Robert Jones

Robert Jones

The main difficulty in solving the Helmholtz equation within polygons is due to non-analytic vertices. By using a method nearly identical to that used by Fox, Henrici, and Moler in their 1967 paper; it is demonstrated that such eigenvalue calculations can be extended to unprecedented precision, very often to well over a hundred digits, and sometimes to over a thousand digits. A curious observation is that as one increases the number of terms in the eigenfunction expansion, the approximate eigenvalue may be made to alternate above and below the exact eigenvalue. This alternation provides a new method to bound eigenvalues, by inspection. Symmetry must be exploited to simplify the geometry, reduce the number of non-analytic vertices and disentangle degeneracies. The symmetry-reduced polygons considered here have at most one non-analytic vertex from which all edges can be seen. Dirichlet, Neumann, and periodic-type edge conditions, are independently imposed on each polygon edge. The full shapes include the regular polygons and some with re-entrant angles (cut-square, L-shape, 5-point star). Thousand-digit results are obtained for the lowest Dirichlet eigenvalue of the L-shape, and regular pentagon and hexagon.

Edward Gunn, Adam Hosford, Robert Jones et al.

We present the Turing Synthetic Radar Dataset, a comprehensive dataset to serve both as a benchmark for radar pulse deinterleaving research and as an enabler of new research methods. The dataset addresses the critical problem of separating interleaved radar pulses from multiple unknown emitters for electronic warfare applications and signal intelligence. Our dataset contains a total of 6000 pulse trains over two receiver configurations, totalling to almost 3 billion pulses, featuring realistic scenarios with up to 110 emitters and significant parameter space overlap. To encourage dataset adoption and establish standardised evaluation procedures, we have launched an accompanying Turing Deinterleaving Challenge, for which models need to associate pulses in interleaved pulse trains to the correct emitter by clustering and maximising metrics such as the V-measure. The Turing Synthetic Radar Dataset is one of the first publicly available, comprehensively simulated pulse train datasets aimed to facilitate sophisticated model development in the electronic warfare community