Mathematics of bioinformatics by He M., Petoukhov S.

By He M., Petoukhov S.

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Moscow: Sovetskoie Radio (in Russian). , and Wright, A. (1998). The simple genetic algorithm and the Walsh transform: I. Theory. J. Evol. , 6(3), 253–274. REFERENCES 23 Waterman, M. S. ) (1999). Mathematical Methods for DNA Sequences. Boca Raton, FL: CRC Press. Wilson, E. (1998). Consilience: The Unity of Knowledge. New York: Random House. , and Hershey, J. (1997). Hadamard Matrix Analysis and Synthesis with Applications to Communications and Signal/Image Processing. New York: Kluwer Academic. Zalmanzon, L.

The solution to this problem became possible due to the theory of noiseimmunity coding created by mathematicians. This theory has appeared rather recently; initial basic work in this field was published by Hamming in 1950 (Hamming, 1980). The theory of such coding utilizes intensive matrix mathematics, including the representation of sets of signals and codes in the form of matrices and their Kronecker powers. Our book describes many interesting results in the field of molecular genetics and bioinformatics which were obtained by its authors on the basis of such matrix mathematics.

Hadamard Matrix Analysis and Synthesis with Applications to Communications and Signal/Image Processing. New York: Kluwer Academic. Zalmanzon, L. A. (1989). Fourier, Walsh and Haar Transformations and Their Application in Control, Communication and Other Systems. Moscow: Nauka (in Russian). 2 Genetic Codes, Matrices, and Symmetrical Techniques The genetic code is a key to bioinformatics and to a science of biological selforganizing on the whole. Modern science faces the necessity of understanding and systematically explaining mysterious features of ensembles of molecular structures of the genetic code.

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