(1) I was particularly dismayed at Lewand's treatment of modular exponentiation , which is the central operation in many cryptosystems.(2) Imposing time reversibility has the computational advantage that the matrix exponentiation can be carried out without much difficulty.(3) One of the main reasons for including an introduction to modular arithmetic is that the two most popular public key algorithms use modular exponentiation as their basic mathematical process.(4) Computing individual hexadecimal digits using that formula relies on a venerable technique known as the binary algorithm for exponentiation .(5) With ordinals you can do addition, multiplication and exponentiation - even infinitely often - but you can't do subtraction or division, as far as I know.(6) To transform the hospital specific regression coefficients into a directly standardised rate on the original scale, we exponentiated and calibrated them so that they had the same overall mean as the crude hospital specific rates.(7) Profiling the code reveals that the majority of time in likelihood evaluation is spent exponentiating the infinitesimal generator.(8) The transition probabilities of the process can be calculated by exponentiating the rate matrix using standard numerical methods.(9) The regression coefficient was exponentiated , and we subtracted this value from 1 to obtain the decline rate.(10) Multivariate results are presented in the form of odds ratios, obtained by exponentiating the regression coefficients from logistic models.
