Multi-dimensional Kronecker sequences with a small number of gap lengths

Recently, generalizations of the classical Three Gap Theorem to higher dimensions attracted a lot of attention. In particular, upper bounds for the number of nearest neighbor distances have been established for the Euclidean and the maximum metric. It was proved that a generic multi-dimensional Kronecker attains the maximal possible number of different gap lengths for every sub-exponential subsequence. We mirror this result in dimension $d \in \left\{ 2, 3 \right\}$ by constructing Kronecker sequences which have a surprisingly low number of different nearest neighbor distances for infinitely $N \in \mathbb{N}$. Our proof relies on simple arguments from the theory of continued fractions

Atomic carbon at redshift ~2.5

Using the IRAM 30m telescope we detected the lower fine structure line of neutral carbon towards three high--redshift sources: IRAS FSC10214 (z=2.3), SMMJ14011+0252 (z=2.5) and H1413+117 (Cloverleaf quasar, z=2.5). SMMJ14011+0252 is the first high--redshift, non--AGN source in which CI has been detected. The CI(1-0) line from FSC10214 is almost an order of magnitude weaker than previously claimed, while our detection in the Cloverleaf is in good agreement with earlier observations. The CI(1-0) linewidths are similar to the CO widths, indicating that both lines trace similar regions of molecular gas on galactic scales. Derived CI masses for all three objects are of order few 10^7 solar masses and the implied CI(1-0)/CO(3-2) line luminosity ratio is about 0.2. This number is similar to values found in local galaxies. We derive a CI abundance of 5x10^{-5} which implies significant metal enrichment of the cold molecular gas at redshifts 2.5 (age of the universe 2.7 Gyr). We conclude that the physical properties of systems at large lookback times are similar to today's starburst/AGN environments.Comment: 4 pages, 2 figures; accepted by A&

Weak 13CO in the Cloverleaf Quasar: evidence for a young, early generation starburst

Observations of 12CO at high redshift indicate rapid metal enrichment in the nuclear regions of at least some galaxies in the early universe. However, the enrichment may be limited to nuclei that are synthesized by short-lived massive stars, excluding classical secondary nuclei like 13CO. Testing this idea, we tentatively detect the 13CO J=3-2 line at a level of 0.3 Jy km/s toward the Cloverleaf Quasar at redshift 2.5. This is the first observational evidence for 13CO at high redshift. The 12CO/13CO J=3-2 luminosity ratio is with at least 40 much higher than ratios observed in molecular clouds of the Milky Way and in the ultraluminous galaxy Arp 220, but may be similar to that observed toward NGC 6240. Large Velocity Gradient (LVG) models simulating seven 12CO transitions and the 13CO line yield 12CO/13CO abundance ratios in excess of 100 for the Cloverleaf. It is possible that the measured ratio is affected by a strong submillimeter radiation field, which reduces the contrast between the 13CO line and the background. It is more likely, however, that the ratio is caused by a real deficiency of 13CO. A potential conflict with optical data, indicating high abundances also for secondary nuclei in quasars of high redshift, may be settled if the bulk of the CO emission is originating sufficiently far from the active galactic nucleus.Comment: 7 pages, 5 figures, accepted for publication in A&A (Main Journal

Open Shop Scheduling with Synchronization

In this paper, we study open shop scheduling problems with synchronization. This model has the same features as the classical open shop model, where each of the n jobs has to be processed by each of the m machines in an arbitrary order. Unlike the classical model, jobs are processed in synchronous cycles, which means that the m operations of the same cycle start at the same time. Within one cycle, machines which process operations with smaller processing times have to wait until the longest operation of the cycle is finished before the next cycle can start. Thus, the length of a cycle is equal to the maximum processing time of its operations. In this paper, we continue the line of research started by Weiß et al. (Discrete Appl Math 211:183–203, 2016). We establish new structural results for the two-machine problem with the makespan objective and use them to formulate an easier solution algorithm. Other versions of the problem, with the total completion time objective and those which involve due dates or deadlines, turn out to be NP-hard in the strong sense, even for m=2 machines. We also show that relaxed models, in which cycles are allowed to contain less than m jobs, have the same complexity status

The neutron time-of-flight facility n-TOF at CERN: Phase II

Neutron-induced reactions are studied at the neutron time-of-flight facility n-TOF at CERN. The facility uses 6∼ns wide pulses of 20 GeV/c protons impinging on a lead spallation target. The large neutron energy range and the high instantaneous neutron flux combined with high resolution are among the key characteristics of the facility. After a first phase of data taking during the period 2001-2004, the facility has been refurbished with an upgraded spallation target and cooling system for a second phase of data taking which started in 2009. Since 2010, the experimental area at 185 m where the neutron beam arrives, has been modified into a worksector of type A, allowing the extension of the physics program to include neutron-induced reactions on radioactive isotopes

Gas and Dust in the Cloverleaf Quasar at Redshift 2.5

We observed the upper fine structure line of neutral carbon, CI(2-1), the CO(3-2) line and the 1.2mm continuum emission from H1413+117 (Cloverleaf quasar, z=2.5) using the IRAM interferometer. Together with the detection of the lower fine structure line (Barvainis etal. 1997), the Cloverleaf quasar is now only the second extragalactic system, besides M82, where both carbon lines have convincingly been detected. Our analysis shows that the carbon lines are optically thin and have an excitation temperature of ~30 K. CO is subthermally excited and the observed line luminosity ratios are consistent with n(H2)=10^(3-4) cm^(-3) at Tkin=30-50 K. Using three independent methods (CI, dust, CO) we derive a total molecular gas mass (corrected for magnification) of M(H2)=1.2+/-0.3*10^(10) SM. Our observations suggest that the molecular disk extends beyond the region seen in CO(7-6) to a zone of more moderately excited molecular gas that dominates the global emission in CI and the low J CO lines.Comment: 5 pages, 3 figures; accepted by A&

Excitation of the molecular gas in the nuclear region of M82

We present high resolution HIFI spectroscopy of the nucleus of the archetypical starburst galaxy M82. Six 12CO lines, 2 13CO lines and 4 fine-structure lines are detected. Besides showing the effects of the overall velocity structure of the nuclear region, the line profiles also indicate the presence of multiple components with different optical depths, temperatures and densities in the observing beam. The data have been interpreted using a grid of PDR models. It is found that the majority of the molecular gas is in low density (n=10^3.5 cm^-3) clouds, with column densities of N_H=10^21.5 cm^-2 and a relatively low UV radiation field (GO = 10^2). The remaining gas is predominantly found in clouds with higher densities (n=10^5 cm^-3) and radiation fields (GO = 10^2.75), but somewhat lower column densities (N_H=10^21.2 cm^-2). The highest J CO lines are dominated by a small (1% relative surface filling) component, with an even higher density (n=10^6 cm^-3) and UV field (GO = 10^3.25). These results show the strength of multi-component modeling for the interpretation of the integrated properties of galaxies.Comment: Accepted for publication in A&A Letter

Grey parrots use inferential reasoning based on acoustic cues alone

Our ability to make logical inferences is considered as one of the cornerstones of human intelligence, fuelling investigations of reasoning abilities in non-human animals. Yet, the evidence to date is equivocal, with apes as the prime candidates to possess these skills. For instance, in a two-choice task, apes can identify the location of hidden food if it is indicated by a rattling noise caused by the shaking of a baited container. More importantly, they also use the absence of noise during the shaking of the empty container to infer that this container is not baited. However, since the inaugural report of apes solving this task, to the best of our knowledge, no comparable evidence could be found in any other tested species such as monkeys and dogs. Here, we report the first successful and instantaneous solution of the shaking task through logical inference by a non-ape species, the African grey parrot. Surprisingly, the performance of the birds was sensitive to the shaking movement: they were successful with containers shaken horizontally, but not with vertical shaking resembling parrot head-bobbing. Thus, grey parrots seem to possess ape-like cross-modal reasoning skills, but their reliance on these abilities is influenced by low-level interferences

Ammonia (J,K) = (1,1) to (4,4) and (6,6) inversion lines detected in the Seyfert 2 galaxy NGC 1068

We present the detection of the ammonia (NH3) (J,K) = (1,1) to (4,4) and (6,6) inversion lines toward the prototypical Seyfert 2 galaxy NGC 1068, made with the Green Bank Telescope (GBT). This is the first detection of ammonia in a Seyfert galaxy. The ortho-to-para-NH3 abundance ratio suggests that the molecule was formed in a warm medium of at least 20 K. For the NH3 column density and fractional abundance, we find (1.09\pm0.23)\times10^14 cm^-2 and (2.9\pm0.6)\times10^-8, respectively, from the inner 1.2 kpc of NGC 1068. The kinetic temperature can be constrained to 80\pm20 K for the bulk of the molecular gas, while some fraction has an even higher temperature of 140\pm30 K.Comment: 5 pages, 3 figures, accepted by A&

Mining ancient microbiomes using selective enrichment of damaged DNA molecules

The identification of bona fide microbial taxa in microbiomes derived from ancient and historical samples is complicated by the unavoidable mixture between DNA from ante- and post-mortem microbial colonizers. One possibility to distinguish between these sources of microbial DNA is querying for the presence of age-associated degradation patterns typical of ancient DNA (aDNA). The presence of uracils, resulting from cytosine deamination, has been detected ubiquitously in aDNA retrieved from diverse sources, and used as an authentication criterion. Here, we employ a library preparation method that separates molecules that carry uracils from those that do not for a set of samples that includes Neandertal remains, herbarium specimens and archaeological plant remains