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not short-circuit is a cause for celebration. Occasionally, however, an exact solution is desired by engineers who want the very best design. In reference to Hamiltonian circuits and the salesman s problem, the best initializations are permutations involving all vertices, obtained as follows. Beginning at vertex 1, the rst choice is limited to n 1, since an edge cannot circle back to its starting point in a Hamiltonian circuit. The second choice can be limited to n 2, since not only can it not return to its own vertex, but it cannot return to a previous vertex. Since no vertex is used twice, the number of possibilities is (n 1)(n 2) (1), or in the language of mathematics, (n 1)! The last vertex goes to close the circuit. Since each trip can be traveled two ways, the number of choices is (n 1)!/2. For n = 11 nodes, there are (n 1)!/ 2 = 1,814,400 valid choices. Permutations involving all vertices are ideal initializations since then vertices do not require accounting as is done in Figure 9-18. There are standard interchange algorithms that will compute all permutations of a given set of digits. In time, a great many numbers could be cranked out and applied to program the initial contents of the words of toggle memory automatically in nanoprocessors. Fusible links are considered to be a standard part of

XMLList. A class representing an ordered set of XML objects. The XMLList class is similar to an Array in that it contains objects in fixed order. Also, like an Array, it doesn t have a complete API to manage, modify, and reliably execute bindings when its data changes at runtime. XMLListCollection. A wrapper class that manages an ArrayList. Just as the ArrayCollection provides sorting, filtering, and other advanced features for managing an Array, the XMLListCollection implements a powerful API that manages an XMLList and reliably executes bindings when its data changes at runtime.

One proof for the converse implication follows by using the singular value decompositions of A and B (cf. Sec. B.6) - see Rob. VII1.2 for another proof:

, , ,

Multiple Fields, 5.6%

(3.6-7 1)

since such resistance would likely decrease the virulence and survival of the bacteria in the host Therefore, it is possible that in a live animal, the development of phage-resistant isolates would coincide with a loss in tness and virulence, rendering the contaminating bacteria unable to cause illness For example, in the case of K1- or LPS-speci c phages, the most likely resistant mutants will be de cient in capsule or LPS Several studies have shown that, in both cases, the mutant bacterial isolates are less virulent Smith and Huggins (1982) inoculated calves with a K1 strain of E coli, followed by the addition of a K1-speci c phage A low number of phage resistant E coli strains were isolated from the calf intestine, but due to the loss of the K1 antigen, the strain had become avirulent in mice.

Therefore, great care must be taken when interpreting the results of phage therapy in vitro studies, since in vitro predator prey studies do not accurately re ect in vivo conditions Such studies cannot account for the complexity of the phage host interaction in the natural environment In pure culture experiments, the only competitor of the phage-resistant cell is its phage susceptible ancestor cell, which is counter-selected in the presence of a phage However, in the natural environment, the phage-resistant clone must also compete with many other strains that are not subject to the pressure of the infecting phage (Br ssow 2005) This principle was demonstrated by Harcombe and Bull (2005), who conducted an in vitro study of E coli, Salmonella enterica serovar typhimurium, and coliphages T5 and T7 The researchers showed that, while resistant mutants could be obtained from pure E coli cultures, when the E.

3

coli cells were mixed with the S typhimurium cells, the resistant E coli cells were outcompeted by the Salmonella 5 GENETIC MANIPULATION OF HOST RANGE In addition to the natural ability of certain phages to expand their host ranges, lytic phages can be engineered to produce recombinant phages with desired host ranges In this scenario, the host range of a respective phage would be modi ed by replacing its tail ber loci with that of another phage that has the required host range Several phages are capable of altering their host range via a sitespeci c recombination system that inverts the sequence that determines the host range (Plasterk et al 1983) For example, phage Mu is a broad host range phage capable of forming plaques on several bacterial species (Harshey 1988).

The Mu genome contains tail ber gene S, which encodes a site recognized by a Mu-encoded invertase, with a second site beyond the gene in inverted orientation Depending on the.

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