Spike Spectra for Recurrences

In recurrence analysis, the τ-recurrence rate encodes the periods of the cycles of the underlying high-dimensional time series. It, thus, plays a similar role to the autocorrelation for scalar time-series in encoding temporal correlations. However, its Fourier decomposition does not have a clean interpretation. Thus, there is no satisfactory analogue to the power spectrum in recurrence analysis. We introduce a novel method to decompose the τ-recurrence rate using an over-complete basis of Dirac combs together with sparsity regularization. We show that this decomposition, the inter-spike spectrum, naturally provides an analogue to the power spectrum for recurrence analysis in the sense that it reveals the dominant periodicities of the underlying time series. We show that the inter-spike spectrum correctly identifies patterns and transitions in the underlying system in a wide variety of examples and is robust to measurement noise.     

Asphalt, Bitumen

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Einen Beitrag zur technischen Sedimentationsanalyse

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Energy dependence of the reactions KLop→KSop,π+Λ, π+Σo from 1540 to 1610 MeV

The reactions K_L^op→K_S^op, π⁺Λ, π⁺Σ^o have been measured for center-of-mass energies from 1540 to 1610 MeV. Channel cross sections and coefficients of the Legendre polynomial expansion of the differential cross sections and hyperon polarizations are presented. We see no evidence in the πΛ channel for the suggested $\text{3}\text{2}{}^{\mathrm{?}}$ resonance at 1580 MeV. The cross section for the K_S^op channel shows an energy dependence which is not predicted by the existing phase shift solutions based on charged kaon data.     

The rearrangement of 4-hydroxyeoumarin carbamates

Carbamate esters of 4-hydroxycoumarin were prepared, and their base-catalyzed and thermal rearrangement to 3-(N-substituted carbamoy])-4-hydroxycoumarins were studied. A mechanism for the rearrangement is proposed.