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Figure 4.9: Bad chains. In the pre-computation phase work is wasted due to cycling and merging. In addition, during the attack phase, cycles and merging lead to false alarms. To see why this is the case, suppose Trudy executes a TMTO attack beginning from C in Figure 4.9. Following the algorithm outlined above, she eventually arrives at the endpoint E P . She then starts from corresponding S P and reconstructs the chain that ends at E P , and she expects this to lead to the key K . In this case, she does not find K since C does not lie on the ( S P ,E P ) chain. If she can decrease the cycling and merging of chains, Trudy can reduce the



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When the increment or decrement operator is placed before the operand, ActionScript processes the operation with a higher precedence.

var x:Number = 5; trace(x++); //prints 5, then increments x to 6 trace(++x); //increments x to 7, then prints 7





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The conducted research has shown that in order to obtain the central line of the analyzed vessel, rather than the operation of morphological erosion of the binarized vessel proposed by some researchers, or manual positioning (performed by a specialist) of the location of the said line, we should use a different technique which gives much better results Similar research has demonstrated that in the course of attempts at automatic understanding of pathological lesions of the structure of the examined organ, and of deformations of the analyzed organ shape indicating those, the best results are obtained when the reference line is a curvilinear axis of the vessel This axis can be laid out by the method of skeletonization of the analyzed anatomical structures used by the authors The method is based on an appropriately modified Pavlidis algorithm [23].

number of false alarms, and thereby reduce the work effective factor during the pre-computation phase. To accomplish this, a random function F is used. With such a function, a chain is computed as

Compound Assignment Operators (+=, -=, *=, /=, and %=)

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The compound assignment operators provide a shorthand solution to performing arithmetic on a variable and storing the result in the same variable. For instance, += adds the left-hand variable to the right-hand expression, storing the result in the left-hand variable.

When n = k , we can choose F to be a permutation. The advantage of using random functions is apparent if we compare Figures 4.10 and 4.11. In Figure 4.10, where no random function (or the same random) is used, once the two chains collide, they merge into a single chain. The points on the merged chains represented duplicated work which makes the pre-computation phase more expensive while not increasing the success rate in the attack phase.

x += 1;

x = x + 1;

The said method is efficient in calculations, and the central line obtained in its result, with precisely central location in relation to its walls (even in the case in which they are pathologically deformed), creates a certain path along which width profiles are determined If we take a numerically straightened axis line of the analyzed vessel for our reference point, then we obtain the diagrams of its unilaterals (the so-called top and bottom or left and right) These diagrams are obtained from the use of a specialist algorithm, the so-called straightening transformation, prepared by the authors; it allows one to obtain width diagrams of the analyzed structures, together with morphological lesions occurring in them [8] These diagrams are subsequently approximated with a polygon, which constitutes the basis for the further-discussed process of automatic understanding of pathological deformations of the analyzed organs shown on images.

On the other hand, in Figure 4.11 we see the effect of using different random functions. In this example, the functions Fo and FI cause the chains to (almost certainly) diverge immediately after a collision. Consequently, with the use of different random functions, collisions can still occur, but the effects of merging and cycling are mitigated.

var x:Number = 0; x x x x x += -= *= /= %= 5; 3; 3; 2; 3; // // // // // x x x x x = = = = = 5 2 6 3 0

Comma Operator (,)

Figure 4.1 1: Non-merging chains. Trudy could use a different random function for each chain, but it would be resource intensive to store all of these functions. Instead. she can obtain

The comma operator joins several subexpressions. The whole expression takes the value of the last subexpression in the list. You don t see this one used frequently, but it can be helpful.

var a:Number = 50; var b:Number = (a *= 2, 50 + 50); trace(a, b); //100 100

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