A new heap game

Given $k\ge 3$ heaps of tokens. The moves of the 2-player game introduced here are to either take a positive number of tokens from at most $k-1$ heaps, or to remove the {\sl same} positive number of tokens from all the $k$ heaps. We analyse this extension of Wythoff's game and provide a polynomial-time strategy for it.Comment: To appear in Computer Games 199

Tunable compression of template banks for fast gravitational-wave detection and localisation

One strategy for reducing the online computational cost of matched-filter searches for gravitational waves is to introduce a compressed basis for the waveform template bank in a grid-based search. In this paper, we propose and investigate several tunable compression schemes for a general template bank. Through offline compression, such schemes are shown to yield faster detection and localisation of signals, along with moderately improved sensitivity and accuracy over coarsened banks at the same level of computational cost. This is potentially useful for any search involving template banks, and especially in the analysis of data from future space-based detectors such as eLISA, for which online grid searches are difficult due to the long-duration waveforms and large parameter spaces.Comment: Published versio

An Evolutionary Approach for Solving the Rubik’s Cube Incorporating Exact Methods

Abstract. Solutions calculated by Evolutionary Algorithms have come to surpass exact methods for solving various problems. The Rubik’s Cube multiobjective optimization problem is one such area. In this work we present an evolutionary approach to solve the Rubik’s Cube with a low number of moves by building upon the classic Thistlethwaite’s approach. We provide a group theoretic analysis of the subproblem complexity in-duced by Thistlethwaite’s group transitions and design an Evolutionary Algorithm from the ground up including detailed derivation of our cus-tom fitness functions. The implementation resulting from these observa-tions is thoroughly tested for integrity and random scrambles, revealing performance that is competitive with exact methods without the need for pre-calculated lookup-tables.

Two examples of minimal Cheeger sets in the plane

We construct two minimal Cheeger sets in the Euclidean plane, i.e., unique minimizers of the ratio \u201cperimeter over area\u201d among their own measurable subsets. The first one gives a counterexample to the so- called weak regularity property of Cheeger sets, as its perimeter does not coincide with the 1-dimensional Hausdorff measure of its topological boundary. The second one is a kind of porous set, whose boundary is not locally a graph at many of its points, yet it is a weakly regular open set admitting a unique (up to vertical translations) nonparametric solution to the prescribed mean curvature equation, in the extremal case corresponding to the capillarity for perfectly wetting fluids in zero gravity

Stepwise Evolutionary Learning using Deep Learned Guidance Functions

This paper explores how Learned Guidance Functions (LGFs)— a pre-training method used to smooth search landscapes—can be used as a fitness function for evolutionary algorithms. A new form of LGF is introduced, based on deep neural network learning, and it is shown how this can be used as a fitness function. This is applied to a test problem: unscrambling the Rubik’s Cube. Comparisons are made with a previous LGF approach based on random forests, and with a baseline approach based on traditional error-based fitness