Combining stochastic and deterministic approaches within high efficiency molecular simulations

Generalized Shadow Hybrid Monte Carlo (GSHMC) is a method for molecular simulations that rigorously alternates Monte Carlo sampling from a canonical ensemble with integration of trajectories using Molecular Dynamics (MD). While conventional hybrid Monte Carlo methods completely re-sample particle’s velocities between MD trajectories, our method suggests a partial velocity update procedure which keeps a part of the dynamic information throughout the simulation. We use shadow (modified) Hamiltonians, the asymptotic expansions in powers of the discretization parameter corresponding to timestep, which are conserved by symplectic integrators to higher accuracy than true Hamiltonians. We present the implementation of this method into the highly efficient MD code GROMACS and demonstrate its performance and accuracy on computationally expensive systems like proteins in comparison with the molecular dynamics techniques already available in GROMACS. We take advantage of the state-of-the-art algorithms adopted in the code, leading to an optimal implementation of the method. Our implementation introduces virtually no overhead and can accurately recreate complex biological processes, including rare event dynamics, saving much computational time compared with the conventional simulation methods.     

An assessment of two approaches to variable metric methods

Two recent suggestions in the field of variable metric methods for function minimization are reviewed: the self-scaling method, first introduced by Oren and Luenberger, and the method of Biggs. The two proposals are considered both from a theoretical and computational aspect. They are compared with methods which use correction formulae from the Broyden one-parameter family, in particular the BFGS formula and the Fletcher switching strategy.     

Linear programming approaches to the measurement and analysis of productive efficiency

Invited by J. T. Pastor     

A comparison of two approaches to nurse rostering problems

Despite decades of research into automated methods for nurse rostering and some academic successes, one may notice that there is no consistency in the knowledge that has been built up over the years and that many healthcare institutions still resort to manual practices. One of the possible reasons for this gap between the nurse rostering theory and practice is that often the academic community focuses on the development of new techniques rather than developing systems for healthcare institutions. In addition, methods suitable for one problem are usually not easily transferable to other problems. In real-world healthcare environments, a personnel manager cannot afford to model a problem and construct a roster using available approaches in order to quantitatively determine which one suits best. There is a lack of criteria for the comparison of approaches to provide a clear picture about their advantages and disadvantages and therefore their suitability to a problem in hand. This paper introduces seven criteria: expressive power, flexibility, algorithmic power, learning capabilities, maintenance, rescheduling capabilities, and parameter tuning, that may offer guidance to researchers and developers of systems for nurse rostering. Two approaches to nurse rostering, which are of very different nature, are evaluated and compared against the introduced criteria. One approach is based on meta-heuristics, while the other employs case-based reasoning.     

On two Hall algebra approaches to odd periodic triangulated categories

Given an odd-periodic algebraic triangulated category, we compare Bridgeland's Hall algebra in the sense of Bridgeland(2013) and Gorsky(2014), and the derived Hall algebra in the sense of Ten(2006), Xiao and Xu(2008) and Xu and Chen(2013), and show that the former one is the twisted form of the tensor product of the latter one and a suitable group algebra.     

Comparison of two approaches to integration on separated topological spaces

A class of integral equations is investigated, particular examples of which occur in the consideration of certain three- and four-part mixed boundary-value problems in applied mathematics. A constructive method is given for reformulating the integral equations as Fredholm integral equations of the second kind and three examples are examined in detail to illustrate the general methods developed in the paper.     

Calibration and convex programming: two approaches to one problem

Calibration is a common technique of data processing in survey sampling. Although convex programming would be an obvious tool for this purpose, usually other methods are used in the practice of statistical institutes. A comparison of those methods and convex programming is reported on in this paper.     

Combining approaches for evaluating auditing populations: A simulation study

This research explores ways of combining four distinct bounds for the mean error in an auditing population. Two competing objectives for a bound are to be close to the true mean being estimated and to be reliable: not less than the true mean in more than 5% of estimations. The optimal combination should provide the best balance of these competing objectives. Estimating the mean error by a single approach is difficult because typically most accounts have no error and the distribution of the errors among those that do is discontinuous and highly skewed. This study reveals that the weights in the optimal combination are not constant but depend on the characteristic of the population being estimated. The optimally combined bound is only 7% smaller overall than the best of the constituents. However, while the best of the constituents fails in 50% of most challenging populations, the optimal combination never fails.     

Some features of two approaches to the affine-metric theory of gravitation

The possibility of constructing a gauge-invariant action of torsion fields in the formalism of tetrad scaling is demonstrated.Central Research Institute MORFIZPRIBOR. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 92, No. 1, pp. 150–153, July, 1992.     

On two homogeneous self-dual approaches to linear programming and its extensions

We investigate the relation between interior-point algorithms applied to two homogeneous self-dual approaches to linear programming, one of which was proposed by Ye, Todd, and Mizuno and the other by Nesterov, Todd, and Ye. We obtain only a partial equivalence of path-following methods (the centering parameter for the first approach needs to be equal to zero or larger than one half), whereas complete equivalence of potential-reduction methods can be shown. The results extend to self-scaled conic programming and to semidefinite programming using the usual search directions. Received: July 1998 / Accepted: September 2000?Published online November 17, 2000     

Comparison of two unified continuity approaches

The paper deals with a decomposition of a topological spaces with respect to a given system of sets. Two new types of generalized continuity are introduced and the characterizations of idealization continuities are given.     

Different approaches to efficiency analysis. An application to the Spanish Trawl fleet operating in Moroccan waters

Several approaches exist for the estimation of technical efficiency. In this paper the four most relevant ones (data envelopment analysis, stochastic production frontiers, panel data and distance functions) have been compared. The different approaches have been applied to the to the Spanish Trawl fishery that operated in Moroccan waters. The study highlights some of the problems arising from the wrong management of the fishery. It can also be concluded that in most cases, the multi- vs single-output feature is determinant in producing higher differences in the efficiency estimates, though the effect of either ignoring or taking into account random error also influences the results.     

DEA environmental assessment: Measurement of damages to scale with unified efficiency under managerial disposability or environmental efficiency

This study proposes a use of Data Envelopment Analysis (DEA) for environmental assessment. Firms usually produce not only desirable but also undesirable outputs as a result of their economic activities. The concept of disposability on undesirable outputs is separated into natural and managerial disposability. Natural disposability is an environmental strategy in which firms decrease their inputs to reduce a vector of undesirable outputs. Given the reduced input vector, they attempt to increase desirable outputs as much as possible. Managerial disposability involves the opposite strategy of increasing an input vector. The concept of disposability expresses an environmental strategy that considers a regulation change on undesirable outputs as a new business opportunity. Firms attempt to improve their unified (operational and environmental) performance by utilizing new technology and/or new management. Considering the two disposability concepts, this study discusses how to measure unified efficiency under managerial disposability and then discusses how to measure environmental efficiency. The proposed uses of DEA can serve as an empirical basis for measuring new economic concepts such as “Scale Damages (SD)”, corresponding to scale economies for undesirable outputs, and “Damages to Scale (DTS)”, corresponding to returns to scale for undesirable outputs.     

Goal programming approaches for data envelopment analysis cross efficiency evaluation

Cross efficiency evaluation has long been proposed as an alternative method for ranking the decision making units (DMUs) in data envelopment analysis (DEA). This study proposes goal programming models that could be used in the second stage of the cross evaluation. Proposed goal programming models have different efficiency concepts as classical DEA, minmax and minsum efficiency criteria. Numerical examples are provided to illustrate the applications of the proposed goal programming cross efficiency models.     

Combining the assumptions of variable and constant returns to scale in the efficiency evaluation of secondary schools

Our paper reports on the use of data envelopment analysis (DEA) for the assessment of performance of secondary schools in Malaysia during the implementation of the policy of teaching and learning mathematics and science subjects in the English language (PPSMI). The novelty of our application is that it makes use of the hybrid returns-to-scale (HRS) DEA model. This combines the assumption of constant returns to scale with respect to quantity inputs and outputs (teaching provision and students) and variable returns to scale (VRS) with respect to quality factors (attainment levels on entry and exit) and socio-economic status of student families. We argue that the HRS model is a better-informed model than the conventional VRS model in the described application. Because the HRS technology is larger than the VRS technology, the new model provides a tangibly better discrimination on efficiency than could be obtained by the VRS model. To assess the productivity change of secondary schools over the years surrounding the introduction of the PPSMI policy, we adapt the Malmquist productivity index and its decomposition to the case of HRS model.