Machine speed scaling by adapting methods for convex optimization with submodular constraints

In this paper, we propose a new methodology for the speed-scaling problem based on its link to scheduling with controllable processing times and submodular optimization. It results in faster algorithms for traditional speed-scaling models, characterized by a common speed/energy function. Additionally, it efficiently handles the most general models with job-dependent speed/energy functions with single and multiple machines. To the best of our knowledge, this has not been addressed prior to this study. In particular, the general version of the single-machine case is solvable by the new technique in O(n2) time

The evolutionary demography of duplicate genes

Key words: gene duplication, genome evolution, genome size Although gene duplication has generally been viewed as a necessary source of material for the origin of evolu-tionary novelties, the rates of origin, loss, and preservation of gene duplicates are not well understood. Applying steady-state demographic techniques to the age distributions of duplicate genes censused in seven completely sequenced genomes, we estimate the average rate of duplication of a eukaryotic gene to be on the order of 0.01/ gene/million years, which is of the same order of magnitude as the mutation rate per nucleotide site. However, the average half-life of duplicate genes is relatively small, on the order of 4.0 million years. Significant inter-specific variation in these rates appears to be responsible for differences in species-specific genome sizes that arise as a consequence of a quasi-equilibrium birth-death process. Most duplicated genes experience a brief period of relaxed selection early in their history and a minority exhibit the signature of directional selection, but those that survive more than a few million years eventually experience strong purifying selection. Thus, although most theoretical work on the gene-duplication process has focused on issues related to adaptive evolution, the origin of a new function appears to be a very rare fate for a duplicate gene. A more significant role of the duplication process may be the generation of microchromosomal rearrangements through reciprocal silencing of alternativ

Competitive Equilibrium and Trading Networks: A Network Flow Approach

Under full substitutability of preferences, it has been shown that a competitive equilibrium exists in trading networks, and is equivalent (after a restriction to equilibrium trades) to (chain) stable outcomes. In this paper, we formulate the problem of finding an efficient outcome as a generalized submodular flow problem on a suitable network. Equivalence with seemingly weaker notions of stability follows directly from the optimality conditions, in particular the absence of improvement cycles in the flow problem. Our formulation yields strongly polynomial algorithms for finding competitive equilibria in trading networks, and testing (chain) stability

A Comparison of Phylogenetic Network Methods Using Computer Simulation

Background: We present a series of simulation studies that explore the relative performance of several phylogenetic network approaches (statistical parsimony, split decomposition, union of maximum parsimony trees, neighbor-net, simulated history recombination upper bound, median-joining, reduced median joining and minimum spanning network) compared to standard tree approaches, (neighbor-joining and maximum parsimony) in the presence and absence of recombination. Principal Findings: In the absence of recombination, all methods recovered the correct topology and branch lengths nearly all of the time when the substitution rate was low, except for minimum spanning networks, which did considerably worse. At a higher substitution rate, maximum parsimony and union of maximum parsimony trees were the most accurate. With recombination, the ability to infer the correct topology was halved for all methods and no method could accurately estimate branch lengths. Conclusions: Our results highlight the need for more accurate phylogenetic network methods and the importance of detecting and accounting for recombination in phylogenetic studies. Furthermore, we provide useful information for choosing a network algorithm and a framework in which to evaluate improvements to existing methods and nove

Models and algorithms for energy-efficient scheduling with immediate start of jobs

We study a scheduling model with speed scaling for machines and the immediate start requirement for jobs. Speed scaling improves the system performance, but incurs the energy cost. The immediate start condition implies that each job should be started exactly at its release time. Such a condition is typical for modern Cloud computing systems with abundant resources. We consider two cost functions, one that represents the quality of service and the other that corresponds to the cost of running. We demonstrate that the basic scheduling model to minimize the aggregated cost function with n jobs is solvable in O(nlogn) time in the single-machine case and in O(n²m) time in the case of m parallel machines. We also address additional features, e.g., the cost of job rejection or the cost of initiating a machine. In the case of a single machine, we present algorithms for minimizing one of the cost functions subject to an upper bound on the value of the other, as well as for finding a Pareto-optimal solution

Sex-related changes in cardiac function following myocardial infarction in mice

Recent awareness of cardiovascular diseases as a number one killer of the middle-aged women has prompted interest in sex differences leading to heart failure (HF). Therefore, we evaluated cardiac function in female and male mice following myocardial infarction (MI) using the Millar pressure-volume (P-V) conductance system in vivo, at time points corresponding to early (2 wk), late compensatory hypertrophy (4 wk), and decompensation (10 wk) to HF. A significant deterioration of the load dependent and independent hemodynamic measurements occurred in both female and male mice during the early phase of hypertrophy. Later, compensatory hypertrophy was marked by a normalization of volumes to control levels in females compared with males. The most notable differences between sexes occurred in the measurements of cardiac contractility during the decompensation to HF. In females, there was a significant improvement in contractility compared with males, which was apparent in the load-independent measurements of preload recruitable stroke work (10 wk post-MI, female = 48.7 ± 8.0 vs. male = 25.2 ± 1.8 mmHg, P < 0.05) and maximum dP/dt vs. maximum end-diastolic volume (10 wk post-MI, female=359 ± 58 vs. male=149 ± 28 mmHg·s−1·μl−1, P < 0.05). Despite these differences, there were no differences in the heart weight to body weight ratio and infarct size between the sexes. These data demonstrate that compensatory hypertrophy is associated with an improvement in contractility and a delayed decompensation to HF in females. However, compensatory hypertrophy in males appears to be undermined by a steady decline in contractility associated with decompensation to HF

Long-term stability of the inversion process for sugar and ethanol production in an existing Japanese sugar mill

In order to utilize sugarcane with a high reducing-sugar content as the raw material for sugar production, a new technology called the ‘inversion process’ has been developed. This new technology aims to enhance raw sugar yield via removal of reducing sugars through selective ethanol fermentation using an invertase-defective yeast, prior to sugar crystallization. To assess the feasibility of the inversion process technology in an existing sugar mill, a test of continuous and repeated-batch fermentation using clear juice was undertaken at a pilot-scale facility at the Shinko Sugar Mill in Japan. Batch fermentation trials were performed at 35°C for 1.5-3 h and repeated 70 times in a 2000 L fermenter using the same culture of invertase-defective yeast strain GYK-10. To confirm the long-term stability of the selective fermentation, the concentrations of saccharides and ethanol in the fermenter were measured every hour and the residual sucrose ratio and the reducing sugars removal ratio were calculated. Each batch was checked for the presence of contaminating bacteria. The results showed that 88.4% of reducing sugars were converted to ethanol and 99.5% of sucrose remained throughout the 70 consecutive batch fermentations. This indicates that the saccharometabolism selectivity of GYK-10 is stable. Although contamination by some microorganisms, such as Clostridium beijerinckii, Bacillus simplex, and Bacillus brevis, was observed, this had little influence on the fermentation outcomes. This paper reports on the feasibility of using the inversion process in an existing sugar mill