Merge-and-shrink abstraction (M&S) is an approach for constructing admissible heuristic functions for cost-optimal planning. It enables the targeted design of abstractions, by allowing to choose individual pairs of (abstract) states to aggregate into one. A key question is how to actually make these choices, so as to obtain an informed heuristic at reasonable computational cost. Recent work has...

The correct wording for the text is: Trajectories of ants displaced laterally were analysed in four categories based on their search patterns: (a) zero turns: paths that did not have any turns 50°; (b) one turn: paths of ants characterised by a single turn 50°, these are usually 90° turns directed towards the route-mark corridor; (c) zero loops: paths of ants with one or more turn/s 50°, but th...

We describe a simple approach to the controlled removal of molecules from the membrane of large unilamellar vesicles made of fatty acids. Such vesicles shrink dramatically upon mixing with micelles composed of a mixture of fatty acid and a phospholipid (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC)), as fatty acid molecules leave the vesicle membrane and accumulate within the mixed mi...

In this paper, we develop a method to find Chung-Feller extensions for three kinds of different rooted lattice paths and prove Chung-Feller theorems for such lattice paths. In particular, we compute a generating function S(z) of a sequence formed by rooted lattice paths. We give combinatorial interpretations to the function of Chung-Feller type S(z)−yS(yz) 1−y for the generating function S(z). ...