Graph colouring approaches for a satellite range scheduling problem

A goal of this paper is to efficiently adapt the best ingredients of the graph colouring techniques to an NP-hard satellite range scheduling problem, called MuRRSP. We propose two new heuristics for the MuRRSP, where as many jobs as possible have to be scheduled on several resources, while respecting time and capacity constraints. In the permutation solution space, which is widely used by other researchers, a solution is represented by a permutation of the jobs, and a schedule builder is needed to generate and evaluate a feasible schedule from the permutation. On the contrary, our heuristics are based on the solution space which contains all the feasible schedules. Based on the similarities between the graph colouring problem and the MuRRSP, we show that the latter solution space has significant advantages. A tabu search and an adaptive memory algorithms are designed to tackle the MuRRSP. These heuristics are derived from efficient graph colouring methods. Numerical experiments, performed on large, realistic, and challenging instances, showed that our heuristics are very competitive, robust, and outperform algorithms based on the permutation solution spac

Information content and aerosol property retrieval potential for different types of in situ polar nephelometer data

Polar nephelometers are in situ instruments used to measure the angular distribution of light scattered by aerosol particles. These types of measurements contain substantial information about the properties of the aerosol being probed (e.g. concentrations, sizes, refractive indices, shape parameters), which can be retrieved through inversion algorithms. The aerosol property retrieval potential (i.e. information content) of a given set of measurements depends on the spectral, polarimetric, and angular characteristics of the polar nephelometer that was used to acquire the measurements. To explore this issue quantitatively, we applied Bayesian information content analysis and calculated the metric degrees of freedom for signal (DOFS) for a range of simulated polar nephelometer instrument configurations, aerosol models and test cases, and assumed levels of prior knowledge about the variances of specific aerosol properties. Assuming a low level of prior knowledge consistent with an unconstrained ambient/field measurement setting, we demonstrate that even very basic polar nephelometers (single wavelength, no polarization capability) will provide informative measurements with a very high retrieval potential for the size distribution and refractive index state parameters describing simple unimodal, spherical test aerosols. As expected, assuming a higher level of prior knowledge consistent with well-constrained laboratory applications leads to a reduction in potential for information gain via performing the polarimetric measurement. Nevertheless, we show that in this situation polar nephelometers can still provide informative measurements: e.g. it can be possible to retrieve the imaginary part of the refractive index with high accuracy if the laboratory setting makes it possible to keep the probed aerosol sample simple. The analysis based on a high level of prior knowledge also allows us to better assess the impact of different polar nephelometer instrument design features in a consistent manner for retrieved aerosol parameters. The results indicate that the addition of multi-wavelength and/or polarimetric measurement capabilities always leads to an increase in information content, although in some cases the increase is negligible, e.g. when adding a fourth, near-IR measurement wavelength for the retrieval of unimodal size distribution parameters or if the added polarization component has high measurement uncertainty. By considering a more complex bimodal, non-spherical-aerosol model, we demonstrate that performing more comprehensive spectral and/or polarimetric measurements leads to very large benefits in terms of the achieved information content. We also investigated the impact of angular truncation (i.e. the loss of measurement information at certain scattering angles) on information content. Truncation at extreme angles (i.e. in the near-forward or near-backward directions) results in substantial decreases in information content for coarse-aerosol test cases. However for fine-aerosol test cases, the sensitivity of DOFS to extreme-angle truncation is noticeably smaller and can be further reduced by performing more comprehensive measurements. Side angle truncation has very little effect on information content for both the fine and coarse test cases. Furthermore, we demonstrate that increasing the number of angular measurements generally increases the information content. However, above a certain number of angular measurements (∼20–40) the observed increases in DOFS plateau out. Finally, we demonstrate that the specific placement of angular measurements within a nephelometer can have a large impact on information content. As a proof of concept, we show that a reductive greedy algorithm based on the DOFS metric can be used to find optimal angular configurations for given target aerosols and applications.</p

Information content and aerosol property retrieval potential for different types of in situ polar nephelometer data

Polar nephelometers are in situ instruments used to measure the angular distribution of light scattered by aerosol particles. These type of measurements contain substantial information about the properties of the aerosol being probed (e.g. concentrations, sizes, refractive indices, shape parameters), which can be retrieved through inversion algorithms. The aerosol property retrieval potential (i.e., information content) of a given set of measurements depends on the spectral, polarimetric and angular characteristics of the polar nephelometer that was used to acquire it. To explore this issue quantitatively, we applied Bayesian information content analysis and calculated the metric Degrees of Freedom for Signal (DOFS) for a range of simulated polar nephelometer instrument configurations, aerosol models and test cases, and assumed levels of prior knowledge about the variances of specific aerosol properties. Assuming a low level of prior knowledge consistent with an unconstrained ambient/field measurement setting, we demonstrate that even very basic polar nephelometers (single wavelength, no polarization capability) will provide informative measurements with very high retrieval potential for the size distribution and refractive index state parameters describing simple unimodal, spherical test aerosols. As expected, assuming a higher level of prior knowledge consistent with well constrained laboratory applications leads to a reduction in potential for information gain via performing the polarimetric measurement. This analysis allows us to better assess the impact of different polar nephelometer instrument design features in a consistent manner for retrieved aerosol parameters. The results indicate that the addition of multi-wavelength and/or polarimetric measurement capabilities always leads to an increase in information content, although in some cases the increase is negligible: e.g. when adding a fourth, near-IR measurement wavelength for the retrieval of unimodal size distribution parameters, or if the added polarization component has high measurement uncertainty. By considering a more complex bimodal, non-spherical aerosol model, we demonstrate that performing the more comprehensive spectral and/or polarimetric measurements leads to very large benefits in terms of the achieved information content. We also investigated the impact of angular truncation (i.e., the loss of measurement information at certain scattering angles) on information content. Truncation at extreme angles (i.e., in the near-forward or &ndash;backward directions) results in substantial decreases in information content for coarse aerosol test cases. However for fine aerosol test cases, the sensitivity of DOFS to extreme angle truncation is noticeably smaller and can be further reduced by performing more comprehensive measurements. Side-angle truncation has very little effect on information content for both the fine and coarse test cases. Furthermore, we demonstrate that increasing the number of angular measurements generally increases the information content. However, above a certain number of angular measurements (~20&ndash;40) the observed increases in DOFS plateau out. Finally, we demonstrate that the specific placement of angular measurements within a nephelometer can have a large impact on information content. As a proof-of-concept, we show that a reductive greedy algorithm based on the DOFS metric can be used to find optimal angular configurations for given target aerosols and applications.</p

Energy Estimation of Cosmic Rays with the Engineering Radio Array of the Pierre Auger Observatory

The Auger Engineering Radio Array (AERA) is part of the Pierre Auger Observatory and is used to detect the radio emission of cosmic-ray air showers. These observations are compared to the data of the surface detector stations of the Observatory, which provide well-calibrated information on the cosmic-ray energies and arrival directions. The response of the radio stations in the 30 to 80 MHz regime has been thoroughly calibrated to enable the reconstruction of the incoming electric field. For the latter, the energy deposit per area is determined from the radio pulses at each observer position and is interpolated using a two-dimensional function that takes into account signal asymmetries due to interference between the geomagnetic and charge-excess emission components. The spatial integral over the signal distribution gives a direct measurement of the energy transferred from the primary cosmic ray into radio emission in the AERA frequency range. We measure 15.8 MeV of radiation energy for a 1 EeV air shower arriving perpendicularly to the geomagnetic field. This radiation energy -- corrected for geometrical effects -- is used as a cosmic-ray energy estimator. Performing an absolute energy calibration against the surface-detector information, we observe that this radio-energy estimator scales quadratically with the cosmic-ray energy as expected for coherent emission. We find an energy resolution of the radio reconstruction of 22% for the data set and 17% for a high-quality subset containing only events with at least five radio stations with signal.Comment: Replaced with published version. Added journal reference and DO

Measurement of the Radiation Energy in the Radio Signal of Extensive Air Showers as a Universal Estimator of Cosmic-Ray Energy

We measure the energy emitted by extensive air showers in the form of radio emission in the frequency range from 30 to 80 MHz. Exploiting the accurate energy scale of the Pierre Auger Observatory, we obtain a radiation energy of 15.8 \pm 0.7 (stat) \pm 6.7 (sys) MeV for cosmic rays with an energy of 1 EeV arriving perpendicularly to a geomagnetic field of 0.24 G, scaling quadratically with the cosmic-ray energy. A comparison with predictions from state-of-the-art first-principle calculations shows agreement with our measurement. The radiation energy provides direct access to the calorimetric energy in the electromagnetic cascade of extensive air showers. Comparison with our result thus allows the direct calibration of any cosmic-ray radio detector against the well-established energy scale of the Pierre Auger Observatory.Comment: Replaced with published version. Added journal reference and DOI. Supplemental material in the ancillary file

Fiber bragg grating characterization by optical low coherence reflectometry and sensing applications

This work connects of three domains of fiber optics : the fiber Bragg gratings (FBG), the optical low coherence reflectometry (OLCR) and the fiber optical sensors (using FBGs, the OLCR or a combination of both). Fiber Bragg gratings are fiber optic devices characterized by permanent and periodic changes of the fiber core refractive index, which translates into a narrowband spectral reflection. FBGs are widely used nowadays in the telecommunications field, for example as reflection filters or dispersion compensators. Moreover, their sensitivity to temperature and strain make them ideal for sensing applications, in particular due to their very small size, their immunity against electromagnetic fields and their multiplexing capabilities. The major challenge with FBGs is to locally characterize the grating properties, in particular the core refractive index distribution along the grating. These data allow correcting imperfections during the writing process or to determine the distributions in sensing applications. In this work, we have reconstructed the complex coupling coefficient distribution of the grating by combining the OLCR technique and a reconstruction technique called "layer-peeling". A novel design for the OLCR has been proposed and realized. This instrument measures precisely the amplitude and phase of the complex fiber Bragg grating impulse response with micrometer resolution and a noise level below –120 dB. Using the layer-peeling method, the FBG complex coupling coefficient can be retrieved with a 20 µm resolution and an error of less than 5% (this value is obtained by comparing the reconstructions from both sides of the grating). Many studies have been conducted on axial strains in various samples and various experimental conditions. The most promising result concerns the study of non-homogeneous strain fields with the reconstruction technique that combines the OLCR and the "layer-peeling". The study of transversal strain field has also been conducted with FBGs written in birefringent fibers. A non-linear behavior has been observed and explained with the rotation of the fiber eigen axis. An important sensitivity anisotropy for different angles has been observed, but not fully explained. The influence of humidity and temperature on a polyimide coated FBG was also investigated. The sensitivities were measured as a function of the coating thickness. From this analysis a novel concept for an intrinsic relative humidity sensor using polyimide-recoated fiber Bragg gratings has been proposed. Tests in a controlled environment indicate that the sensor has a linear, reversible and accurate response behavior between 10 and 90 %RH and between 13 and 60 °C. The last but not least, a new fiber optic sub-nanometric scale vibrometer based on the OLCR technique has been developed. This sensor allows for the control of a fiber SNOM (Scanning Nearfield Optical Microscopy) tip oscillations in the air and in water. A very good accuracy is achieved with a noise level around 1 pm. The compactness and the easiness to use (auto-calibration and stability) of this sensor open up new measurement fields for the SNOM technique as, for example, with biological samples in liquids

Graph colouring approaches for a satellite range scheduling problem

A goal of this paper is to efficiently adapt the best ingredients of the graph colouring techniques to an NPhard satellite range scheduling problem, called MuRRSP. We propose two new heuristics for the MuRRSP, where as many jobs as possible have to be scheduled on several resources, while respecting time and capacity constraints. In the permutation solution space, which is widely used by other researchers, a solution is represented by a permutation of the jobs, and a schedule builder is needed to generate and evaluate a feasible schedule from the permutation. On the contrary, our heuristics are based on the solution space which contains all the feasible schedules. Based on the similarities between the graph colouring problem and the MuRRSP, we show that the latter solution space has significant advantages. A tabu search and an adaptive memory algorithms are designed to tackle the MuRRSP. These heuristics are derived from efficient graph colouring methods. Numerical experiments, performed on large, realistic, and challenging instances, showed that our heuristics are very competitive, robust, and outperform algorithms based on the permutation solution space

Graph colouring approaches for a satellite range scheduling problem

A goal of this paper is to efficiently adapt the best ingredients of the graph colouring techniques to an NP-hard satellite range scheduling problem, called MuRRSP. We propose two new heuristics for the MuRRSP, where as many jobs as possible have to be scheduled on several resources, while respecting time and capacity constraints. In the permutation solution space, which is widely used by other researchers, a solution is represented by a permutation of the jobs, and a schedule builder is needed to generate and evaluate a feasible schedule from the permutation. On the contrary, our heuristics are based on the solution space which contains all the feasible schedules. Based on the similarities between the graph colouring problem and the MuRRSP, we show that the latter solution space has significant advantages. A tabu search and an adaptive memory algorithms are designed to tackle the MuRRSP. These heuristics are derived from efficient graph colouring methods. Numerical experiments, performed on large, realistic, and challenging instances, showed that our heuristics are very competitive, robust, and outperform algorithms based on the permutation solution space