Winning Cores in Parity Games

We introduce the novel notion of winning cores in parity games and develop a deterministic polynomial-time under-approximation algorithm for solving parity games based on winning core approximation. Underlying this algorithm are a number properties about winning cores which are interesting in their own right. In particular, we show that the winning core and the winning region for a player in a parity game are equivalently empty. Moreover, the winning core contains all fatal attractors but is not necessarily a dominion itself. Experimental results are very positive both with respect to quality of approximation and running time. It outperforms existing state-of-the-art algorithms significantly on most benchmarks

Single shot imaging of trapped Fermi gas

Recently developed techniques allow for simultaneous measurements of the positions of all ultra cold atoms in a trap with high resolution. Each such single shot experiment detects one element of the quantum ensemble formed by the cloud of atoms. Repeated single shot measurements can be used to determine all correlations between particle positions as opposed to standard measurements that determine particle density or two-particle correlations only. In this paper we discuss the possible outcomes of such single shot measurements in case of cloud of ultra-cold non-interacting Fermi atoms. We show that the Pauli exclusion principle alone leads to correlations between particle positions that originate from unexpected spatial structures formed by the atoms

An accurate and efficient algorithm for the computation of the characteristic polynomial of a general square matrix

An algorithm is presented for the efficient and accurate computation of the coefficients of the characteristic polynomial of a general square matrix. The algorithm is especially suited for the evaluation of canonical traces in determinant quantum Monte-Carlo methods.Comment: 8 pages, no figures, to appear in J. Comp. phy

Formation of soliton trains in Bose-Einstein condensates by temporal Talbot effect

We study the recent observation of formation of matter-wave soliton trains in Bose-Einstein condensates. We emphasize the role of the box-like confinement of the Bose-Einstein condensate and find that there exist time intervals for the opening the box that support the generation of real solitons. When the box-like potential is switched off outside the existing time windows, the number of peaks in a train changes resembling missing solitons observed in the experiment. Our findings indicate that a new way of generating soliton trains in condensates through the temporal, matter-wave Talbot effect is possible.Comment: 4 pages, 4 figures, new result

Aggregation of chemotactic organisms in a differential flow

We study the effect of advection on the aggregation and pattern formation in chemotactic systems described by Keller-Segel type models. The evolution of small perturbations is studied analytically in the linear regime complemented by numerical simulations. We show that a uniform differential flow can significantly alter the spatial structure and dynamics of the chemotactic system. The flow leads to the formation of anisotropic aggregates that move following the direction of the flow, even when the chemotactic organisms are not directly advected by the flow. Sufficiently strong advection can stop the aggregation and coarsening process that is then restricted to the direction perpendicular to the flow