverse mechanisms.

01 Jan 2004·Methods in EnzymologyQ4 · BIOLOGY

Large Reduction in Singular Value Calculation Time Using Savitzsky–Golay Data Precompression

Q4 · BIOLOGY

Article

Author: Matheson, I B C

A data precompression method that markedly reduces the calculation time for data sets with many wavelengths is presented.The new PCSVD procedure is many hundreds of times faster than the original GRSVD procedure on real data arrays of typical sizes.There is no loss of accuracy on real data sets.

01 Jan 2004·Methods in EnzymologyQ4 · BIOLOGY

A Practical Approach to Interpretation of Singular Value Decomposition Results

Q4 · BIOLOGY

Article

Author: Matheson, I. B. C. ; de Sa, R. J.

Several ways of displaying singular value decomposition (SVD) results are described, and a practical, largely graphic, approach to their interpretation is proposed.To illustrate this approach, the application of SVD to the data concerning the reaction of tyrosine phenol-lyase with aspartate is examined

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