Informally, a set of abstractions of a state space S is additive if the distance between any two states in S is always greater than or equal to the sum of the corresponding distances in the abstract spaces. The first known additive abstractions, called disjoint pattern databases, were experimentally demonstrated to produce state of the art performance on certain state spaces. However, previous ...

We study a construction of the Mathieu group M12 using a game reminiscent of Loyd’s “15-puzzle”. The elements of M12 are realized as permutations on 12 of the 13 points of the finite projective plane of order 3. There is a natural extension to a “pseudogroup” M13 acting on all 13 points, which exhibits a limited form of sextuple transitivity. Another corollary of the construction is a metric, a...

The most commonly used material for constructing complete dentures is polymethyl methacrylate (PMMA). However, the strength characteristics of PMMA, such as impact and fatigue strength, are poor, fracturing PMMA a common problem in prosthodontic practice. Reinforcing with various materials, carbon fibers, glass fibers (fiberglass), ultrahigh modulus polyethylene has been suggested to strengthen...

We study a construction of the Mathieu group M12 using a game reminiscent of Loyd’s “15-puzzle”. The elements of M12 are realized as permutations on 12 of the 13 points of the finite projective plane of order 3. There is a natural extension to a “pseudogroup” M13 acting on all 13 points, which exhibits a limited form of sextuple transitivity. Another corollary of the construction is a metric, a...

A heuristic improvement technique referred to as multi-dimensional heuristics is presented. Instead of only applying the heuristic between two states X 1 and X 2 , when a distance esti­ mate of X 1 X 2 is needed, this technique uses a reference state R and applies the heuristic func­ tion to {X 1 ,R) and (X' 2 ,R) and compares the resulting values. If two states are close to each other, then th...

Piano players need to learn various techniques such as correct keying and fingering. However, the lighted keyboards, which light up the key and are the most commonly used piano learning supports, have several problems for learners, such as difficulty in understanding the presented fingering information and flow of keying positions, and lack of a fingering check function. To resolve these proble...

Two kinds of vision science are distinguished: a representational versus a nonrepresentational one. Seeing in the former is conceived of as creating an internal replica of the external world, while in the latter seeing is taken to be a process of active engagement with the environment. The potential of each theory for elucidating artistic creation and aesthetic appreciation is considered, neces...