An EPTAS for scheduling jobs on uniform processors using an MILP relaxation with a constant number of integral variables

We present an efficient polynomial time approximation scheme (EPTAS) for scheduling on uniform processors, i.e. finding a minimum length schedule for a set of n independent jobs on m processors with different speeds (a fundamental NP-hard scheduling problem). The previous best polynomial time approximation scheme (PTAS) by Hochbaum and Shmoys has a running time of (n/\epsilon)^{O(1/\epsilon^2)}. Our algorithm, based on a new mixed integer linear programming (MILP) formulation with a constant number of integral variables and an interesting rounding method, finds a schedule whose length is within a relative error $\epsilon$ of the optimum, and has running time 2^{O(1/\epsilon^2 \log(1/\epsilon)^3)} + poly(n)

Fast divide-and-conquer algorithms for preemptive scheduling problems with controllable processing times – A polymatroid optimization approach

We consider a variety of preemptive scheduling problems with controllable processing times on a single machine and on identical/uniform parallel machines, where the objective is to minimize the total compression cost. In this paper, we propose fast divide-and-conquer algorithms for these scheduling problems. Our approach is based on the observation that each scheduling problem we discuss can be formulated as a polymatroid optimization problem. We develop a novel divide-and-conquer technique for the polymatroid optimization problem and then apply it to each scheduling problem. We show that each scheduling problem can be solved in O(Tfeas(n) log n) time by using our divide-and-conquer technique, where n is the number of jobs and Tfeas(n) denotes the time complexity of the corresponding feasible scheduling problem with n jobs. This approach yields faster algorithms for most of the scheduling problems discussed in this paper

Sequencing wild and cultivated cassava and related species reveals extensive interspecific hybridization and genetic diversity

Cassava (Manihot esculenta) provides calories and nutrition for more than half a billion people. It was domesticated by native Amazonian peoples through cultivation of the wild progenitor M. esculenta ssp. flabellifolia and is now grown in tropical regions worldwide. Here we provide a high-quality genome assembly for cassava with improved contiguity, linkage, and completeness; almost 97% of genes are anchored to chromosomes. We find that paleotetraploidy in cassava is shared with the related rubber tree Hevea, providing a resource for comparative studies. We also sequence a global collection of 58 Manihot accessions, including cultivated and wild cassava accessions and related species such as Ceará or India rubber (M. glaziovii), and genotype 268 African cassava varieties. We find widespread interspecific admixture, and detect the genetic signature of past cassava breeding programs. As a clonally propagated crop, cassava is especially vulnerable to pathogens and abiotic stresses. This genomic resource will inform future genome-enabled breeding efforts to improve this staple crop

New hadrons as ultra-high energy cosmic rays

Ultra-high energy cosmic ray (UHECR) protons produced by uniformly distributed astrophysical sources contradict the energy spectrum measured by both the AGASA and HiRes experiments, assuming the small scale clustering of UHECR observed by AGASA is caused by point-like sources. In that case, the small number of sources leads to a sharp exponential cutoff at the energy E<10^{20} eV in the UHECR spectrum. New hadrons with mass 1.5-3 GeV can solve this cutoff problem. For the first time we discuss the production of such hadrons in proton collisions with infrared/optical photons in astrophysical sources. This production mechanism, in contrast to proton-proton collisions, requires the acceleration of protons only to energies E<10^{21} eV. The diffuse gamma-ray and neutrino fluxes in this model obey all existing experimental limits. We predict large UHE neutrino fluxes well above the sensitivity of the next generation of high-energy neutrino experiments. As an example we study hadrons containing a light bottom squark. These models can be tested by accelerator experiments, UHECR observatories and neutrino telescopes.Comment: 17 pages, revtex style; v2: shortened, as to appear in PR

Abundances of the elements in the solar system

A review of the abundances and condensation temperatures of the elements and their nuclides in the solar nebula and in chondritic meteorites. Abundances of the elements in some neighboring stars are also discussed.Comment: 42 pages, 11 tables, 8 figures, chapter, In Landolt- B\"ornstein, New Series, Vol. VI/4B, Chap. 4.4, J.E. Tr\"umper (ed.), Berlin, Heidelberg, New York: Springer-Verlag, p. 560-63

Global relationships in tree functional traits

Due to massive energetic investments in woody support structures, trees are subject to unique physiological, mechanical, and ecological pressures not experienced by herbaceous plants. Despite a wealth of studies exploring trait relationships across the entire plant kingdom, the dominant traits underpinning these unique aspects of tree form and function remain unclear. Here, by considering 18 functional traits, encompassing leaf, seed, bark, wood, crown, and root characteristics, we quantify the multidimensional relationships in tree trait expression. We find that nearly half of trait variation is captured by two axes: one reflecting leaf economics, the other reflecting tree size and competition for light. Yet these orthogonal axes reveal strong environmental convergence, exhibiting correlated responses to temperature, moisture, and elevation. By subsequently exploring multidimensional trait relationships, we show that the full dimensionality of trait space is captured by eight distinct clusters, each reflecting a unique aspect of tree form and function. Collectively, this work identifies a core set of traits needed to quantify global patterns in functional biodiversity, and it contributes to our fundamental understanding of the functioning of forests worldwide.Environmental Biolog

Velocity-space sensitivity of the time-of-flight neutron spectrometer at JET

The velocity-space sensitivities of fast-ion diagnostics are often described by so-called weight functions. Recently, we formulated weight functions showing the velocity-space sensitivity of the often dominant beam-target part of neutron energy spectra. These weight functions for neutron emission spectrometry (NES) are independent of the particular NES diagnostic. Here we apply these NES weight functions to the time-of-flight spectrometer TOFOR at JET. By taking the instrumental response function of TOFOR into account, we calculate time-of-flight NES weight functions that enable us to directly determine the velocity-space sensitivity of a given part of a measured time-of-flight spectrum from TOFOR

Relationship of edge localized mode burst times with divertor flux loop signal phase in JET

A phase relationship is identified between sequential edge localized modes (ELMs) occurrence times in a set of H-mode tokamak plasmas to the voltage measured in full flux azimuthal loops in the divertor region. We focus on plasmas in the Joint European Torus where a steady H-mode is sustained over several seconds, during which ELMs are observed in the Be II emission at the divertor. The ELMs analysed arise from intrinsic ELMing, in that there is no deliberate intent to control the ELMing process by external means. We use ELM timings derived from the Be II signal to perform direct time domain analysis of the full flux loop VLD2 and VLD3 signals, which provide a high cadence global measurement proportional to the voltage induced by changes in poloidal magnetic flux. Specifically, we examine how the time interval between pairs of successive ELMs is linked to the time-evolving phase of the full flux loop signals. Each ELM produces a clear early pulse in the full flux loop signals, whose peak time is used to condition our analysis. The arrival time of the following ELM, relative to this pulse, is found to fall into one of two categories: (i) prompt ELMs, which are directly paced by the initial response seen in the flux loop signals; and (ii) all other ELMs, which occur after the initial response of the full flux loop signals has decayed in amplitude. The times at which ELMs in category (ii) occur, relative to the first ELM of the pair, are clustered at times when the instantaneous phase of the full flux loop signal is close to its value at the time of the first ELM