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specifies the semantics of these models for the sensitivity analysis The concern with how
purposes of exchanging computations. Each site the solution changes if some changes are made
offering data or computations to the network in either the data or in some of the solution values
would locally maintain a publicly readable list (by fixing their value). Marginal analysis, which
of mappings between its internal representation is concerned with the effects of small perturba-
andthesemiotesandaparserimplementingthose tions, may be measurable by derivatives. Para-
mappings as needed by the local engine. Simi- metric analysis is concerned with larger changes
larly, sites posing computations would maintain in parameter values that affect the data in the
mappings and parser between their internal rep- mathematical program, such as a cost coeffi-
resentation and the semiotes. All sites are free ciency or resource limit.
to change their schema, engines, and proffered Under suitable assumptions, the multipliers in
services at any time in any manner. Flexibil- the Lagrange multiplier rule provide derivatives
ity of use and ease of definition is promoted by of the optimal response function, i.e., under cer-
∗
making semiotes representing the smallest use- tain conditions, (u, v) = grad f (b, c).
ful part, and combining these together. See also
representation and semantics. separable program The functions are sep-

arable: f(x) = j f (x ), g(x) = j g (x ),
j
j
j
j

and h(x) = h (x ). The classical (LP)
j
j
sensitivity (1) (in mass spectrometry) Two j
approaches to separable programming are called
different measures of sensitivity are recom-
lambda-form and delta-form, both using piece-
mended. The first, which is suitable for relatively
wise linear approximations.
involatile materials as well as gases, depends k
Let {x } be a specified set of points, where
upon the observed change in ion current for a k
x = [x(k, 1), x(k, 2),...,x(k,n)], and let y =
particular amount or change of flow rate of sam-
{y(k, j)} be decision variables that are the coef-
ple through the ion source. A second method of
ficients of convex combinations, giving the fol-
stating sensitivity, that is most suitable for gases,
lowing linear program:
depends upon the change of ion current related
to the change of partial pressure of the sample in
Max Sum j{y(k, j)f (x(k, j))} : y ≥ 0,
k
j
the ion source.
It is important that the relevant experimental
y(k, j) = 1 for each j,
conditions corresponding to sensitivity measure- k
ment should always be stated. These include in a
typical case details of the instrument type, bom- y(k, j)g (x(k, j)) ≤ 0,
j
kj
barding electron current, slit dimensions, angular

collimation, gain of the multiplier detector, scan y(k, j)h (x(k, j)) = 0.
j
kj
speed, and whether the measured signal corre-
sponds to a single mass peak or to the ion beam A restricted basis entry rule is invoked during
integrated over all masses. Some indication of the simplex method to yield an approximate solu-
the time involved in the determination should be tion. (However, this is dominated by the general-
given, e.g., counting time or bandwidth. The sen- ized Lagrange multiplier method, which can be
viewed as generating the approximating break-
sitivity should be differentiated from the detec-
tion limit. points a posteriori, getting successively finer
(2) (in metrology and analytical chemistry) near the solution.)
The slope of the calibration curve. If the curve Thedeltaformusesthedifferences: u(k, j) =
x(k, j) − x(k − 1,j). The associated functional
is in fact a “curve,” rather than a straight line,
differences are:
then of course sensitivity will be a function of
analytic concentration or amount. If sensitivity
Df (k, j) = f (x(k, j)) − f (x(k − 1, j)),
j
j
is to be a unique performance characteristic, it
must depend only on the chemical measurement Dg(k, j) = g (x(k, j)) − g (x(k − 1, j)),
j
j
process, not upon scale factors. Dh(k, j) = h (x(k, j)) − h (x(k − 1, j)).
j j
© 2003 by CRC Press LLC
© 2003 by CRC Press LLC