On the Asymptotic Worst Case Behavior of Harmonic Fit

In the parametric bin packing problem we must pack a list of items with size smaller than or equal to 1/r in a minimal number of unit-capacity bins. Among the approximation algorithms, the class of Harmonic Fit algorithms (HFM) plays an important role. Lee and Lee (J. Assoc. Comput. Mach. 32 (1985), 562-572) and Galambos (Ann. Univ. Sci. Budapest Sect. Comput. 9 (1988), 121-126) provide upper bounds for the asymptotic worst case ratio of HFM and show tightness for certain values of the parameter M. In this paper we provide worst case examples that meet the known upper bound for additional values of M, and we show that for remaining values of M the known upper bound is not tight. For the classical bin packing problem (r = 1), we prove an asymptotic worst case ratio of 12/7 for the case M = 4 and 1.7 for the case M = 5. We give improved lower bounds for some interesting cases that are left open

Pan-European backcasting exercise, enriched with regional perspective, and including a list of short-term policy options

This deliverable reports on the results of the third and final pan-European stakeholder meeting and secondly, on the enrichment with a Pilot Area and regional perspective. The main emphasis is on backcasting as a means to arrive at long-term strategies and short-term (policy) actions

Lower bounds for 1-, 2- and 3-dimensional on-line bin packing algorithms

In this paper we discuss lower bounds for the asymptotic worst case ratio of on-line algorithms for different kind of bin packing problems. Recently, Galambos and Frenk gave a simple proof of the 1.536 ... lower bound for the 1-dimensional bin packing problem. Following their ideas, we present a general technique that can be used to derive lower bounds for other bin packing problems as well. We apply this technique to prove new lower bounds for the 2-dimensional (1.802...) and 3-dimensional (1.974...) bin packing problem

Climate change impact on the leaching of a heavy metal contamination in a small lowland catchment

The objective of this study was to assess the potential effects of climate change on the transport of pre-existing spatially-extensive trace metal contamination to a small lowland catchment in the south of the Netherlands. The area surrounding the Keersop has been contaminated with heavy metals by the atmospheric emissions of four zinc ore smelters. This heavy metal contamination, e.g. with Cd and Zn, has accumulated in the topsoil and leaches towards surface water system, especially during high groundwater levels and high discharge rates. Simulated projections of future climate predict increased precipitation in winter, less precipitation in summer, and higher air temperatures throughout the year. These climate change scenarios projected lower groundwater levels and lower discharge rates. As a result of lower groundwater levels, transport of Cd and Zn towards surface water is also projected to decrease in the future climate. These results indicate a positive effect of climate change on a limited aspect of surface water quality

Cosmic-ray energy spectrum and composition up to the ankle - the case for a second Galactic component

We have carried out a detailed study to understand the observed energy spectrum and composition of cosmic rays with energies up to ~10^18 eV. Our study shows that a single Galactic component with subsequent energy cut-offs in the individual spectra of different elements, optimised to explain the observed spectra below ~10^14 eV and the knee in the all-particle spectrum, cannot explain the observed all-particle spectrum above ~2x10^16 eV. We discuss two approaches for a second component of Galactic cosmic rays -- re-acceleration at a Galactic wind termination shock, and supernova explosions of Wolf-Rayet stars, and show that the latter scenario can explain almost all observed features in the all-particle spectrum and the composition up to ~10^18 eV, when combined with a canonical extra-galactic spectrum expected from strong radio galaxies or a source population with similar cosmological evolution. In this two-component Galactic model, the knee at ~ 3x10^15 eV and the second knee at ~10^17 eV in the all-particle spectrum are due to the cut-offs in the first and second components, respectively. We also discuss several variations of the extra-galactic component, from a minimal contribution to scenarios with a significant component below the ankle (at ~4x10^18 eV), and find that extra-galactic contributions in excess of regular source evolution are neither indicated nor in conflict with the existing data. Our main result is that the second Galactic component predicts a composition of Galactic cosmic rays at and above the second knee that largely consists of helium or a mixture of helium and CNO nuclei, with a weak or essentially vanishing iron fraction, in contrast to most common assumptions. This prediction is in agreement with new measurements from LOFAR and the Pierre Auger Observatory which indicate a strong light component and a rather low iron fraction between ~10^17 and 10^18 eV.Comment: Added Table 4; Published in A&A, 595 (2016) A33 (Highlight paper