An MILP-based heuristic for staff scheduling problems with acceptance levels

We present a real-world staff-assignment problem that was reported to us by a provider of an online workforce scheduling software. The problem consists of assigning employees to work shifts subject to a large variety of requirements related to work laws, work shift compatibility, workload balancing, and personal preferences of employees. A target value is given for each requirement, and all possible deviations from these values are associated with acceptance levels. The objective is to minimize the total number of deviations in ascending order of the acceptance levels. We present an exact lexicographic goal programming MILP formulation and an MILP-based heuristic. The heuristic consists of two phases: in the first phase a feasible schedule is built and in the second phase parts of the schedule are iteratively re-optimized by applying an exact MILP model. A major advantage of such MILP-based approaches is the flexibility to account for additional constraints or modified planning objectives, which is important as the requirements may vary depending on the company or planning period. The applicability of the heuristic is demonstrated for a test set derived from real-world data. Our computational results indicate that the heuristic is able to devise optimal solutions to non-trivial problem instances, and outperforms the exact lexicographic goal programming formulation on medium- and large-sized problem instances.

Prognostic value of PCSK9 levels in patients with acute coronary syndromes.

AIMS Proprotein convertase subtilisin kexin 9 (PCSK9) is an emerging target for the treatment of hypercholesterolaemia, but the clinical utility of PCSK9 levels to guide treatment is unknown. We aimed to prospectively assess the prognostic value of plasma PCSK9 levels in patients with acute coronary syndromes (ACS). METHODS AND RESULTS Plasma PCSK9 levels were measured in 2030 ACS patients undergoing coronary angiography in a Swiss prospective cohort. At 1 year, the association between PCSK9 tertiles and all-cause death was assessed adjusting for the Global Registry of Acute Coronary Events (GRACE) variables, as well as the achievement of LDL cholesterol targets of <1.8 mmol/L. Patients with higher PCSK9 levels at angiography were more likely to have clinical familial hypercholesterolaemia (rate ratio, RR 1.21, 95% confidence interval, CI 1.09-1.53), be treated with lipid-lowering therapy (RR 1.46, 95% CI 1.30-1.63), present with longer time interval of chest pain (RR 1.29, 95% CI 1.09-1.53) and higher C-reactive protein levels (RR 1.22, 95% CI 1.16-1.30). PCSK9 increased 12-24 h after ACS (374 ± 149 vs. 323 ± 134 ng/mL, P < 0.001). At 1 year follow-up, HRs for upper vs. lower PCSK9-level tertiles were 1.13 (95% CI 0.69-1.85) for all-cause death and remained similar after adjustment for the GRACE score. Patients with higher PCSK9 levels were less likely to reach the recommended LDL cholesterol targets (RR 0.81, 95% CI 0.66-0.99). CONCLUSION In ACS patients, high initial PCSK9 plasma levels were associated with inflammation in the acute phase and hypercholesterolaemia, but did not predict mortality at 1 year.

hp-DGFEM for second-order mixed elliptic problems polyhedra

We prove exponential rates of convergence of hp-version discontinuous Galerkin (dG) interior penalty finite element methods for second-order elliptic problems with mixed Dirichlet-Neumann boundary conditions in axiparallel polyhedra. The dG discretizations are based on axiparallel, σ-geometric anisotropic meshes of mapped hexahedra and anisotropic polynomial degree distributions of μ-bounded variation. We consider piecewise analytic solutions which belong to a larger analytic class than those for the pure Dirichlet problem considered in [11, 12]. For such solutions, we establish the exponential convergence of a nonconforming dG interpolant given by local L 2 -projections on elements away from corners and edges, and by suitable local low-order quasi-interpolants on elements at corners and edges. Due to the appearance of non-homogeneous, weighted norms in the analytic regularity class, new arguments are introduced to bound the dG consistency errors in elements abutting on Neumann edges. The non-homogeneous norms also entail some crucial modifications of the stability and quasi-optimality proofs, as well as of the analysis for the anisotropic interpolation operators. The exponential convergence bounds for the dG interpolant constructed in this paper generalize the results of [11, 12] for the pure Dirichlet case.

SOP: Parallel surrogate global optimization with Pareto center selection for computationally expensive single objective problems

This paper presents a parallel surrogate-based global optimization method for computationally expensive objective functions that is more effective for larger numbers of processors. To reach this goal, we integrated concepts from multi-objective optimization and tabu search into, single objective, surrogate optimization. Our proposed derivative-free algorithm, called SOP, uses non-dominated sorting of points for which the expensive function has been previously evaluated. The two objectives are the expensive function value of the point and the minimum distance of the point to previously evaluated points. Based on the results of non-dominated sorting, P points from the sorted fronts are selected as centers from which many candidate points are generated by random perturbations. Based on surrogate approximation, the best candidate point is subsequently selected for expensive evaluation for each of the P centers, with simultaneous computation on P processors. Centers that previously did not generate good solutions are tabu with a given tenure. We show almost sure convergence of this algorithm under some conditions. The performance of SOP is compared with two RBF based methods. The test results show that SOP is an efficient method that can reduce time required to find a good near optimal solution. In a number of cases the efficiency of SOP is so good that SOP with 8 processors found an accurate answer in less wall-clock time than the other algorithms did with 32 processors.

Interstellar neutral helium in the heliosphere from Interstellar Boundary Explorer observations. III. Mach number of the flow, velocity vector, and temperature from the first six years of measurements

We analyzed observations of interstellar neutral helium (ISN He) obtained from the Interstellar Boundary Explorer (IBEX) satellite during its first six years of operation. We used a refined version of the ISN He simulation model, presented in the companion paper by Sokol et al. (2015b), along with a sophisticated data correlation and uncertainty system and parameter fitting method, described in the companion paper by Swaczyna et al. We analyzed the entire data set together and the yearly subsets, and found the temperature and velocity vector of ISN He in front of the heliosphere. As seen in the previous studies, the allowable parameters are highly correlated and form a four-dimensional tube in the parameter space. The inflow longitudes obtained from the yearly data subsets show a spread of similar to 6 degrees, with the other parameters varying accordingly along the parameter tube, and the minimum chi(2) value is larger than expected. We found, however, that the Mach number of the ISN He flow shows very little scatter and is thus very tightly constrained. It is in excellent agreement with the original analysis of ISN He observations from IBEX and recent reanalyses of observations from Ulysses. We identify a possible inaccuracy in the Warm Breeze parameters as the likely cause of the scatter in the ISN He parameters obtained from the yearly subsets, and we suppose that another component may exist in the signal or a process that is not accounted for in the current physical model of ISN He in front of the heliosphere. From our analysis, the inflow velocity vector, temperature, and Mach number of the flow are equal to lambda(ISNHe) = 255 degrees.8 +/- 0 degrees.5, beta(ISNHe) = 5 degrees.16 +/- 0 degrees.10, T-ISNHe = 7440 +/- 260 K, nu(SNHe) = 25.8 +/- 0.4 km s(-1), and M-ISNHe = 5.079 +/- 0.028, with uncertainties strongly correlated along the parameter tube.

Determination of sulfite and manganese in sediments from the K/T boundary

The solid-state-physics technique of electron spin resonance (ESR) has been employed in an exploratory study of marine limestones and impact-related deposits from Cretaceous-Tertiary (KT) boundary sites including Spain (Sopelana and Caravaca), New Jersey (Bass River), the U.S. Atlantic continental margin (Blake Nose, ODP Leg 171B/1049/A), and several locations in Belize and southern Mexico within -600 km of the Chicxulub crater. The ESR spectra of SO3(1-) (a radiation-induced point defect involving a sulfite ion substitutional for CO3(2-) which has trapped a positive charge) and Mn(2+) in calcite were singled out for analysis because they are unambiguously interpretable and relatively easy to record. ESR signal strengths of calcite-related SO3(1-) and Mn(2+) have been studied as functions of stratigraphic position in whole-rock samples across the KT boundary at Sopelana, Caravaca, and Blake Nose. At all three of these sites, anomalies in SO3(1-) and/or Mn(2+) intensities are noted at the KT boundary relative to the corresponding background levels in the rocks above and below. At Caravaca, the SO3(1-) background itself is found to be lower by a factor of 2.7 in the first 30,000 years of the Tertiary relative to its steady-state value in the last 15,000 years of the Cretaceous, indicating either an abrupt and quasi-permanent change in ocean chemistry (or temperature) or extinction of the marine biota primarily responsible for fixing sulfite in the late Cretaceous limestones. An exponential decrease in the Mn(2+) concentration per unit mass calcite, [Mn(2+)], as the KT boundary at Caravaca is approached from below (1/e characteristic length =1.4 cm) is interpreted as a result of post-impact leaching of the seafloor. Absolute ESR quantitative analyses of proximal impact deposits from Belize and southern Mexico group naturally into three distinct fields in a twodimensional [SO3(1-)]-versus-[Mn(2+)] scatter plot. These fields contain (I) limestone ejecta clasts, (II) accretionary lapilli, and (III) a variety of SO3(1-) -depleted/Mn(2+) enriched impact deposits. Data for the investigated non-impact-related Cretaceous and Tertiary marine limestones (Spain and Blake Nose) fall outside of these three fields. With reference to thes enon-impact deposits, fields I, II, and III can be respectively characterized as Mn(2+) -depleted, SO3(1-) -enhanced, and SO3(1-) -depleted. It is proposed that (1) field I represents calcites from the Yucatin Platform, and that the Mn(2+) -depleted signature can be used as an indicator of primary Chicxulub ejecta in deep marine environments and (2) field II represents calcites that include a component formed in the vapor plume, either from condensation in the presence of CO2/SO3(1-) -rich vapors, or reactions between CaO and CO2/SO3 rich vapors, and that this SO3(1-) -enhanced signature can be used as an indicator of impact vapor plume deposits. Given these two propositions, the ESR data for the Blake Nose deposits are ascribed to the presence of basal coarse calcitic Chicxulub ejecta clasts, while the finer components that are increasingly represented toward the top are interpreted to contain high- SO3(1-) calcite from the vapor plume. The apparently-undisturbed Bass River deposit may contain even higher concentrations of vapor-plume calcite. None of the three components included in field III appear to be represented at distal, deep marine KT-boundary sites; this field may include several types of impact-related deposits of diverse origins and diagenetic histories.

Stratigraphy of the Campanian-Maastrichtian boundary in ODP Hole 122-762C

An integrated framework of magnetostratigraphy, calcareous microfossil bio-events, cyclostratigraphy and d13C stratigraphy is established for the upper Campanian-Maastrichtian of ODP Hole 762C (Exmouth Plateau, Northwestern Australian margin). Bulk-carbonate d13C events and nannofossil bio-events have been recorded and plotted against magnetostratigraphy, and provided absolute ages using the results of the cyclostratigraphic study and the recent astronomical calibration of the Maastrichtian. Thirteen carbon-isotope events and 40 nannofossil bio-events are recognized and calibrated with cyclostratigraphy, as well as 14 previously published foraminifer events, thus constituting a solid basis for large-scale correlations. Results show that this site is characterized by a nearly continuous sedimentation from the upper Campanian to the K-Pg boundary, except for a 500 kyr gap in magnetochron C31n. Correlation of the age-calibrated d13C profile of ODP Hole 762C to the d13C profile of the Tercis les Bains section, Global Stratotype Section and Point of the Campanian-Maastrichtian boundary (CMB), allowed a precise recognition and dating of this stage boundary at 72.15 ± 0.05 Ma. This accounts for a total duration of 6.15 ± 0.05 Ma for the Maastrichtian stage. Correlation of the boundary level with northwest Germany shows that the CMB as defined at the GSSP is ~800 kyr younger than the CMB as defined by Belemnite zonation in the Boreal realm. ODP Hole 762C is the first section to bear at the same time an excellent recovery of sediments throughout the upper Campanian-Maastrichtian, a precise and well-defined magnetostratigraphy, a high-resolution record of carbon isotope events and calcareous plankton biostratigraphy, and a cyclostratigraphic study tied to the La2010a astronomical solution. This section is thus proposed as an excellent reference for the upper Campanian-Maastrichtian in the Indian Ocean.

Mineralogy and stable oxygen isotope ratios of the Cretaceous-Tertiary boundary

Results of detailed mineralogical, chemical, and oxygen isotope analyses of the clay minerals and zeolites from two Cretaceous-Tertiary (K/T) boundary regions, Stevns Klint, Denmark, and Deep Sea Drilling Project (DSDP) Hole 465A in the north central Pacific Ocean, are presented. In the central part of the Stevns Klint K/T boundary layer, the only clay mineral detected by x-ray diffraction is a pure smectite with > 95 percent expandable layers. No detrital clay minerals or quartz were observed in the clay size fraction in these beds, whereas the clay minerals above and below the boundary layer are illite and mixed-layer smectite-illite of detrital origin as well as quartz. The mineralogical purity of the clay fraction, the presence of smectite only at the boundary, and the d18O value of the smectite (27.2 ± 0.2 per mil) suggest that it formed in situ by alteration of glass. Formation from impact rather than from volcanic glass is supported by its major element chemistry. The high content of iridium and other siderophile elements is not due to the cessation of calcium carbonate deposition and resulting slow sedimentation rates. At DSDP Hole 465A, the principal clay mineral in the boundary zone (80 to 143 centimeters) is a mixed-layer smectite-illite with >=90 percent expandable layers, accompanied by some detrital quartz and small amounts of a euhedral authigenic zeolite (clinoptilolite). The mixed-layer smectite-illite from the interval 118 to 120 centimeters in the zone of high iridium abundance has a very low rare earth element content; the negative cerium anomaly indicates formation in the marine environment. This conclusion is corroborated by the d18O value of this clay mineral (27.1 ± 0.2 per mil). Thus, this mixed-layer smectite-illite formed possibly from the same glass as the K/T boundary smectite at Stevns Klint, Denmark.

Tracing CO2 emissions in global value chains

This paper integrates two lines of research into a unified conceptual framework: trade in global value chains and embodied emissions. This allows both value added and emissions to be systematically traced at the country, sector, and bilateral levels through various production network routes. By combining value-added and emissions accounting in a consistent way, the potential environmental cost (amount of emissions per unit of value added) along global value chains can be estimated. Using this unified accounting method, we trace CO2 emissions in the global production and trade network among 41 economies in 35 sectors from 1995 to 2009, basing our calculations on the World Input–Output Database, and show how they help us to better understand the impact of cross-country production sharing on the environment.

A unified framework of trade in value added : physical, monetary, exchange rates, and GHG emissions

Koopman et al. (2014) developed a method to consistently decompose gross exports in value-added terms that accommodate infinite repercussions of international and inter-sector transactions. This provides a better understanding of trade in value added in global value chains than does the conventional gross exports method, which is affected by double-counting problems. However, the new framework is based on monetary input--output (IO) tables and cannot distinguish prices from quantities; thus, it is unable to consider financial adjustments through the exchange market. In this paper, we propose a framework based on a physical IO system, characterized by its linear programming equivalent that can clarify the various complexities relevant to the existing indicators and is proved to be consistent with Koopman's results when the physical decompositions are evaluated in monetary terms. While international monetary tables are typically described in current U.S. dollars, the physical framework can elucidate the impact of price adjustments through the exchange market. An iterative procedure to calculate the exchange rates is proposed, and we also show that the physical framework is also convenient for considering indicators associated with greenhouse gas (GHG) emissions.

Reduced order models for industrial thermo-fluid problems

A new method is presented to generate reduced order models (ROMs) in Fluid Dynamics problems of industrial interest. The method is based on the expansion of the flow variables in a Proper Orthogonal Decomposition (POD) basis, calculated from a limited number of snapshots, which are obtained via Computational Fluid Dynamics (CFD). Then, the POD-mode amplitudes are calculated as minimizers of a properly defined overall residual of the equations and boundary conditions. The method includes various ingredients that are new in this field. The residual can be calculated using only a limited number of points in the flow field, which can be scattered either all over the whole computational domain or over a smaller projection window. The resulting ROM is both computationally efficient(reconstructed flow fields require, in cases that do not present shock waves, less than 1 % of the time needed to compute a full CFD solution) and flexible(the projection window can avoid regions of large localized CFD errors).Also, for problems related with aerodynamics, POD modes are obtained from a set of snapshots calculated by a CFD method based on the compressible Navier Stokes equations and a turbulence model (which further more includes some unphysical stabilizing terms that are included for purely numerical reasons), but projection onto the POD manifold is made using the inviscid Euler equations, which makes the method independent of the CFD scheme. In addition, shock waves are treated specifically in the POD description, to avoid the need of using a too large number of snapshots. Various definitions of the residual are also discussed, along with the number and distribution of snapshots, the number of retained modes, and the effect of CFD errors. The method is checked and discussed on several test problems that describe (i) heat transfer in the recirculation region downstream of a backwards facing step, (ii) the flow past a two-dimensional airfoil in both the subsonic and transonic regimes, and (iii) the flow past a three-dimensional horizontal tail plane. The method is both efficient and numerically robust in the sense that the computational effort is quite small compared to CFD and results are both reasonably accurate and largely insensitive to the definition of the residual, to CFD errors, and to the CFD method itself, which may contain artificial stabilizing terms. Thus, the method is amenable for practical engineering applications. Resumen Se presenta un nuevo método para generar modelos de orden reducido (ROMs) aplicado a problemas fluidodinámicos de interés industrial. El nuevo método se basa en la expansión de las variables fluidas en una base POD, calculada a partir de un cierto número de snapshots, los cuales se han obtenido gracias a simulaciones numéricas (CFD). A continuación, las amplitudes de los modos POD se calculan minimizando un residual global adecuadamente definido que combina las ecuaciones y las condiciones de contorno. El método incluye varios ingredientes que son nuevos en este campo de estudio. El residual puede calcularse utilizando únicamente un número limitado de puntos del campo fluido. Estos puntos puede encontrarse dispersos a lo largo del dominio computacional completo o sobre una ventana de proyección. El modelo ROM obtenido es tanto computacionalmente eficiente (en aquellos casos que no presentan ondas de choque reconstruir los campos fluidos requiere menos del 1% del tiempo necesario para calcular una solución CFD) como flexible (la ventana de proyección puede escogerse de forma que evite contener regiones con errores en la solución CFD localizados y grandes). Además, en problemas aerodinámicos, los modos POD se obtienen de un conjunto de snapshots calculados utilizando un código CFD basado en la versión compresible de las ecuaciones de Navier Stokes y un modelo de turbulencia (el cual puede incluir algunos términos estabilizadores sin sentido físico que se añaden por razones puramente numéricas), aunque la proyección en la variedad POD se hace utilizando las ecuaciones de Euler, lo que hace al método independiente del esquema utilizado en el código CFD. Además, las ondas de choque se tratan específicamente en la descripción POD para evitar la necesidad de utilizar un número demasiado grande de snapshots. Varias definiciones del residual se discuten, así como el número y distribución de los snapshots,el número de modos retenidos y el efecto de los errores debidos al CFD. El método se comprueba y discute para varios problemas de evaluación que describen (i) la transferencia de calor en la región de recirculación aguas abajo de un escalón, (ii) el flujo alrededor de un perfil bidimensional en regímenes subsónico y transónico y (iii) el flujo alrededor de un estabilizador horizontal tridimensional. El método es tanto eficiente como numéricamente robusto en el sentido de que el esfuerzo computacional es muy pequeño comparado con el requerido por el CFD y los resultados son razonablemente precisos y muy insensibles a la definición del residual, los errores debidos al CFD y al método CFD en sí mismo, el cual puede contener términos estabilizadores artificiales. Por lo tanto, el método puede utilizarse en aplicaciones prácticas de ingeniería.

Theoretical Analysis of the No-Slip Boundary Condition Enforcement in SPH Methods

The aim of the present work is to provide an in-depth analysis of the most representative mirroring techniques used in SPH to enforce boundary conditions (BC) along solid profiles. We specifically refer to dummy particles, ghost particles, and Takeda et al. [Prog. Theor. Phys. 92 (1994), 939] boundary integrals. The analysis has been carried out by studying the convergence of the first- and second-order differential operators as the smoothing length (that is, the characteristic length on which relies the SPH interpolation) decreases. These differential operators are of fundamental importance for the computation of the viscous drag and the viscous/diffusive terms in the momentum and energy equations. It has been proved that close to the boundaries some of the mirroring techniques leads to intrinsic inaccuracies in the convergence of the differential operators. A consistent formulation has been derived starting from Takeda et al. boundary integrals (see the above reference). This original formulation allows implementing no-slip boundary conditions consistently in many practical applications as viscous flows and diffusion problems.

A set of canonical problems in sloshing. Part 0: Experimental setup and data processing

In a series of attempts to research and document relevant sloshing type phenomena, a series of experiments have been conducted. The aim of this paper is to describe the setup and data processing of such experiments. A sloshing tank is subjected to angular motion. As a result pressure registers are obtained at several locations, together with the motion data, torque and a collection of image and video information. The experimental rig and the data acquisition systems are described. Useful information for experimental sloshing research practitioners is provided. This information is related to the liquids used in the experiments, the dying techniques, tank building processes, synchronization of acquisition systems, etc. A new procedure for reconstructing experimental data, that takes into account experimental uncertainties, is presented. This procedure is based on a least squares spline approximation of the data. Based on a deterministic approach to the first sloshing wave impact event in a sloshing experiment, an uncertainty analysis procedure of the associated first pressure peak value is described.

Tranversal motion and flow structure of fully nonlinear streaks in a laminar boundary layer

Typical streak computations present in the literature correspond to linear streaks or to small amplitude nonlinear streaks computed using DNS or nonlinear PSE. We use the Reduced Navier-Stokes (RNS) equations to compute the streamwise evolution of fully non-linear streaks with high amplitude in a laminar flat plate boundary layer. The RNS formulation provides Reynolds number independent solutions that are asymptotically exact in the limit $Re \gg 1$, it requires much less computational effort than DNS, and it does not have the consistency and convergence problems of the PSE. We present various streak computations to show that the flow configuration changes substantially when the amplitude of the streaks grows and the nonlinear effects come into play. The transversal motion (in the wall normal-streamwise plane) becomes more important and strongly distorts the streamwise velocity profiles, that end up being quite different from those of the linear case. We analyze in detail the resulting flow patterns for the nonlinearly saturated streaks and compare them with available experimental results.

Linear instability of orthogonal compressible leading-edge boundary layer flow

Instability analysis of compressible orthogonal swept leading-edge boundary layer flow was performed in the context of BiGlobal linear theory. 1, 2 An algorithm was developed exploiting the sparsity characteristics of the matrix discretizing the PDE-based eigenvalue problem. This allowed use of the MUMPS sparse linear algebra package 3 to obtain a direct solution of the linear systems associated with the Arnoldi iteration. The developed algorithm was then applied to efficiently analyze the effect of compressibility on the stability of the swept leading-edge boundary layer and obtain neutral curves of this flow as a function of the Mach number in the range 0 ≤ Ma ≤ 1. The present numerical results fully confirmed the asymptotic theory results of Theofilis et al. 4 Up to the maximum Mach number value studied, it was found that an increase of this parameter reduces the critical Reynolds number and the range of the unstable spanwise wavenumbers.