More properties of (β,γ)-Chebyshev functions and points

Recently, (β,γ)-Chebyshev functions, as well as the corresponding zeros, have been introduced as a generalization of classical Chebyshev polynomials of the first kind and related roots. They consist of a family of orthogonal functions on a subset of [−1,1], which indeed satisfies a three-term recurrence formula. In this paper we present further properties, which are proven to comply with various results about classical orthogonal polynomials. In addition, we prove a conjecture concerning the Lebesgue constant's behavior related to the roots of (β,γ)-Chebyshev functions in the corresponding orthogonality interval

Potential of satellite and reanalysis evaporation datasets for hydrological modelling under various model calibration strategies

Twelve actual evaporation datasets are evaluated for their ability to improve the performance of the fully distributed mesoscale Hydrologic Model (mHM). The datasets consist of satellite-based diagnostic models (MOD16A2, SSEBop, ALEXI, CMRSET, SEBS), satellite-based prognostic models (GLEAM v3.2a, GLEAM v3.3a, GLEAM v3.2b, GLEAM v3.3b), and reanalysis (ERA5, MERRA-2, JRA-55). Four distinct multivariate calibration strategies (basin-average, pixel-wise, spatial bias-accounting and spatial bias-insensitive) using actual evaporation and streamflow are implemented, resulting in 48 scenarios whose results are compared with a benchmark model calibrated solely with streamflow data. A process-diagnostic approach is adopted to evaluate the model responses with in-situ data of streamflow and independent remotely sensed data of soil moisture from ESA-CCI and terrestrial water storage from GRACE. The method is implemented in the Volta River basin, which is a data scarce region in West Africa, for the period from 2003 to 2012. Results show that the evaporation datasets have a good potential for improving model calibration, but this is dependent on the calibration strategy. All the multivariate calibration strategies outperform the streamflow-only calibration. The highest improvement in the overall model performance is obtained with the spatial bias-accounting strategy (+29%), followed by the spatial bias-insensitive strategy (+26%) and the pixel-wise strategy (+24%), while the basin-average strategy (+20%) gives the lowest improvement. On average, using evaporation data in addition to streamflow for model calibration decreases the model performance for streamflow (-7%), which is counterbalance by the increase in the performance of the terrestrial water storage (+11%), temporal dynamics of soil moisture (+6%) and spatial patterns of soil moisture (+89%). In general, the top three best performing evaporation datasets are MERRA-2, GLEAM v3.3a and SSEBop, while the bottom three datasets are MOD16A2, SEBS and ERA5. However, performances of the evaporation products diverge according to model responses and across climatic zones. These findings open up avenues for improving process representation of hydrological models and advancing the spatiotemporal prediction of floods and droughts under climate and land use changes

A 3D geological model of a structurally complex Alpine region as a basis for interdisciplinary research

Dataset representing a 3D geological reconstruction of the a section of the Nappe de Morlces, Switzerland. Associated with "A 3D geological model of a structurally complex Alpine region as a basis for interdisciplinary research" (Thornton et al.

Multisensory 3D saliency for artficial attention systems

In this paper we present proof-of-concept for a novel solution consisting of a short-term 3D memory for artificial attention systems, loosely inspired in perceptual processes believed to be implemented in the human brain. Our solution supports the implementation of multisensory perception and stimulus-driven processes of attention. For this purpose, it provides (1) knowledge persistence with temporal coherence tackling potential salient regions outside the field of view, via a panoramic, log-spherical inference grid; (2) prediction, by using estimates of local 3D velocity to anticipate the effect of scene dynamics; (3) spatial correspondence between volumetric cells potentially occupied by proto-objects and their corresponding multisensory saliency scores. Visual and auditory signals are processed to extract features that are then filtered by a proto-object segmentation module that employs colour and depth as discriminatory traits. We consider as features, apart from the commonly used colour and intensity contrast, colour bias, the presence of faces, scene dynamics and also loud auditory sources. Combining conspicuity maps derived from these features we obtain a 2D saliency map, which is then processed using the probability of occupancy in the scene to construct the final 3D saliency map as an additional layer of the Bayesian Volumetric Map (BVM) inference grid

Reconstruction of three-dimensional porous media using generative adversarial neural networks

To evaluate the variability of multi-phase flow properties of porous media at the pore scale, it is necessary to acquire a number of representative samples of the void-solid structure. While modern x-ray computer tomography has made it possible to extract three-dimensional images of the pore space, assessment of the variability in the inherent material properties is often experimentally not feasible. We present a novel method to reconstruct the solid-void structure of porous media by applying a generative neural network that allows an implicit description of the probability distribution represented by three-dimensional image datasets. We show, by using an adversarial learning approach for neural networks, that this method of unsupervised learning is able to generate representative samples of porous media that honor their statistics. We successfully compare measures of pore morphology, such as the Euler characteristic, two-point statistics and directional single-phase permeability of synthetic realizations with the calculated properties of a bead pack, Berea sandstone, and Ketton limestone. Results show that GANs can be used to reconstruct high-resolution three-dimensional images of porous media at different scales that are representative of the morphology of the images used to train the neural network. The fully convolutional nature of the trained neural network allows the generation of large samples while maintaining computational efficiency. Compared to classical stochastic methods of image reconstruction, the implicit representation of the learned data distribution can be stored and reused to generate multiple realizations of the pore structure very rapidly.Comment: 21 pages, 20 figure

Insights in paleoclimate variability through the variographic analysis of stalagmite time series

Abstract Stalagmites are an increasingly important archive of paleoenvironmental change. The rate of annual growth rates of stalagmites is recorded in changes of calcite fabric, annual fluxes of fluorescent organic matter or annual variations in trace element composition. The determining processes governing stalagmite growth are increasingly well understood and modeled. At the scale of chemical processes, the physical controls of stalagmite growth are the flux of water, the CO 2 saturation of drip water relative to the cave atmosphere, and the temperature. The processes determining all three are complex and inter-related. Therefore, although past climates are recorded in the growth laminaes, the climatic signal is perturbed by a noise component related to local hydrologic factors. To separate local from global factors, we used geostatistical tools to analyze annual growth rate data from 11 stalagmites located on 4 different continents. The records range from 200 to 2500 years before present. Detailed variographic analyses showed that the temporal correlation of growth rates is of a specific type in all 11 stalagmites, which has never been observed before. The growth derivative is highly anticorrelated at a lag of 1 year, meaning that an increase in growth rate tends to be systematically followed by a decrease in growth rate. We call this behavior a "flickering" growth. Flickering cannot be explained by climatic factors that tend to vary on larger time scales, and therefore must be related to changes in local hydrologic conditions. We show that the intensity of flickering fluctuates in the last millennia, giving insights in the temporal scale of variability of hydrologic systems under natural conditions

GIM (Groundwater Integrated Modelling). The hydrogeological compiler

Complex problems in Earth Sciences demand the use of numerical models. To this end, a large number of codes have been developed during the last two decades. In spite of their power, as displayed in their many applications, these codes are sparse and, most often, used in the academic framework. To make things worse, they are aimed at solving a given set of physical phenomena (e.g. most codes solve groundwater flow and contaminant transport, but they do not take into account material defor- mation, others include deformation but not heat transfer, etc.) and most often they do not integrate stochastic techniques. GIM (Groundwater Integrated Modelling) is aimed at providing a platform to fill this gap. The objective is to integrate the existing codes in an overall fully-parallel object oriented FORTRAN 95 structure. Thus, the capabilities of GIM are numerous (differ- ent solvers of direct and inverse problem, of groundwater flow, contaminant (conservative or not) or heat transport, etc.) as it takes profit of those of the codes embedded in its structure. The use of GIM is illustrated with a simple example consisting of a Monte Carlo analysis of flow and transport problem: 1. Read data common to most of the existing \u201chost\u201d codes (finite elements or finite differences mesh, geostatistical model, state variable measurements, etc.) in an XML fashion. \u201cHost\u201d code particular variables (options, tolerances, convergence criteria, etc.) are supplied separately. 2. The data are used to pre-process the initial hydraulic conductivity fields on the basis of the geostatistical model. These fields will be calibrated in step 4.3. Write data in the appropriate format for the \u201chost\u201d code. 4. Execute \u201chost\u201d code(s). In this example, an inversion code is used. However, many codes can be used at step 4 (e.g. for solving the inherent direct problem, modeller can use a flow simulator to calculate the velocity field driving the con- taminant transport, which will be simulated using a \u201craw\u201d transport simulator). 5. Collect results (the calibrated fields). 6. Post-process the output (e.g. histogram of hydraulic conductivity). Including \u201chost\u201d codes in the overall structure of GIM is easy. One needs to add a routine for writing data at step 3 and a routine for reading the output at step 5. This confers versatility and an ample room for future developments

POWERING INTERLOCK SYSTEMS AT CERN WITH INDUSTRIAL CONTROLLERS

ABSTRACT Several systems at CERN to protect both superconducting and normal conducting magnets are realised with commercially available industrial PLC's, however, their challenges are slightly different. The Powering Interlock Controller (PIC) for superconducting magnets permits powering when all conditions are fulfilled by communicating with Power Converters and the Quench Protection System. In the case of failure, magnet powering is stopped and the beams are dumped. The response time must be in the order of a few ms. Safety is of utmost importance and critical signals are additionally routed outside the PLC. The Warm Magnet Interlock Controller (WIC) protects the normal conducting magnets from overheating by switching off the power converter when a fault occurs. One system recently became operational, protecting about 300 magnets in the 3 km long transfer line from the SPS to LHC. In order to optimise safety for future installations, the Siemens F Series PLC is being used, offering a self checking safety environment that ensures system integrity. The same technology will be used for a number of accelerators, in particular the LHC. Before deployment in the LHC, a configurable system has been designed and commissioned for the ion accumulator LEIR, demonstrating the flexibility of using the PLC based system. In this paper we describe the architecture and implementation of the magnet interlock systems, and discuss first operational experience