Intrinsic heuristic

Example 4-6 For the compressll problem, the intrinsic heuristic leads towards selecting is the tail of as well-founded relation over the type of L. Weaker relations such as has less elements than or is a suffix of are also suitable, but it is best to start with strong relations, and relax them as needed. 

Example 4-7 For the compressll problem, the extrinsic heuristic leads towards selecting has one plateau less than as well-founded relation over the type of L, because it reflects the structure of the C parameter. But we retain the well-founded relation suggested by the Intrinsic Heuristic for the remainder of this section, and come back to this decision in Section 5.2.1. 

Let s now reconsider Step 1 (Selection of an Induction Parameter), and select the other parameter, C, as induction parameter. At Step 2 (Selection of a Well-Founded Relation), we first follow the Intrinsic Heuristic, and select is the tail of as well-founded relation over the type of the induction parameter. Step 3 is straightforward, and after Step 4, the result is ... 

Example 5-11 The following logic algorithm for sort L,S) has been designed with L as induction parameter, following the Intrinsic Heuristic. The result is the Insertion-Sort algorithm. 

An intrinsic decomposition reflects a well-founded relation selected via the Intrinsic Heuristic, and an extrinsic or logarithmic decomposition reflects a well-founded relation selected via the Extrinsic Heuristic (see Chapter 4). Sample classifications are given below. 

An intrinsic decomposition reflects a well-founded relation selected via the Intrinsic Heuristic (Heuristic 4-3), and an extrinsic or logarithmic decomposition reflects a well-founded relation selected via the Extrinsic Heuristic (Heuristic 4-4). The selection of a strategy is a high-level decision that may significantly affect the complexity of the resulting algorithm (but probably not its existence). A reasonable implementation of this synthesis mechanism would accept a preference hint from the specifier. 

In this paper we will not pursue such formal developments any further, and instead use mean field ideas and heuristic arguments to motivate the choice of the appropriate free energy functional. We represent the intrinsic free energy functional in the form of an effective 2D step Hamiltonian H and imagine on physical grounds that it has the... 

Mislow el at.301 have pointed out that the distinction between population difference and intrinsic difference is artificial nuclei are either symmetry related (i.e. interchanged by operation of a symmetry element), in which case they are homotopic or enantiotopic and thus isochronous, or they are not so related, in which case they are diastereotopic or constitutionally heterotopic and therefore anisochronous. While this is certainly correct, the present author believes that the dissection between population and intrinsic difference, like many such dissections in science, is at least pedagogically and possibly in some situations even heuristically useful. 

Dirac showed in 1928 that a fourth quantum number associated with intrinsic angular momentum appears in a relativistic treatment of the free electron, it is customary to treat spin heuristically. In general, the wavefunction of an electron is written as the product of the usual spatial part (which corresponds to a solution of the non-relativistic Schrodinger equation and involves only the Cartesian coordinates of the particle) and a spin part a, where a is either a or p. A common shorthand notation is often used, whereby... 

None of these two heuristics is superior to the other. In the sequel, when talking about a logic algorithm LA(r), we sometimes write LA r-int-X), or LA r-ext-X), to show that X was selected as induction parameter, and that the intrinsic (respectively extrinsic) heuristic was applied. Again, the predicate defined by LA(r-/>u-X) still is r, and not r-int-X. 

AGO methods provide efficient heuristic algorithms to solve TSP (see [4,3]). However, they also suffer from some intrinsic problems. On the one hand, let us note that this method lies in the idea that pheromone trails interact with each other in such a way that good paths are cooperatively constructed by ants. However, this characteristic is twofold. Sometimes paths may interfere and damage each other. For instance, local cycles involving only some nodes may be created and, even worse, be reinforced by subsequent ants. On the other hand, sometimes a local oriented method hke AGO may miss some simple graph peculiarities such that, if they were taken into account, then they would allow to easily find better paths. For instance, when a better path is found by ants, it takes a lot of subsequent ant movements to reinforce the new path until it is actually preferred to other older weU-estabhshed paths. 

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