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compact support A continuous function f complex conjugate The complex conjugate
has compact support if its support supp(f ) = ofthecomplexnumberz = x + iy isthecomplex
{x : f (x) = 0} is a compact set. number ¯z = x − iy.
competition One class of models for popu- complex number A number of the form x+
lation dynamics in which species are competing iy, where x and y are real numbers and i =−1.
2
for the same, limited resource. Hence, the growth
rate of one species decreases with increasing complex structure A complex structure on
population of the other and vice versa. Such
a real vector space V is a linear map J : V → V
a system is likely to exhibit extinction of the 2
such that J = Id. Setting iz = J(z) gives V
weaker species. Stable co-existence is possible,
the structure of a complex vector space.
however, under a delicate balance.
complex vector space A complex vector
complement Given a set A, the set of all space V is a vector space over the field of com-
c
elements not in A, denoted A or A .
¯
plex numbers C; i.e., scalar multiplication λz is
complete space A metric space (M, d) is defined for complex number λ ∈ C,z ∈ V .
complete if every Cauchy sequence {X } in M
n
converges in M. That is, there is x ∈ M such composition Consider two functions,
f : A → B and g : C → D, over four sets
that d(x , x) → 0, as n →∞
n
A, B, C, D.If f (A) ⊆ C, then the result of
complete vector field A vector field X on a applying f and g in succession is equivalent to
manifold M is complete if its flow φ is defined the application of a single composite function,
t
d
for all t ∈ R,( φ (x) = X(φ (x)) for all denoted g ◦ f : A → D. g ◦ f is defined for
dt t t
t ∈ R). any x ∈ A as (g ◦ f )(x) = g(f (x)).
completely continuous See compact oper-
compound Any molecule or assembly of
ator.
molecules.
Comment: These range in size from single
completely integrable system A Hamilto-
nuclei (H ) to DNA to transport complexes
+
nian system defined over a symplectic manifold
embedded in cell membranes on up. One often
(P, ω) of dimension 2n with n first integrals F i
in involution, i.e., such that {F ,F }= 0 for all distinguishes between enzymes and metabolites,
i j
pairs (i, j). The equations of motion of a com- smaller molecules. The boundary between
“macromolecular” and “smaller” is not fixed pre-
pletely integrable system can be formally inte-
cisely, but is perhaps about 1000 daltons.
grated. Explicitly, a Hamiltonian system (vector
field) X on R 2n is called completely integrable
H
if there exist n constants of the motion f ,...f n compound’s reactions A compound’s reac-
1
which are linearly independent and in involution, tions is the set of reactions in which that com-
pound participates.
i.e., {f ,f }= 0 for all i, j = 1, ..., n.
i j
Comment: See reaction’s compounds.
complex Amolecularentityformedbyloose
association involving two or more component computational biology The development
molecular entities (ionic or uncharged), or the and application of theory, algorithms, heuristics,
corresponding chemical species. The bonding and computational systems, including electronic
between the components is normally weaker than databases, to biological problems; and equally,
in a covalent bond. the application of biological concepts, materials,
The term has also been used with a variety or processes to problems not originating in bio-
of shades of meaning in different contexts; it logy; and activities at the interface of these two.
is therefore best avoided when a more explicit Comment: This definition is broad, but still
alternative is applicable. In inorganic chemistry useful; it includes areas such as the representa-
the term “coordination entity” is recommended tion of information in electronic databases, the
instead of “complex.” construction and maintenance of those databases

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