Kauffman

Procarione W L and Kauffman J W 1974 The electrical properties of phospholipid bilayer Langmuir films Chem. Phys. Lipids 12 251-60... 

G. B. Kauffman, Inorganic Coordination Compounds, Heyden, London, 1981. An excellent volume on the history of coordination compounds prior to 1935. 

Forveiy thin hquids, Eqs. (14-206) and (14-207) are expected to be vahd up to a gas-flow Reynolds number of 200 (Valentin, op. cit., p. 8). For liquid viscosities up to 100 cP, Datta, Napier, and Newitt [Trans. In.st. Chem. Eng., 28, 14 (1950)] and Siems and Kauffman [Chem. Eng. Sci, 5, 127 (1956)] have shown that liquid viscosity has veiy little effec t on the bubble volume, but Davidson and Schuler [Trans. Instn. Chem. Eng., 38, 144 (I960)] and Krishnamiirthi et al. [Ind. Eng. Chem. Fundam., 7, 549 (1968)] have shown that bubble size increases considerably over that predic ted by Eq. (14-206) for hquid viscosities above 1000 cP. In fac t, Davidson et al. (op. cit.) found that their data agreed veiy well with a theoretical equation obtained by equating the buoyant force to drag based on Stokes law and the velocity of the bubble equator at break-off ... 

For a lupiid depth of 0.9 m (3 ft , Kauffman recommended that the li.sted rates be doubled. 

Y. Guo and C. W. Kauffman, An Experimental Investigation of Air Line Explosions Caused by Eilm Detonation, Paper presented at Combustion Institute Eastern Section Eall Meeting, Albany, N.Y., Oct./Nov. 1989. 

Kauffman, G. B., and Priebe, P. M., 1990. The Emil Fi.scher-William Ram.sey friendship. Journal of Chemical Education 67 93-101. 

G. B. Kauffman, Alfred Werner Founder of Coordination Theory, Springer, Berlin, 1966, 127 fp. G. B. Kauffman (ed.) Coordination Chemistry A Century of Progress, ACS Symposium Series 565, Washington DC, 1994, 464 pp. 

The question of the occurrence of cine or aryne substitution in some of these reactions has been raised but not answered adequately. The normal product, 2-methoxynaphthalene was shown to be formed from 2-chloronaphthalene and methoxide ion, and the normal 6- and 8-piperidinoquinolines were proved to be products of piperidino-debromination of 6- and 8-bromoquinolines, all in unspecified yield. More highly activated compounds were then assumed not to react via the aryne mechanism. Even if the major product had been characterized, the occurrence of a substantial or predominant amount of aryne reaction may escape notice when strong orientation or steric effects lead to formation of the normal displacement product from the aryne. A substantial amoimt of concurrent aryne reaction may also escape detection if it yields an amount of cine-substituted material easily removed in purification or if the entire reaction mixture is not chromatographed Kauffman and Boettcher have demonstrated that activated compounds such as 4-chloropyridine do indeed react partially via the aryne mechanism (Section I,C,1). 

Non-homogeneous CA. These are CA in which the state-transition rules are allowed to vary from cell to cell. The simplest such example is one where there are only two different rules randomly distributed throughout the lattice. Kauffman [kauff84] has studied the otlier extreme in whidi tlie lattice is randomly populated with all possible Boolean functions of k inputs. 

Non-Homogeneous CA a characteristic feature of all CA rules defined so far has been that of homogeneity - each cell of the system evolves according to the same rule 0. Hartman and Vichniac [hartSfi] were the first to systematically study a class of inhomogeneous CA (INCA), in which the state-transition rules are allowed to vary from cell to cell. The simplest such example is one where there are only two different 0 s, which are randomly distributed throughout the lattice. Kauffman has studied the other extreme in which the lattice is randomly populated with all 2 possible boolean functions of k inputs. The results of such studies, as well as the relationship with the dynamics of random, mappings, are covered in detail in chapter 8.3. 

We might mention here in passing that while class-1, class-3 and class-4 (but not class-2) can all be obtained from one another with these two simple rules, class-2 behavior can only be obtained if the system is first quenched [vich86b]. That is, if the lattice is initially randomly populated with AND and XOR rules according to the prescribed value of p and is then frozen for all later times. Such quenched random rules harbor some interesting properties of their own in dimensions d > 1, and are the basis of much of Kauffman s findings on random Boolean networks (see section 8.6). 

This model was first introduced by Kauffman [kauff69] in a study of cellular differentiation in a biological system (binary sites were interpreted as elements of an ensemble of genes switching on and off according to some set of random rules). Since its original conception, however, related models have found wide application in an... 

Kauffman [kauff86b] describes two related mechanisms respon.sible for the formation of such percolating walls (1) forcing structunrs and (2) internaJ homogeneity clusters. An important point to keep in mind is that these two mechanisms, described below, currently represent the only establi.shed means by which the ordered behavior of = 2 nets can (in part) be deduced. 

Forcing Structures Consider the Boolean OR function. Note that the value of cti or CT2 is fixed as 1 whenever either a or C2 is equal to 1. Kauffman calls any function with the property that at least one value of at least one of its inputs fixes its output, a canalizing function [kauff84]. The Boolean functions OR and AND , for example, are both canalizing functions, but the EXCLUSIVE OR function is not. 

The situation is more complicated for nonisolated systems consisting of strongly interacting particles and when the system is no longer in equilibrium with the environment. Kauffman [kauff93] notes that the second law really states that any system will tend to the maximum disorder possible, within the constraints due to the dynamics of the system. ... 

Kauffman ([kauffSO], [kauffOOa]) has introduced a class of parametrizable fitness landscapes called NK-landscapes, that provide a formalism for studying the efficacy of GA evolution as a function of certain statistical properties of the landscape. Given N binary variables Xi = 1, so that x = (xi, X2, , Xjv) represents a vertex of an A -dimensional hypercube, an NK-landscape is defined by a fitness function, JF, of the form... 

Some preliminary suggestions of how NK-landscapes can be used to predict GA performance are discussed by Kauffman [kauff89] and Manderick, de Weger and Spiessens [mand91]. 

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