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• Implementations of efficient algorithms for computing the permanent. • Algorithms for matrices of limited bandwidth and sparse matrices. • Distribution of permanents for Gaussian matrices gives support for Aaronson & Arkhipov's anti-concentration conjecture. • Variational distance between permanents of two families of random matrices suggests another conjecture by A&A is too strong. In order to find the outcome probabilities of quantum mechanical systems like the optical networks underlying Boson sampling, it is necessary to be able to compute the permanents of unitary matrices, a computationally hard task. Here we first discuss how to compute the permanent efficiently on a parallel computer, followed by algorithms which provide an exponential speed-up for sparse matrices and linear run times for matrices of limited bandwidth. The parallel algorithm has been implemented in a freely available software package, also available in an efficient serial version. As part of the timing runs for this package we set a new world record for the matrix order on which a permanent has been computed. Next we perform a simulation study of several conjectures regarding the distribution of the permanent for random matrices. Here we focus on permanent anti-concentration conjecture, which has been used to find the classical computational complexity of Boson sampling. We find a good agreement with the basic versions of these conjectures, and based on our data we propose refined versions of some of them. For small systems we also find noticeable deviations from a proposed strengthening of a bound for the number of photons in a Boson sampling system. [ABSTRACT FROM AUTHOR]

Abstract: The present paper analyses the confluence of agendas held by Danish mathematicians and German refugees from Nazi oppression as they unfolded and shaped the mathematical milieu in Copenhagen during the 1930s. It does so by outlining the initiatives to aid emigrant intellectuals in Denmark and contextualises the few mathematicians who would be aided. For most of those, Denmark would be only a transit on the route to more permanent immigration, mainly in the US. Thus, their time in Copenhagen would exert only temporary influence over Danish mathematics; but as it will be argued, the impacts of their transit would be more durable both for the emigrants and for the Danish mathematical milieu. It is thus argued that the influx of emigrant mathematicians helped develop the institutional conditions of mathematics in Copenhagen in important ways that simultaneously bolstered the international outlook of Danish mathematicians. These confluences of agendas became particularly important for Danish mathematics after the war, when the networks developed during the 1930s could be drawn upon. [Copyright &y& Elsevier]

Abstract: Motivated by the set–antiset method for codes over permutations under the infinity norm, we study anticodes under this metric. For half of the parameter range we classify all the optimal anticodes, which is equivalent to finding the maximum permanent of certain -matrices. For the rest of the cases we show constraints on the structure of optimal anticodes. [Copyright &y& Elsevier]

Abstract: In this paper, general nonautonomous discrete-time single-species Kolmogorov model with delays is studied. Some sufficient conditions on the boundedness, persistence, permanence and global attractivity of solutions are established. As application, the discrete time nonautonomous delayed Allee-effect model is discussed. The sufficient conditions on the permanence and global attractivity are obtained. [Copyright &y& Elsevier]

Abstract: We build a chain of nested involutions in the Bruhat ordering of , with the maximal element for the Bruhat order, and we study the cardinality of the Bruhat intervals for all , and the number of permutations incomparable with , for all . [Copyright &y& Elsevier]