Low-complexity algorithms for sequencing jobs with a fixed number of job-classes

In this paper we consider the problem of scheduling n jobs such that makespan is minimized. It is assumed that the jobs can be divided into K job-classes and that the change-over time between two consecutive jobs depends on the job-classes to which the two jobs belong. In this setting, we discuss the one machine scheduling problem with arbitrary processing times and the parallel machines scheduling problem with identical processing times. In both cases it is assumed that the number of job-classes K is fixed. By using an appropriate integer programming formulation with a fixed number of variables and constraints, it is shown that these two problems are solvable in polynomial time. For the one machine scheduling case it is shown that the complexity of our algorithm is linear in the number of jobs n. Moreover, if the problem is encoded according to the high multiplicity model of Hochbaum and Shamir, the time complexity of the algorithm is shown to be a polynomial in log n. In the parallel machine scheduling case, it is shown that if the number of machines is fixed the same results hold. Copyrigh

Soil networks become more connected and take up more carbon as nature restoration progresses

Soil organisms have an important role in aboveground community dynamics and ecosystem functioning in terrestrial ecosystems. However, most studies have considered soil biota as a black box or focussed on specific groups, whereas little is known about entire soil networks. Here we show that during the course of nature restoration on abandoned arable land a compositional shift in soil biota, preceded by tightening of the belowground networks, corresponds with enhanced efficiency of carbon uptake. In mid- and long-term abandoned field soil, carbon uptake by fungi increases without an increase in fungal biomass or shift in bacterial-to-fungal ratio. The implication of our findings is that during nature restoration the efficiency of nutrient cycling and carbon uptake can increase by a shift in fungal composition and/or fungal activity. Therefore, we propose that relationships between soil food web structure and carbon cycling in soils need to be reconsidered

Genome-wide association study identifies 32 novel breast cancer susceptibility loci from overall and subtype-specific analyses.

Breast cancer susceptibility variants frequently show heterogeneity in associations by tumor subtype1-3. To identify novel loci, we performed a genome-wide association study including 133,384 breast cancer cases and 113,789 controls, plus 18,908 BRCA1 mutation carriers (9,414 with breast cancer) of European ancestry, using both standard and novel methodologies that account for underlying tumor heterogeneity by estrogen receptor, progesterone receptor and human epidermal growth factor receptor 2 status and tumor grade. We identified 32 novel susceptibility loci (P < 5.0 × 10-8), 15 of which showed evidence for associations with at least one tumor feature (false discovery rate < 0.05). Five loci showed associations (P < 0.05) in opposite directions between luminal and non-luminal subtypes. In silico analyses showed that these five loci contained cell-specific enhancers that differed between normal luminal and basal mammary cells. The genetic correlations between five intrinsic-like subtypes ranged from 0.35 to 0.80. The proportion of genome-wide chip heritability explained by all known susceptibility loci was 54.2% for luminal A-like disease and 37.6% for triple-negative disease. The odds ratios of polygenic risk scores, which included 330 variants, for the highest 1% of quantiles compared with middle quantiles were 5.63 and 3.02 for luminal A-like and triple-negative disease, respectively. These findings provide an improved understanding of genetic predisposition to breast cancer subtypes and will inform the development of subtype-specific polygenic risk scores

The 'long' 16th century : a key period of animal husbandry change in England

Although many historians have extensively discussed the agricultural history of England between the Late Middle Ages and the Modern Era, this period of crucial changes has received less attention by archaeologists. In this paper, zooarchaeological evidence dated between the Late Middle Ages and the Early Modern period is analysed to investigate changes in animal husbandry during the ‘long’ sixteenth century. The size and shape of the main domestic animals (cattle, sheep, pig and chicken) is explored through biometrical data and discussed in line with evidence of taxonomic frequencies, ageing and sex ratios. Data from 12 sites with relevant chronologies and located in different areas of the country are considered. The results show that, although a remarkable size increase of animals occurred in England throughout the post-medieval period, much of this improvement occurred as early as the sixteenth century. The nature and causes of such improvement are discussed, with the aim of understanding the development of Early Modern farming and the foundations of the so-called Agricultural Revolution