We show that there are universal positive constants c and C such the mixing time τmix for the fifteen puzzle in an n× n torus satisfies cn logn ≤ τmix ≤ Cn log n.

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...

A novel route is proposed for the preparation of mesopore containing zeolite ZSM-5 via in situ hydrothermal treatment of a solution containing alkali-dissolved SBA-15 containing carbonized surfactant P123 in the mesopores; it exhibited prominent stability enhancement for methanol to propylene reaction.

The successful in situ synthesis of metallophthalocyanines in mesoporous matrices is presented in this report. To overcome the high hydrophobicity of phthalocyanine (Pc) compounds in conventional wet chemical methods, a simple but effective route is developed to incorporate the metallophthalocyanines into the mesoporous matrix via an in situ reaction process between pre-loaded metal ions and 1,...

A novel type of material encapsulating phase-change materials (PCMs) is reported concerning their implication for use as thermal energy storage devices. The composites of siliceous SBA-15 or carbonaceous CMK-3 mesoporous assemblies and organic PCMs could be used to make leak-free devices that retain their capabilities over many thermal cycles for heat storage/release. A confinement effect was o...

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...

Interleukin-15 (IL-15) is generally considered to be a regulator of T cell homeostasis because it works with other common gamma-chain cytokines like IL-2 and IL-7 to control the maintenance of naive and memory T cell populations. However, recent reports highlight new roles for IL-15 during the primary immune responses that involve promoting the survival of antigen-specific CD8(+) T cells. These...