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

Phase structure of black branes in grand canonical ensemble

This is a companion paper of our previous work [1] where we studied the thermodynamics and phase structure of asymptotically flat black $p$-branes in a cavity in arbitrary dimensions $D$ in a canonical ensemble. In this work we study the thermodynamics and phase structure of the same in a grand canonical ensemble. Since the boundary data in two cases are different (for the grand canonical ensemble boundary potential is fixed instead of the charge as in canonical ensemble) the stability analysis and the phase structure in the two cases are quite different. In particular, we find that there exists an analog of one-variable analysis as in canonical ensemble, which gives the same stability condition as the rather complicated known (but generalized from black holes to the present case) two-variable analysis. When certain condition for the fixed potential is satisfied, the phase structure of charged black $p$-branes is in some sense similar to that of the zero charge black $p$-branes in canonical ensemble up to a certain temperature. The new feature in the present case is that above this temperature, unlike the zero-charge case, the stable brane phase no longer exists and `hot flat space' is the stable phase here. In the grand canonical ensemble there is an analog of Hawking-Page transition, even for the charged black $p$-brane, as opposed to the canonical ensemble. Our study applies to non-dilatonic as well as dilatonic black $p$-branes in $D$ space-time dimensions.Comment: 32 pages, 2 figures, various points refined, discussion expanded, references updated, typos corrected, published in JHEP 1105:091,201

Phase transitions and critical behavior of black branes in canonical ensemble

We study the thermodynamics and phase structure of asymptotically flat non-dilatonic as well as dilatonic black branes in a cavity in arbitrary dimensions ($D$). We consider the canonical ensemble and so the charge inside the cavity and the temperature at the wall are fixed. We analyze the stability of the black brane equilibrium states and derive the phase structures. For the zero charge case we find an analog of Hawking-Page phase transition for these black branes in arbitrary dimensions. When the charge is non-zero, we find that below a critical value of the charge, the phase diagram has a line of first-order phase transition in a certain range of temperatures which ends up at a second order phase transition point (critical point) as the charge attains the critical value. We calculate the critical exponents at that critical point. Although our discussion is mainly concerned with the non-dilatonic branes, we show how it easily carries over to the dilatonic branes as well.Comment: 37 pages, 6 figures, the validity of using the effective action discussed, references adde

Acute lyme infection presenting with amyopathic dermatomyositis and rapidly fatal interstitial pulmonary fibrosis: a case report

<p>Abstract</p> <p>Introduction</p> <p>Dermatomyositis has been described in the setting of lyme infection in only nine previous case reports. Although lyme disease is known to induce typical clinical findings that are observed in various collagen vascular diseases, to our knowledge, we believe that our case is the first presentation of acute lyme disease associated with amyopathic dermatomyositis, which was then followed by severe and fatal interstitial pulmonary fibrosis only two months later.</p> <p>Case presentation</p> <p>We present a case of a 64-year-old African-American man with multiple medical problems who was diagnosed with acute lyme infection after presenting with the pathognomonic rash and confirmatory serology. In spite of appropriate antimicrobial therapy for lyme infection, he developed unexpected amyopathic dermatomyositis and then interstitial lung disease.</p> <p>Conclusions</p> <p>This case illustrates a potential for lyme disease to produce clinical syndromes that may be indistinguishable from primary connective tissue diseases. An atypical and sequential presentation (dermatomyositis and interstitial lung disease) of a common disease (lyme infection) is discussed. This case illustrates that in patients who are diagnosed with lyme infection who subsequently develop atypical muscular, respiratory or other systemic complaints, the possibility of severe rheumatological and pulmonary complications should be considered.</p

Ковчег Ноя: рух матерії у Сонячній системі та на ядерних рівнях Землі

У Стародавньому світі пророку Мойсею було відкрито таємницю створення світу. Як науковий геній свого часу, Мойсей зашифрував у алегоричну форму в родоводі Адама і Потопі прикладну науку про будову ядра Землі, Сонячної системи і рухи космічної водневої і сонячної вуглецевої матерій (енергій) крізь Землю.В Древнем мире пророку Моисею была открыта тайна создания мира. Как научный гений своего времени Моисей зашифровал в форму аллегории в родословной Адама и Потопе прикладную науку о строении ядра Земли, Солнечной системы и движениях космической водородной и солнечной углеродной материи (энергии) сквозь Землю.In the Ancient history the mystery of the Creation of the world was revealed to the Prophet Moses. As a scientific genius of that époque Moses codified in allegoric way in the genealogy of Adam and The Flood the applied science on the structure of the Earth core, of the Solar System and motion of cosmic hydrogenous and solar carbonic substance (energy) through the Earth

A meta-analytic review of stand-alone interventions to improve body image

Objective Numerous stand-alone interventions to improve body image have been developed. The present review used meta-analysis to estimate the effectiveness of such interventions, and to identify the specific change techniques that lead to improvement in body image. Methods The inclusion criteria were that (a) the intervention was stand-alone (i.e., solely focused on improving body image), (b) a control group was used, (c) participants were randomly assigned to conditions, and (d) at least one pretest and one posttest measure of body image was taken. Effect sizes were meta-analysed and moderator analyses were conducted. A taxonomy of 48 change techniques used in interventions targeted at body image was developed; all interventions were coded using this taxonomy. Results The literature search identified 62 tests of interventions (N = 3,846). Interventions produced a small-to-medium improvement in body image (d+ = 0.38), a small-to-medium reduction in beauty ideal internalisation (d+ = -0.37), and a large reduction in social comparison tendencies (d+ = -0.72). However, the effect size for body image was inflated by bias both within and across studies, and was reliable but of small magnitude once corrections for bias were applied. Effect sizes for the other outcomes were no longer reliable once corrections for bias were applied. Several features of the sample, intervention, and methodology moderated intervention effects. Twelve change techniques were associated with improvements in body image, and three techniques were contra-indicated. Conclusions The findings show that interventions engender only small improvements in body image, and underline the need for large-scale, high-quality trials in this area. The review identifies effective techniques that could be deployed in future interventions

Structural correlations in bacterial metabolic networks

<p>Abstract</p> <p>Background</p> <p>Evolution of metabolism occurs through the acquisition and loss of genes whose products acts as enzymes in metabolic reactions, and from a presumably simple primordial metabolism the organisms living today have evolved complex and highly variable metabolisms. We have studied this phenomenon by comparing the metabolic networks of 134 bacterial species with known phylogenetic relationships, and by studying a neutral model of metabolic network evolution.</p> <p>Results</p> <p>We consider the 'union-network' of 134 bacterial metabolisms, and also the union of two smaller subsets of closely related species. Each reaction-node is tagged with the number of organisms it belongs to, which we denote organism degree (OD), a key concept in our study. Network analysis shows that common reactions are found at the centre of the network and that the average OD decreases as we move to the periphery. Nodes of the same OD are also more likely to be connected to each other compared to a random OD relabelling based on their occurrence in the real data. This trend persists up to a distance of around five reactions. A simple growth model of metabolic networks is used to investigate the biochemical constraints put on metabolic-network evolution. Despite this seemingly drastic simplification, a 'union-network' of a collection of unrelated model networks, free of any selective pressure, still exhibit similar structural features as their bacterial counterpart.</p> <p>Conclusions</p> <p>The OD distribution quantifies topological properties of the evolutionary history of bacterial metabolic networks, and lends additional support to the importance of horizontal gene transfer during bacterial metabolic evolution where new reactions are attached at the periphery of the network. The neutral model of metabolic network growth can reproduce the main features of real networks, but we observe that the real networks contain a smaller common core, while they are more similar at the periphery of the network. This suggests that natural selection and biochemical correlations can act both to diversify and to narrow down metabolic evolution.</p

A network perspective on the topological importance of enzymes and their phylogenetic conservation

<p>Abstract</p> <p>Background</p> <p>A metabolic network is the sum of all chemical transformations or reactions in the cell, with the metabolites being interconnected by enzyme-catalyzed reactions. Many enzymes exist in numerous species while others occur only in a few. We ask if there are relationships between the phylogenetic profile of an enzyme, or the number of different bacterial species that contain it, and its topological importance in the metabolic network. Our null hypothesis is that phylogenetic profile is independent of topological importance. To test our null hypothesis we constructed an enzyme network from the KEGG (Kyoto Encyclopedia of Genes and Genomes) database. We calculated three network indices of topological importance: the degree or the number of connections of a network node; closeness centrality, which measures how close a node is to others; and betweenness centrality measuring how frequently a node appears on all shortest paths between two other nodes.</p> <p>Results</p> <p>Enzyme phylogenetic profile correlates best with betweenness centrality and also quite closely with degree, but poorly with closeness centrality. Both betweenness and closeness centralities are non-local measures of topological importance and it is intriguing that they have contrasting power of predicting phylogenetic profile in bacterial species. We speculate that redundancy in an enzyme network may be reflected by betweenness centrality but not by closeness centrality. We also discuss factors influencing the correlation between phylogenetic profile and topological importance.</p> <p>Conclusion</p> <p>Our analysis falsifies the hypothesis that phylogenetic profile of enzymes is independent of enzyme network importance. Our results show that phylogenetic profile correlates better with degree and betweenness centrality, but less so with closeness centrality. Enzymes that occur in many bacterial species tend to be those that have high network importance. We speculate that this phenomenon originates in mechanisms driving network evolution. Closeness centrality reflects phylogenetic profile poorly. This is because metabolic networks often consist of distinct functional modules and some are not in the centre of the network. Enzymes in these peripheral parts of a network might be important for cell survival and should therefore occur in many bacterial species. They are, however, distant from other enzymes in the same network.</p

Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe

In three spacetime dimensions, general relativity drastically simplifies, becoming a ``topological'' theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are still present. In this review, I summarize the rather large body of work that has gone towards quantizing (2+1)-dimensional vacuum gravity in the setting of a spatially closed universe.Comment: 61 pages, draft of review for Living Reviews; comments, criticisms, additions, missing references welcome; v2: minor changes, added reference