Page 37 -

(including interfaces), the development of bio- (ii.) recognizing K (the set of outputs
i,O
logically realistic automated reasoning methods, actually produced by the computational step)
and any underlying mathematical techniques, from K (the set of possible outputs for the total
O
the management of computations over widely computation);
distributed, very heterogeneous systems like (iii.) mapping c : K → K (its compu-
i
the World Wide Web; molecular computing; i,I i,O
tation for that step), c ∈ C, the set of all compu-
i
nanotechnology (where computational issues are
tations.
raised or where biological artifacts are used in
computation); and the problems that biology Comment: This definition is a bit unusual in
poses for the foundations of computer science. that it explicitly includes the recognition of the
In a nutshell, computational biology is “com- actual inputs and outputs from among the sets
puting about biology and computing with biol- of possible ones, rather than just the mapping
ogy.” among them. The reason is that one can then
Occasionally, one sees a distinction between place discrete, Turing computations firmly in a
computational biology and bioinformatics, with framework which accommodates both them and
the notion that computational biology is theory the analog computations of molecular machines,
and algorithms and bioinformatics are databases for example, for DNA computers. See determin-
and retrieval. This is a distinction without a dif- istic, nondeterministic computations.
ference, since most biological problems require
both. To the extent that biological problems are concerted process Two or more primitive
molecular, computational biology overlaps with changes are said to be concerted (or to consti-
computational chemistry. Often the distinction tute a concerted process) if they occur within
the same elementary reaction. Such changes
is more one of investigator origin (chemist vs.
will normally (though perhaps not inevitably) be
biologist), degree of resolution of the question
(quantum-mechanical vs. tissue), and platform “energetically coupled.” (In the present context
choice (SGI vs. Sun). the term “energetically coupled” means that the
simultaneous progress of the primitive changes
computational complexity The time and involves a transition state of lower energy than
space an algorithm requires to solve a problem. that for their successive occurrence.) In a con-
Comment: Time and space have a mathemat- certed process the primitive changes may be syn-
ical relationship to the size N and complexity chronous or asynchronous.
of the problem. Thus algorithms are described
as being linear, polynomial, etc., depending on configuration space The configuration
the function of N in the relation between it space of a mechanical system is an n dimen-
and time or space. Functions are designated sional manifold Q with local (position) coord-
n
i
O(f (N)), meaning the algorithm requires on the inates q ,...,q . Then T Q is the momentum
∗
order of f (N) resources. Algorithms which are phase space.
polynomial represent the practical upper bound
of feasibility for large N, with lower values conformal mapping A map which pre-
for exponents and determinism of the algorithm serves angles. A conformal diffeomorphism on
obviously preferable. Many problems requir- a Riemannian manifold (M, g) is a diffeomor-
ing supra-polynomial resources can be addressed phism φ : (M, g) → (M, g) such that φ g =
∗
2
in favorable cases. Occasionally other metrics, f g for a nowhere vanishing function f .
such as the number of statements in the program,
are defined for particular purposes. conformation The spatial arrangement
of the atoms affording distinction between
computational step A computational step stereoisomers which can be interconverted by
s ∈ S consists of three components: rotations about formally single bonds. Some
i
(i.) recognizing K (the set of inputs authorities extend the term to include inversion
i,I
actually presented for that computational step) at trigonal pyramidal centers and other polytopal
from K (the set of possible inputs for the total rearrangements.
I
computation); See also tub conformation.

© 2003 by CRC Press LLC
© 2003 by CRC Press LLC