Single machine scheduling with controllable processing times by submodular optimization

In scheduling with controllable processing times the actual processing time of each job is to be chosen from the interval between the smallest (compressed or fully crashed) value and the largest (decompressed or uncrashed) value. In the problems under consideration, the jobs are processed on a single machine and the quality of a schedule is measured by two functions: the maximum cost (that depends on job completion times) and the total compression cost. Our main model is bicriteria and is related to determining an optimal trade-off between these two objectives. Additionally, we consider a pair of associated single criterion problems, in which one of the objective functions is bounded while the other one is to be minimized. We reduce the bicriteria problem to a series of parametric linear programs defined over the intersection of a submodular polyhedron with a box. We demonstrate that the feasible region is represented by a so-called base polyhedron and the corresponding problem can be solved by the greedy algorithm that runs two orders of magnitude faster than known previously. For each of the associated single criterion problems, we develop algorithms that deliver the optimum faster than it can be deduced from a solution to the bicriteria problem

Application of submodular optimization to single machine scheduling with controllable processing times subject to release dates and deadlines

In this paper, we study a scheduling problem on a single machine, provided that the jobs have individual release dates and deadlines, and the processing times are controllable. The objective is to find a feasible schedule that minimizes the total cost of reducing the processing times. We reformulate the problem in terms of maximizing a linear function over a submodular polyhedron intersected with a box. For the latter problem of submodular optimization, we develop a recursive decomposition algorithm and apply it to solving the single machine scheduling problem to achieve the best possible running time

The potential to narrow uncertainty in projections of stratospheric ozone over the 21st century

Future stratospheric ozone concentrations will be determined both by changes in the concentration of ozone depleting substances (ODSs) and by changes in stratospheric and tropospheric climate, including those caused by changes in anthropogenic greenhouse gases (GHGs). Since future economic development pathways and resultant emissions of GHGs are uncertain, anthropogenic climate change could be a significant source of uncertainty for future projections of stratospheric ozone. In this pilot study, using an "ensemble of opportunity" of chemistry-climate model (CCM) simulations, the contribution of scenario uncertainty from different plausible emissions pathways for ODSs and GHGs to future ozone projections is quantified relative to the contribution from model uncertainty and internal variability of the chemistry-climate system. For both the global, annual mean ozone concentration and for ozone in specific geographical regions, differences between CCMs are the dominant source of uncertainty for the first two-thirds of the 21st century, up-to and after the time when ozone concentrations return to 1980 values. In the last third of the 21st century, dependent upon the set of greenhouse gas scenarios used, scenario uncertainty can be the dominant contributor. This result suggests that investment in chemistry-climate modelling is likely to continue to refine projections of stratospheric ozone and estimates of the return of stratospheric ozone concentrations to pre-1980 levels

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

Attribution of observed changes in stratospheric ozone and temperature

Three recently-completed sets of simulations of multiple chemistry-climate models with greenhouse gases only, with all anthropogenic forcings, and with anthropogenic and natural forcings, allow the causes of observed stratospheric changes to be quantitatively assessed using detection and attribution techniques. The total column ozone response to halogenated ozone depleting substances and to natural forcings is detectable in observations, but the total column ozone response to greenhouse gas changes is not separately detectable. In the middle and upper stratosphere, simulated and observed SBUV/SAGE ozone changes are broadly consistent, and separate anthropogenic and natural responses are detectable in observations. The influence of ozone depleting substances and natural forcings can also be detected separately in observed lower stratospheric temperature, and the magnitudes of the simulated and observed responses to these forcings and to greenhouse gas changes are found to be consistent. In the mid and upper stratosphere the simulated natural and combined anthropogenic responses are detectable and consistent with observations, but the influences of greenhouse gases and ozone-depleting substances could not be separately detected in our analysis

Decomposition algorithms for submodular optimization with applications to parallel machine scheduling with controllable processing times

In this paper we present a decomposition algorithm for maximizing a linear function over a submodular polyhedron intersected with a box. Apart from this contribution to submodular optimization, our results extend the toolkit available in deterministic machine scheduling with controllable processing times. We demonstrate how this method can be applied to developing fast algorithms for minimizing total compression cost for preemptive schedules on parallel machines with respect to given release dates and a common deadline. Obtained scheduling algorithms are faster and easier to justify than those previously known in the scheduling literature

Faddeev Calculations of Proton-Deuteron Radiative Capture with Exchange Currents

pd capture processes at various energies have been analyzed based on solutions of 3N-Faddeev equations and using modern NN forces. The application of the Siegert theorem is compared to the explicit use of $\pi$- and $\rho$-like exchange currents connected to the AV18 NN interaction. Overall good agreement with cross sections and spin observables has been obtained but leaving room for improvement in some cases. Feasibility studies for 3NF's consistently included in the 3N continuum and the 3N bound state have been performed as well.Comment: Minor changes in notation, ps files for figure

The effect of atmospheric nudging on the stratospheric residual circulation in chemistry–climate models

We perform the first multi-model intercomparison of the impact of nudged meteorology on the stratospheric residual circulation using hindcast simulations from the Chemistry–Climate Model Initiative (CCMI). We examine simulations over the period 1980–2009 from seven models in which the meteorological fields are nudged towards a reanalysis dataset and compare these with their equivalent free-running simulations and the reanalyses themselves. We show that for the current implementations, nudging meteorology does not constrain the mean strength of the stratospheric residual circulation and that the inter-model spread is similar, or even larger, than in the free-running simulations. The nudged models generally show slightly stronger upwelling in the tropical lower stratosphere compared to the free-running versions and exhibit marked differences compared to the directly estimated residual circulation from the reanalysis dataset they are nudged towards. Downward control calculations applied to the nudged simulations reveal substantial differences between the climatological lower-stratospheric tropical upward mass flux (TUMF) computed from the modelled wave forcing and that calculated directly from the residual circulation. This explicitly shows that nudging decouples the wave forcing and the residual circulation so that the divergence of the angular momentum flux due to the mean motion is not balanced by eddy motions, as would typically be expected in the time mean. Overall, nudging meteorological fields leads to increased inter-model spread for most of the measures of the mean climatological stratospheric residual circulation assessed in this study. In contrast, the nudged simulations show a high degree of consistency in the inter-annual variability in the TUMF in the lower stratosphere, which is primarily related to the contribution to variability from the resolved wave forcing. The more consistent inter-annual variability in TUMF in the nudged models also compares more closely with the variability found in the reanalyses, particularly in boreal winter. We apply a multiple linear regression (MLR) model to separate the drivers of inter-annual and long-term variations in the simulated TUMF; this explains up to ∼75 % of the variance in TUMF in the nudged simulations. The MLR model reveals a statistically significant positive trend in TUMF for most models over the period 1980–2009. The TUMF trend magnitude is generally larger in the nudged models compared to their free-running counterparts, but the intermodel range of trends doubles from around a factor of 2 to a factor of 4 due to nudging. Furthermore, the nudged models generally do not match the TUMF trends in the reanalysis they are nudged towards for trends over different periods in the interval 1980–2009. Hence, we conclude that nudging does not strongly constrain long-term trends simulated by the chemistry–climate model (CCM) in the residual circulation. Our findings show that while nudged simulations may, by construction, produce accurate temperatures and realistic representations of fast horizontal transport, this is not typically the case for the slower zonal mean vertical transport in the stratosphere. Consequently, caution is required when using nudged simulations to interpret the behaviour of stratospheric tracers that are affected by the residual circulation