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But here there is no resort to transposition or other manipulation to derive many pitches from one.
Second, lineage-restricted progenitors require less elaborate manipulation to derive more mature cell populations.
The pre-processing step makes use of symbolic manipulation to derive the sensitivity equations and Jacobians (both of residuals and dynamics), and automatically generates C code to be compiled and linked with the CVODES solver.
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And there will be more manipulation to come within Labour.
For the case of the average distance error, similar manipulation can be easily applied to derive the corresponding relation.
The symbolic manipulation of Maple provides an excellent platform to derive the recursive algorithm.
In particular, all levels of network protocols are completely exposed to eavesdropping and manipulation by an attacker, so using cryptography properly is a first-class requirement to derive any benefit from its use.
The authors also included patients in whom neither apoptosis nor mitosis could be observed, requiring mathematical manipulation of the data obtained in all cases examined in order to derive mitotic and apoptotic frequencies.
Typical examples of manipulation include converting data to different types and discretizing or summarizing data to derive new attributes.
The above manipulations of the optimality condition are by no means the only ways to derive a fixed-point equation for power optimization.
For example, EST resources provide the opportunity to derive finished coding sequences that will be more useful for genetic manipulation as well as for comparative bioinformatics.
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