Magic numbers in the discrete tomography of cyclotomic model sets

We report recent progress in the problem of distinguishing convex subsets of cyclotomic model sets $\varLambda$ by (discrete parallel) X-rays in prescribed $\varLambda$-directions. It turns out that for any of these model sets $\varLambda$ there exists a `magic number' $m_{\varLambda}$ such that any two convex subsets of $\varLambda$ can be distinguished by their X-rays in any set of $m_{\varLambda}$ prescribed $\varLambda$-directions. In particular, for pentagonal, octagonal, decagonal and dodecagonal model sets, the least possible numbers are in that very order 11, 9, 11 and 13.Comment: 6 pages, 1 figure; based on the results of arXiv:1101.4149 [math.MG]; presented at Aperiodic 2012 (Cairns, Australia

Discrete Tomography of Planar Model Sets

Discrete tomography is a well-established method to investigate finite point sets, in particular finite subsets of periodic systems. Here, we start to develop an efficient approach for the treatment of finite subsets of mathematical quasicrystals. To this end, the class of cyclotomic model sets is introduced, and the corresponding consistency, reconstruction and uniqueness problems of the discrete tomography of these sets are discussed.Comment: 27 pages, 9 figure

Uniqueness in Discrete Tomography of Delone Sets with Long-Range Order

We address the problem of determining finite subsets of Delone sets $\varLambda\subset\R^d$ with long-range order by $X$-rays in prescribed $\varLambda$-directions, i.e., directions parallel to non-zero interpoint vectors of $\varLambda$. Here, an $X$-ray in direction $u$ of a finite set gives the number of points in the set on each line parallel to $u$. For our main result, we introduce the notion of algebraic Delone sets $\varLambda\subset\R^2$ and derive a sufficient condition for the determination of the convex subsets of these sets by $X$-rays in four prescribed $\varLambda$-directions.Comment: 15 pages, 2 figures; condensed and revised versio

Till death (or an intruder) do us part: intrasexual-competition in a monogamous Primate

Polygynous animals are often highly dimorphic, and show large sex-differences in the degree of intra-sexual competition and aggression, which is associated with biased operational sex ratios (OSR). For socially monogamous, sexually monomorphic species, this relationship is less clear. Among mammals, pair-living has sometimes been assumed to imply equal OSR and low frequency, low intensity intra-sexual competition; even when high rates of intra-sexual competition and selection, in both sexes, have been theoretically predicted and described for various taxa. Owl monkeys are one of a few socially monogamous primates. Using long-term demographic and morphological data from 18 groups, we show that male and female owl monkeys experience intense intra-sexual competition and aggression from solitary floaters. Pair-mates are regularly replaced by intruding floaters (27 female and 23 male replacements in 149 group-years), with negative effects on the reproductive success of both partners. Individuals with only one partner during their life produced 25% more offspring per decade of tenure than those with two or more partners. The termination of the pair-bond is initiated by the floater, and sometimes has fatal consequences for the expelled adult. The existence of floaters and the sporadic, but intense aggression between them and residents suggest that it can be misleading to assume an equal OSR in socially monogamous species based solely on group composition. Instead, we suggest that sexual selection models must assume not equal, but flexible, context-specific, OSR in monogamous species.Wenner-Gren Foundation, L.S.B. Leakey Foundation, the National Geographic Society, National Science Foundation (BCS- 0621020), the University of Pennsylvania Research Foundation and the Zoological Society of San Diego, German Science Foundation (HU 1746-2/1

Studies on charge production from Cs2Te photocathodes in the PITZ L-band normal conducting radio frequency photo injector

This paper discusses the behavior of electron bunch charge produced in an L-band normal conducting radio frequency cavity (RF gun) from Cs2Te photocathodes illuminated with ps-long UV laser pulses when the laser transverse distribution consists of a flat-top core with Gaussian-like decaying halo. The produced charge shows a linear dependence at low laser pulse energies as expected in the quantum efficiency limited emission regime, while its dependence on laser pulse energy is observed to be much weaker for higher values, due to space charge limited emission. However, direct plug-in of experimental parameters into the space charge tracking code ASTRA yields lower output charge in the space charge limited regime compared to measured values. The rate of increase of the produced charge at high laser pulse energies close to the space charge limited emission regime seems to be proportional to the amount of halo present in the radial laser profile since the charge from the core has saturated already. By utilizing core + halo particle distributions based on measured radial laser profiles, ASTRA simulations and semi-analytical emission models reproduce the behavior of the measured charge for a wide range of RF gun and laser operational parameters within the measurement uncertainties.Comment: 15 pages, 16 figures, 2 table

On reminder effects, drop-outs and dominance: evidence from an online experiment on charitable giving

We present the results of an experiment that (a) shows the usefulness of screening out drop-outs and (b) tests whether different methods of payment and reminder intervals affect charitable giving. Following a lab session, participants could make online donations to charity for a total duration of three months. Our procedure justifying the exclusion of drop-outs consists in requiring participants to collect payments in person flexibly and as known in advance and as highlighted to them later. Our interpretation is that participants who failed to collect their positive payments under these circumstances are likely not to satisfy dominance. If we restrict the sample to subjects who did not drop out, but not otherwise, reminders significantly increase the overall amount of charitable giving. We also find that weekly reminders are no more effective than monthly reminders in increasing charitable giving, and that, in our three months duration experiment, standing orders do not increase giving relative to one-off donations

Meson-exchange enhancement in first-forbidden β\beta -transitions: the case of 50^{50}K and 38^{38}Ca

The $\beta$- decay of $^{50}$K and $^{38}$Ca have been investigated with the main motive of determining more accurately the first-forbidden $\beta$- branches, in particular the rank-zero, $\Delta$J = 0, $\,\beta$ -transitions. $^{50}$K and $^{38}$Ca have been produced by fragmentation of U and Ti targets respectively, with a 1 GeV proton beam and subsequent on-line mass separation. For $^{50}$K, $\gamma$-ray spectroscopy, as well as delayed neutron spectroscopy by time of flight, were carried out to obtain a detailed decay scheme to 20 (bound and unbound) levels in $^{50}$Ca. The level structur e of $^{50}$Ca can be compared to recent calculations which incorporate 1p1h excitations from the f$_{7/2}$ shell. The first-forbidden $\beta^-$ transition $^{50}$ K(0$^-$)$\,\to{}^{50}$Ca(0$^+$) g.s. has been evaluated for the first time by a direct measurement of $\beta$- and $\gamma$- activities. Its importance (61.0 $\pm$ 7.4$\%$) is interpreted as an effect of the meson-exchange current (MEC) l eading to an enhancement factor of 62(5)$\%$ in comparison with the value predicted by shell-model calculations using the impulse approximation. For the $^{38}$ Ca$\,\to{}^{38}$K decay, chemical selec tive production was obtained through separation of the molecular ion CaF$^+$ without contamination by isobars. In these conditions, the measurement of very weak $\beta$-branches, at a level of 10$^{-3}\%$ decays, could be made and a limit, at the 2$\sigma$-confidence level, has been obtained for the 0$^+\to$ 0$^-$ branch to the level at E$_x$ = 2993 keV (I$_\beta$ < 0.0046$\%$). Imp lications of these results on the general trend of meson-exchange enhancements of first-forbidden transitions within the framework of the spherical shell model are discussed

Superconducting d-wave junctions: The disappearance of the odd ac components

We study voltage-biased superconducting planar d-wave junctions for arbitrary transmission and arbitrary orientation of the order parameters of the superconductors. For a certain orientation of the superconductors the odd ac components disappear, resulting in a doubling of the Josephson frequency. We study the sensitivity of this disappearance to orientation and compare with experiments on grain boundary junctions. We also discuss the possibility of a current flow parallel to the junction.Comment: 5 pages, 3 figure