An EPTAS for Scheduling on Unrelated Machines of Few Different Types

In the classical problem of scheduling on unrelated parallel machines, a set of jobs has to be assigned to a set of machines. The jobs have a processing time depending on the machine and the goal is to minimize the makespan, that is the maximum machine load. It is well known that this problem is NP-hard and does not allow polynomial time approximation algorithms with approximation guarantees smaller than $1.5$ unless P$=$NP. We consider the case that there are only a constant number $K$ of machine types. Two machines have the same type if all jobs have the same processing time for them. This variant of the problem is strongly NP-hard already for $K=1$. We present an efficient polynomial time approximation scheme (EPTAS) for the problem, that is, for any $\varepsilon > 0$ an assignment with makespan of length at most $(1+\varepsilon)$ times the optimum can be found in polynomial time in the input length and the exponent is independent of $1/\varepsilon$. In particular we achieve a running time of $2^{\mathcal{O}(K\log(K) \frac{1}{\varepsilon}\log^4 \frac{1}{\varepsilon})}+\mathrm{poly}(|I|)$, where $|I|$ denotes the input length. Furthermore, we study three other problem variants and present an EPTAS for each of them: The Santa Claus problem, where the minimum machine load has to be maximized; the case of scheduling on unrelated parallel machines with a constant number of uniform types, where machines of the same type behave like uniformly related machines; and the multidimensional vector scheduling variant of the problem where both the dimension and the number of machine types are constant. For the Santa Claus problem we achieve the same running time. The results are achieved, using mixed integer linear programming and rounding techniques

Associations of eczema phenotypes with emotional and behavioural problems from birth until school age. The Generation R Study.

Background Eczema phenotypes and emotional and behavioural problems are highly prevalent in childhood, but their mutual relationship is not fully clear. Objectives To examine the associations of eczema phenotypes with school-age emotional and behavioural problems, and the bidirectional associations of eczema and emotional and behavioural problems from birth until 10 years. Methods This study among 5265 individuals was embedded in a prospective population-based cohort study. Never, early transient, mid-transient, late transient and persistent eczema phenotypes were identified based on parent-reported, physician-diagnosed eczema from age 6 months until 10 years. Emotional (internalizing) and behavioural (externalizing) problems were measured repeatedly using the Child Behavior Checklist from age 15 to 10 years. Cross-lagged models were applied for bidirectional analyses. Results All eczema phenotypes were associated with more internalizing problems and attention problems at age 10 years, compared with never having eczema: range of Z-score differences 014 [95% confidence interval (CI) 001–027] to 039 (95% CI 018–060). Children with early transient eczema had more aggressive behaviour symptoms at age 10 years (Z = 016, 95% CI 005–027). Bidirectional analysis showed that eczema at 0–2 years was associated with more internalizing and externalizing problems at ages 3–6 and 10 years, while, inversely, only internalizing problems at 0–2 years were associated with an increased risk of eczema at age 10 years. Conclusions Eczema phenotypes are very modestly associated with more somatic symptoms and attention problems at school age. Early transient eczema is associated with more aggressive behaviour symptoms. Directional effects seem to occur from early-life eczema to later-life internalizing and externalizing problems, rather than the reverse

Geriatric Medical Care in the Area of the Regional Association Westphalia-Lippe Dokkyo Medical University 5th grade

Dokkyo Medical University 5th YearDokkyo Medical University 5th YearDokkyo Medical University 5th YearDokkyo Medical University 5th YearDokkyo Medical University 5th YearDokkyo Medical University 5th YearDokkyo MedicalUniversity, Division of Languages and HumanitiesWestphalian Wilhelms University, IfASWestphalian Wilhelms University, General PracticeKlinik Maria Frieden, Abt. f. GeriatrieDokkyo Medical University, Office for German-Japanese CooperationDokkyo Medical University, Office for German-Japanese Cooperatio

Associations between Health Effects and Particulate Matter and Black Carbon in Subjects with Respiratory Disease

We measured fractional exhaled nitric oxide (FE(NO)), spirometry, blood pressure, oxygen saturation of the blood (SaO(2)), and pulse rate in 16 older subjects with asthma or chronic obstructive pulmonary disease (COPD) in Seattle, Washington. Data were collected daily for 12 days. We simultaneously collected PM(10) and PM(2.5) (particulate matter ≤10 μm or ≤2.5 μm, respectively) filter samples at a central outdoor site, as well as outside and inside the subjects’ homes. Personal PM(10) filter samples were also collected. All filters were analyzed for mass and light absorbance. We analyzed within-subject associations between health outcomes and air pollution metrics using a linear mixed-effects model with random intercept, controlling for age, ambient relative humidity, and ambient temperature. For the 7 subjects with asthma, a 10 μg/m(3) increase in 24-hr average outdoor PM(10) and PM(2.5) was associated with a 5.9 [95% confidence interval (CI), 2.9–8.9] and 4.2 ppb (95% CI, 1.3–7.1) increase in FE(NO), respectively. A 1 μg/m(3) increase in outdoor, indoor, and personal black carbon (BC) was associated with increases in FE(NO) of 2.3 ppb (95% CI, 1.1–3.6), 4.0 ppb (95% CI, 2.0–5.9), and 1.2 ppb (95% CI, 0.2–2.2), respectively. No significant association was found between PM or BC measures and changes in spirometry, blood pressure, pulse rate, or SaO(2) in these subjects. Results from this study indicate that FE(NO) may be a more sensitive marker of PM exposure than traditional health outcomes and that particle-associated BC is useful for examining associations between primary combustion constituents of PM and health outcomes

How does reviewing the evidence change veterinary surgeons' beliefs regarding the treatment of ovine footrot? A quantitative and qualitative study

Footrot is a widespread, infectious cause of lameness in sheep, with major economic and welfare costs. The aims of this research were: (i) to quantify how veterinary surgeons’ beliefs regarding the efficacy of two treatments for footrot changed following a review of the evidence (ii) to obtain a consensus opinion following group discussions (iii) to capture complementary qualitative data to place their beliefs within a broader clinical context. Grounded in a Bayesian statistical framework, probabilistic elicitation (roulette method) was used to quantify the beliefs of eleven veterinary surgeons during two one-day workshops. There was considerable heterogeneity in veterinary surgeons’ beliefs before they listened to a review of the evidence. After hearing the evidence, seven participants quantifiably changed their beliefs. In particular, two participants who initially believed that foot trimming with topical oxytetracycline was the better treatment, changed to entirely favour systemic and topical oxytetracycline instead. The results suggest that a substantial amount of the variation in beliefs related to differences in veterinary surgeons’ knowledge of the evidence. Although considerable differences in opinion still remained after the evidence review, with several participants having non-overlapping 95% credible intervals, both groups did achieve a consensus opinion. Two key findings from the qualitative data were: (i) veterinary surgeons believed that farmers are unlikely to actively seek advice on lameness, suggesting a proactive veterinary approach is required (ii) more attention could be given to improving the way in which veterinary advice is delivered to farmers. In summary this study has: (i) demonstrated a practical method for probabilistically quantifying how veterinary surgeons’ beliefs change (ii) revealed that the evidence that currently exists is capable of changing veterinary opinion (iii) suggested that improved transfer of research knowledge into veterinary practice is needed (iv) identified some potential obstacles to the implementation of veterinary advice by farmers

Whole home exercise intervention for depression in older care home residents (the OPERA study) : a process evaluation

Background: The ‘Older People’s Exercise intervention in Residential and nursing Accommodation’ (OPERA) cluster randomised trial evaluated the impact of training for care home staff together with twice-weekly, physiotherapist-led exercise classes on depressive symptoms in care home residents, but found no effect. We report a process evaluation exploring potential explanations for the lack of effect. Methods: The OPERA trial included over 1,000 residents in 78 care homes in the UK. We used a mixed methods approach including quantitative data collected from all homes. In eight case study homes, we carried out repeated periods of observation and interviews with residents, care staff and managers. At the end of the intervention, we held focus groups with OPERA research staff. We reported our first findings before the trial outcome was known. Results: Homes showed large variations in activity at baseline and throughout the trial. Overall attendance rate at the group exercise sessions was low (50%). We considered two issues that might explain the negative outcome: whether the intervention changed the culture of the homes, and whether the residents engaged with the intervention. We found low levels of staff training, few home champions for the intervention and a culture that prioritised protecting residents from harm over encouraging activity. The trial team delivered 3,191 exercise groups but only 36% of participants attended at least 1 group per week and depressed residents attended significantly fewer groups than those who were not depressed. Residents were very frail and therefore most groups only included seated exercises. Conclusions: The intervention did not change the culture of the homes and, in the case study homes, activity levels did not change outside the exercise groups. Residents did not engage in the exercise groups at a sufficient level, and this was particularly true for those with depressive symptoms at baseline. The physical and mental frailty of care home residents may make it impossible to deliver a sufficiently intense exercise intervention to impact on depressive symptoms

Individual differences in metabolomics: individualised responses and between-metabolite relationships

Many metabolomics studies aim to find ‘biomarkers’: sets of molecules that are consistently elevated or decreased upon experimental manipulation. Biological effects, however, often manifest themselves along a continuum of individual differences between the biological replicates in the experiment. Such differences are overlooked or even diminished by methods in standard use for metabolomics, although they may contain a wealth of information on the experiment. Properly understanding individual differences is crucial for generating knowledge in fields like personalised medicine, evolution and ecology. We propose to use simultaneous component analysis with individual differences constraints (SCA-IND), a data analysis method from psychology that focuses on these differences. This method constructs axes along the natural biochemical differences between biological replicates, comparable to principal components. The model may shed light on changes in the individual differences between experimental groups, but also on whether these differences correspond to, e.g., responders and non-responders or to distinct chemotypes. Moreover, SCA-IND reveals the individuals that respond most to a manipulation and are best suited for further experimentation. The method is illustrated by the analysis of individual differences in the metabolic response of cabbage plants to herbivory. The model reveals individual differences in the response to shoot herbivory, where two ‘response chemotypes’ may be identified. In the response to root herbivory the model shows that individual plants differ strongly in response dynamics. Thereby SCA-IND provides a hitherto unavailable view on the chemical diversity of the induced plant response, that greatly increases understanding of the system

Strain-controlled criticality governs the nonlinear mechanics of fibre networks

Disordered fibrous networks are ubiquitous in nature as major structural components of living cells and tissues. The mechanical stability of networks generally depends on the degree of connectivity: only when the average number of connections between nodes exceeds the isostatic threshold are networks stable (Maxwell, J. C., Philosophical Magazine 27, 294 (1864)). Upon increasing the connectivity through this point, such networks undergo a mechanical phase transition from a floppy to a rigid phase. However, even sub-isostatic networks become rigid when subjected to sufficiently large deformations. To study this strain-controlled transition, we perform a combination of computational modeling of fibre networks and experiments on networks of type I collagen fibers, which are crucial for the integrity of biological tissues. We show theoretically that the development of rigidity is characterized by a strain-controlled continuous phase transition with signatures of criticality. Our experiments demonstrate mechanical properties consistent with our model, including the predicted critical exponents. We show that the nonlinear mechanics of collagen networks can be quantitatively captured by the predictions of scaling theory for the strain-controlled critical behavior over a wide range of network concentrations and strains up to failure of the material