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A deep learning approach to real-time HIV outbreak detection using genetic data

Pathogen genomic sequence data are increasingly made available for epidemiological monitoring. A main interest is to identify and assess the potential of infectious disease outbreaks. While popular methods to analyze sequence data often involve phylogenetic tree inference, they are vulnerable to errors from recombination and impose a high computational cost, making it difficult to obtain real-time results when the number of sequences is in or above the thousands. Here, we propose an alternative strategy to outbreak detection using genomic data based on deep learning methods developed for image classification. The key idea is to use a pairwise genetic distance matrix calculated from viral sequences as an image, and develop convolutional neutral network (CNN) models to classify areas of the images that show signatures of active outbreak, leading to identification of subsets of sequences taken from an active outbreak. We showed that our method is efficient in finding HIV-1 outbreaks with R0 ≥ 2.5, and overall a specificity exceeding 98% and sensitivity better than 92%. We validated our approach using data from HIV-1 CRF01 in Europe, containing both endemic sequences and a well-known dual outbreak in intravenous drug users. Our model accurately identified known outbreak sequences in the background of slower spreading HIV. Importantly, we detected both outbreaks early on, before they were over, implying that had this method been applied in real-time as data became available, one would have been able to intervene and possibly prevent the extent of these outbreaks. This approach is scalable to processing hundreds of thousands of sequences, making it useful for current and future real-time epidemiological investigations, including public health monitoring using large databases and especially for rapid outbreak identification.

59 BASIC BIOLOGICAL SCIENCES↗

Quantum annealing algorithms for Boolean tensor networks

Abstract Quantum annealers manufactured by D-Wave Systems, Inc., are computational devices capable of finding high-quality heuristic solutions of NP-hard problems. In this contribution, we explore the potential and effectiveness of such quantum annealers for computing Boolean tensor networks. Tensors offer a natural way to model high-dimensional data commonplace in many scientific fields, and representing a binary tensor as a Boolean tensor network is the task of expressing a tensor containing categorical (i.e., $$\{0, 1\}$$ { 0 , 1 } ) values as a product of low dimensional binary tensors. A Boolean tensor network is computed by Boolean tensor decomposition, and it is usually not exact. The aim of such decomposition is to minimize the given distance measure between the high-dimensional input tensor and the product of lower-dimensional (usually three-dimensional) tensors and matrices representing the tensor network. In this paper, we introduce and analyze three general algorithms for Boolean tensor networks: Tucker, Tensor Train, and Hierarchical Tucker networks. The computation of a Boolean tensor network is reduced to a sequence of Boolean matrix factorizations, which we show can be expressed as a quadratic unconstrained binary optimization problem suitable for solving on a quantum annealer. By using a novel method we introduce called parallel quantum annealing, we demonstrate that Boolean tensor’s with up to millions of elements can be decomposed efficiently using a DWave 2000Q quantum annealer.

97 MATHEMATICS AND COMPUTING↗

Space Launch System Liftoff and Separation Dynamics Analysis Tool Chain

A flexible, hierarchical tool chain that is being applied to NASA’s Space Launch System (SLS) for critical dynamics phenomena is described. This tool chain, called CLVTOPS, is used to investigate lateral liftoff movement of the vehicle as it departs and clears the mobile launch tower and separation of the two solid rocket boosters without collision with the core stage and payload. The toolset’s architecture was configured to take advantage of a modern software-engineering approach for maximum flexibility and utilization of open-source simulations and associated tools. As opposed to a “monolithic” approach, scripting languages were used to “bind” together a tool chain to configure and organize input data, execute and produce analysis results, and post-process these results to facilitate a rapid iterative analysis process to quickly address issues and pursue alternatives with emphasis on analysis automation. Key capabilities in the tool chain include processing and mining of very large data sets, a wide range of graphical depictions, and high-fidelity, physics-based simulations. The paper begins with a problem description and the motivation for liftoff and separation dynamics analysis followed by a historical survey of dynamics analyses for previous NASA human-rated launch vehicles. Details of the tool chain and its components are then introduced divided, first, into description of the scripting language architecture used to “bind” the simulation tools, programs, and scripts together and, second, the physics models and simulations. Representative analyses and data products are shown for liftoff and booster separation dynamics that provide in-depth insight to the tool chain’s capabilities. Supporting activities such as simulation tool chain verification, version archiving and data management, and training are addressed. The paper concludes with case examples on how the tool chain can be tailored to related aerospace dynamics analyses, both large and small. These patterns and techniques for SLS dynamics tool construction can be applied for other aerospace simulations.

6DOF↗

The effects of well damage and completion designs on geoelectrical responses in mature wellbore environments

Well integrity is one of the major concerns in long-term geologic storage sites due to the potential risk of well leakage and groundwater contamination. Evaluating changes in electrical responses due to energized steel-cased wells has the potential to quantify and predict possible wellbore failures because any kind of breakage or corrosion along highly conductive well casings will have an impact on the distribution of the subsurface electrical potential. However, realistic wellbore-geoelectrical models that can fully capture fine-scale details of well completion design and the state of well damage at the field scale require extensive computational effort, or they can even be intractable to simulate. To overcome this computational burden while still keeping the model realistic, we have used the hierarchical finite-element method that represents electrical conductivity at each dimensional component (1D edges, 2D planes, and 3D cells) of a tetrahedral mesh. This allows well completion designs with real-life geometric scales and well systems with realistic, detailed, progressive corrosion and damage in our models. We have developed a comparison of possible discretization approaches of a multicasing completion design in the finite-element model. The effects of the surface casing and the coupling between concentric well casings as well as the effects of the degree and the location of well damage on the electrical responses are also examined. As a result, we analyze real surface electric field data to detect wellbore integrity failure associated with damage.

58 GEOSCIENCES↗

Central Atlantic regional ecological test site: A prototype regional environmental information system

The author has identified the following significant results. A comparison of photomorphic regions from an uncontrolled ERTS-1 mosaic of CARETS to land use areas on a map published in the National Atlas revealed close correlations in non-urban regions. Such regional scale analysis of ERTS-1 data has the potential for providing an economical sampling strategy for selecting sites for more detailed field measurements if other environmental variables can be correlated with patterns on ERTS-1 imagery. ERTS-1 imagery has also revealed for the first time the appearance of CARETS during the winter months. Investigators have identified extensive areas of conifers, which have previously been indistinguishable from deciduous vegetation. Imagery has also shown very clearly the extent of snow cover at a particular time over the region. The evaluation of ERTS-1 imagery used for the land use mapping of the shore zone of CARETS, has shown that the presence or absence of elements of an hierarchal system of shoreline landforms can help identify areas of potential rapid change. Changes in land use class distributions on the Barrier Islands signify the environmental response to natural and man-caused processes. Both environmental vulnerability and sensitivity can be estimated from the repetitive ERTS-1 coverage of long reaches of the CARETS coast. Results indicate potential applications to land use planning, management, and regional environmental quality analysis.

Alexander, R. H.↗

Extremely massive disc galaxies in the nearby Universe form through gas-rich minor mergers

ABSTRACT In our hierarchical structure-formation paradigm, the observed morphological evolution of massive galaxies – from rotationally supported discs to dispersion-dominated spheroids – is largely explained via galaxy merging. However, since mergers are likely to destroy discs, and the most massive galaxies have the richest merger histories, it is surprising that any discs exist at all at the highest stellar masses. Recent theoretical work by our group has used a cosmological, hydrodynamical simulation to suggest that extremely massive (M* > 1011.4 M⊙) discs form primarily via minor mergers between spheroids and gas-rich satellites, which create new rotational stellar components and leave discs as remnants. Here, we use UV-optical and H i data of massive galaxies, from the Sloan Digital Sky Survey, Galaxy Evolution Explorer, Dark Energy Camera Legacy Survey (DECaLS), and Arecibo Legacy Fast ALFA surveys, to test these theoretical predictions. Observed massive discs account for ∼13 per cent of massive galaxies, in good agreement with theory (∼11 per cent). ∼64 per cent of the observed massive discs exhibit tidal features, which are likely to indicate recent minor mergers, in the deep DECaLS images (compared to ∼60 per cent in their simulated counterparts). The incidence of these features is at least four times higher than in low-mass discs, suggesting that, as predicted, minor mergers play a significant (and outsized) role in the formation of these systems. The empirical star formation rates agree well with theoretical predictions and, for a small galaxy sample with H i detections, the H i masses and fractions are consistent with the range predicted by the simulation. The good agreement between theory and observations indicates that extremely massive discs are indeed remnants of recent minor mergers between spheroids and gas-rich satellites.

79 ASTRONOMY AND ASTROPHYSICS↗

A class Hierarchical, object-oriented approach to virtual memory management

The Choices family of operating systems exploits class hierarchies and object-oriented programming to facilitate the construction of customized operating systems for shared memory and networked multiprocessors. The software is being used in the Tapestry laboratory to study the performance of algorithms, mechanisms, and policies for parallel systems. Described here are the architectural design and class hierarchy of the Choices virtual memory management system. The software and hardware mechanisms and policies of a virtual memory system implement a memory hierarchy that exploits the trade-off between response times and storage capacities. In Choices, the notion of a memory hierarchy is captured by abstract classes. Concrete subclasses of those abstractions implement a virtual address space, segmentation, paging, physical memory management, secondary storage, and remote (that is, networked) storage. Captured in the notion of a memory hierarchy are classes that represent memory objects. These classes provide a storage mechanism that contains encapsulated data and have methods to read or write the memory object. Each of these classes provides specializations to represent the memory hierarchy.

Russo, Vincent F.↗

FPGA-Accelerated Range-Limited Molecular Dynamics

Long timescale Molecular Dynamics (MD) simulation of small molecules is crucial in drug design and basic science. To accelerate a small data set that is executed for a large number of iterations, high-efficiency is required. Recent work in this domain has demonstrated that among COTS devices only FPGA-centric clusters can scale beyond a few processors. The problem addressed here is that, as the number of on-chip processors has increased from fewer than 10 into the hundreds, previous intra-chip routing solutions are no longer viable. We find, however, that through various design innovations, high efficiency can be maintained. These include replacing the previous broadcast networks with ring-routing and then augmenting the rings with out-of-order and caching mechanisms. Others are adding a level of hierarchical filtering and memory recycling. Two novel optimized architectures emerge, together with a number of variations. These are validated, analyzed, and evaluated. We find that in the domain of interest speed-ups over GPUs are achieved. Finally, the potential impact is that this system promises to be the basis for scalable long timescale MD with commodity clusters.

97 MATHEMATICS AND COMPUTING↗

Using action space clustering to constrain the recent accretion history of Milky Way-like galaxies

ABSTRACT In the currently favoured cosmological paradigm galaxies form hierarchically through the accretion of satellites. Since a satellite is less massive than the host, its stars occupy a smaller volume in action space. Actions are conserved when the potential of the host halo changes adiabatically, so stars from an accreted satellite would remain clustered in action space as the host evolves. In this paper, we identify recently disrupted accreted satellites in three Milky Way-like disc galaxies from the cosmological baryonic FIRE-2 simulations by tracking satellites through simulation snapshots. We try to recover these satellites by applying the cluster analysis algorithm Enlink to the orbital actions of accreted star particles in the z = 0 snapshot. Even with completely error-free mock data we find that only 35 per cent (14/39) satellites are well recovered while the rest (25/39) are poorly recovered (i.e. either contaminated or split up). Most (10/14 ∼70 per cent) of the well-recovered satellites have infall times <7.1 Gyr ago and total mass >4 × 108M⊙ (stellar mass more than 1.2 × 106 M⊙, although our upper mass limit is likely to be resolution dependent). Since cosmological simulations predict that stellar haloes include a population of in situ stars, we test our ability to recover satellites when the data include 10–50 per cent in situ contamination. We find that most previously well-recovered satellites stay well recovered even with 50 per cent contamination. With the wealth of 6D phase space data becoming available we expect that cluster analysis in action space will be useful in identifying the majority of recently accreted and moderately massive satellites in the Milky Way.

79 ASTRONOMY AND ASTROPHYSICS↗

Abstracts of the Annual Meeting of Planetary Geologic Mappers, Flagstaff, AZ, 2010

Topics covered include: Detailed Analysis of the Intra-Ejecta Dark Plains of Caloris Basin, Mercury; The Formation and Evolution of Tessera and Insights into the Beginning of Recorded History on Venus: Geology of the Fortuna Tessera Quadrangle (V-2); Geologic Map of the Snegurochka Planitia Quadrangle (V-1): Implications for the Volcanic History of the North Polar Region of Venus; Geological Map of the Fredegonade (V-57) Quadrangle, Venus: Status Report; Geologic Mapping of V-19; Geology of the Lachesis Tessera Quadrangle (V-18), Venus; Comparison of Mapping Tessera Terrain in the Phoebe Regio (V-41) and Tellus Tessera (V-10) Quadrangles; Geologic Mapping of the Devana Chasma (V-29) Quadrangle, Venus; Geologic Mapping of the Aristarchus Plateau Region on the Moon; Geologic Mapping of the Lunar South Pole Quadrangle (LQ-30); The Pilot Lunar Geologic Mapping Project: Summary Results and Recommendations from the Copernicus Quadrangle; Geologic Mapping of the Nili Fossae Region of Mars: MTM Quadrangles 20287, 20282, 25287, 25282, 30287, and 30282; Geologic Mapping of the Mawrth Vallis Region, Mars: MTM Quadrangles 25022, 25017, 25012, 20022, 20017, and 20012; Evidence for an Ancient Buried Landscape on the NW Rim of Hellas Basin, Mars; New Geologic Map of the Argyre Region of Mars: Deciphering the Geologic History Through Mars Global Surveyor, Mars Odyssey, and Mars Express Data; Geologic Mapping in the Hesperia Planum Region of Mars; Geologic Mapping of the Meridiani Region of Mars; Geologic Mapping in Southern Margaritifer Terra; Geology of -30247, -35247, and -40247 Quadrangles, Southern Hesperia Planum, Mars; The Interaction of Impact Melt, Impact-Derived Sediment, and Volatiles at Crater Tooting, Mars; Geologic Map of the Olympia Cavi Region of Mars (MTM 85200): A Summary of Tactical Approaches; Geology of the Terra Cimmeria-Utopia Planitia Highland Lowland Transitional Zone: Final Technical Approach and Scientific Results; Geology of Libya Montes and the Interbasin Plains of Northern Tyrrhena Terra, Mars: First Year Results and Second Year Work Plan; Mars Global Geologic Mapping Progress and Suggested Geographic-Based Hierarchal Systems for Unit Grouping and Naming; Progress in the Scandia Region Geologic Map of Mars; Geomorphic Mapping of MTMS -20022 and -20017; Geologic Mapping of the Medusae Fossae Formation, Mars, and the Northern Lowland Plains, Venus; Volcanism on Io: Results from Global Geologic Mapping; Employing Geodatabases for Planetary Mapping Conduct - Requirements, Concepts and Solutions; and Planetary Geologic Mapping Handbook - 2010.

Bleamaster, Leslie F., III↗

"Hierarchical Speed Planner for Automated Vehicles: A Framework for Lagrangian Variable Speed Limit in Mixed Autonomy Traffic"

This paper introduces a novel control framework for Lagrangian variable speed limits in hybrid traffic flow environments utilizing automated vehicles (AVs). The framework was validated using a fleet of 100 connected automated vehicles as part of the largest coordinated open-road test designed to smooth traffic flow. The framework includes two main components: a high-level controller deployed on the server side, named Speed Planner, and low-level controllers called vehicle controllers deployed on the vehicle side. The Speed Planner designs and updates target speeds for the vehicle controllers based on real-time Traffic State Estimation (TSE) [1]. The Speed Planner comprises two modules: a TSE enhancement module and a target speed design module. The TSE enhancement module is designed to minimize the effects of inherent latency in the received traffic information and to improve the spatial and temporal resolution of the input traffic data. The target speed design module generates target speed profiles with the goal of improving traffic flow. The vehicle controllers are designed to track the target speed meanwhile responding to the surrounding situation. The numerical simulation indicates the performance of the proposed method: the bottleneck throughput has increased by 5.01%, and the speed standard deviation has been reduced by a significant 34.36%. We further showcase an operational study with a description of how the controller was implemented on a field-test with 100 AVs and its comprehensive effects on the traffic flow.

Wang, Han↗

High performance FPGA embedded system for machine learning based tracking and trigger in sPhenix and EIC

We present a comprehensive end-to-end pipeline to classify triggers versus background events in this paper. This pipeline makes online decisions to select signal data and enables the intelligent trigger system for efficient data collection in the Data Acquisition System (DAQ) of the upcoming sPHENIX and future EIC (Electron-Ion Collider) experiments. Starting from the coordinates of pixel hits that are lightened by passing particles in the detector, the pipeline applies three-stage of event processing (hits clustering, track reconstruction, and trigger detection) and labels all processed events with the binary tag of trigger versus background events. The pipeline consists of deterministic algorithms such as clustering pixels to reduce event size, tracking reconstruction to predict candidate edges, and advanced graph neural network-based models for recognizing the entire jet pattern. In particular, we apply the message-passing graph neural network to predict links between hits and reconstruct tracks and a hierarchical pooling algorithm (DiffPool) to make the graph-level trigger detection. We obtain an impressive performance (≥70% accuracy) for trigger detection with only 3200 neuron weights in the end-to-end pipeline. We deploy the end-to-end pipeline into a field-programmable gate array (FPGA) and accelerate the three stages with speedup factors of 1152, 280, and 21, respectively.

Instruments & Instrumentation↗

Performance of the engineering analysis and data system 2 common file system

The Engineering Analysis and Data System (EADS) was used from April 1986 to July 1993 to support large scale scientific and engineering computation (e.g. computational fluid dynamics) at Marshall Space Flight Center. The need for an updated system resulted in a RFP in June 1991, after which a contract was awarded to Cray Grumman. EADS II was installed in February 1993, and by July 1993 most users were migrated. EADS II is a network of heterogeneous computer systems supporting scientific and engineering applications. The Common File System (CFS) is a key component of this system. The CFS provides a seamless, integrated environment to the users of EADS II including both disk and tape storage. UniTree software is used to implement this hierarchical storage management system. The performance of the CFS suffered during the early months of the production system. Several of the performance problems were traced to software bugs which have been corrected. Other problems were associated with hardware. However, the use of NFS in UniTree UCFM software limits the performance of the system. The performance issues related to the CFS have led to a need to develop a greater understanding of the CFS organization. This paper will first describe the EADS II with emphasis on the CFS. Then, a discussion of mass storage systems will be presented, and methods of measuring the performance of the Common File System will be outlined. Finally, areas for further study will be identified and conclusions will be drawn.

Debrunner, Linda S.↗

Hydrogen Bond Benchmark: Focal‐Point Analysis and Assessment of DFT Functionals

We performed a hierarchical, convergent ab initio benchmark study and systematically analyzed the performance of density functional approximations for describing hydrogen bonds in small neutral, cationic, and anionic complexes, as well as in larger systems involving amide, urea, deltamide, and squaramide moieties. Focal point analyses (FPA), extrapolating to the ab initio limit, were carried out using correlated wave function methods up to CCSDT(Q) for the small complexes and CCSD(T) for the larger systems, together with correlation-consistent Gaussian basis sets up to the complete basis set limit. Optimized geometries and vibrational frequencies were obtained at the CCSD(T) level. The resulting FPA hydrogen-bond energies converge within a few tenths of a kcal mol −1 . These reference data were used to evaluate 60 density functionals (including 12 dispersion-corrected), spanning the local-density approximation (LDA), generalized gradient approximations (GGAs), meta-GGAs, hybrids, meta-hybrids, double-hybrids, and range-separated hybrids. Overall, the meta-hybrid M06-2X provides the best performance for both hydrogen bond energies and geometries, while the dispersion-corrected GGAs BLYP-D3(BJ) and BLYP-D4 also yield accurate hydrogen-bond data and can serve as cost-effective options for studying large and complex systems.

coupled cluster theory↗

Scalable/Secure Cooperative Algorithms and Framework for Extremely-high Penetration Solar Integration (SolarExPert) (Final Technical Report)

This SolarExPert project has developed a Sustainable Grid Platform (SGP) with scalable architecture of distributed control and optimization. The SGP consists of the following major functions: 1) an advanced grid architecture with hierarchical and distributed communication and control, combined with the OpenFMB standard and implemented on the Multi-Agent OpenDSS (MA-OpenDSS) platform; 2) an online distributed stochastic optimal power flow; 3) an online distributed system state estimation algorithm; 4) the distributed Volt/VAR optimization and frequency control algorithms; 5) the distributed distribution system restoration strategy. The developed SGP together with advanced functions are tested in 1 million (1M)-node distribution system on the MA-OpenDSS platform. Furthermore, the models and algorithms are tested in 100,000-node system HiL simulation, and also in P-HiL implementation with 100 physical devices. The developed functions haven been validated and tested on the selected actual distribution feeder with the data collected from the field of Maui Meadows in Hawaii. The distributed PV hosting capacities with cooperative Volt/VAR and Volt/VAR/Watt control are estimated and compared to provide recommendations for customers and the utility company.

14 SOLAR ENERGY↗

Cooperative high-performance storage in the accelerated strategic computing initiative

The use and acceptance of new high-performance, parallel computing platforms will be impeded by the absence of an infrastructure capable of supporting orders-of-magnitude improvement in hierarchical storage and high-speed I/O (Input/Output). The distribution of these high-performance platforms and supporting infrastructures across a wide-area network further compounds this problem. We describe an architectural design and phased implementation plan for a distributed, Cooperative Storage Environment (CSE) to achieve the necessary performance, user transparency, site autonomy, communication, and security features needed to support the Accelerated Strategic Computing Initiative (ASCI). ASCI is a Department of Energy (DOE) program attempting to apply terascale platforms and Problem-Solving Environments (PSEs) toward real-world computational modeling and simulation problems. The ASCI mission must be carried out through a unified, multilaboratory effort, and will require highly secure, efficient access to vast amounts of data. The CSE provides a logically simple, geographically distributed, storage infrastructure of semi-autonomous cooperating sites to meet the strategic ASCI PSE goal of highperformance data storage and access at the user desktop.

Gary, Mark↗

Lessons Learned in the Livingstone 2 on Earth Observing One Flight Experiment

The Livingstone 2 (L2) model-based diagnosis software is a reusable diagnostic tool for monitoring complex systems. In 2004, L2 was integrated with the JPL Autonomous Sciencecraft Experiment (ASE) and deployed on-board Goddard's Earth Observing One (EO-1) remote sensing satellite, to monitor and diagnose the EO-1 space science instruments and imaging sequence. This paper reports on lessons learned from this flight experiment. The goals for this experiment, including validation of minimum success criteria and of a series of diagnostic scenarios, have all been successfully net. Long-term operations in space are on-going, as a test of the maturity of the system, with L2 performance remaining flawless. L2 has demonstrated the ability to track the state of the system during nominal operations, detect simulated abnormalities in operations and isolate failures to their root cause fault. Specific advances demonstrated include diagnosis of ambiguity groups rather than a single fault candidate; hypothesis revision given new sensor evidence about the state of the system; and the capability to check for faults in a dynamic system without having to wait until the system is quiescent. The major benefits of this advanced health management technology are to increase mission duration and reliability through intelligent fault protection, and robust autonomous operations with reduced dependency on supervisory operations from Earth. The work-load for operators will be reduced by telemetry of processed state-of-health information rather than raw data. The long-term vision is that of making diagnosis available to the onboard planner or executive, allowing autonomy software to re-plan in order to work around known component failures. For a system that is expected to evolve substantially over its lifetime, as for the International Space Station, the model-based approach has definite advantages over rule-based expert systems and limit-checking fault protection systems, as these do not scale well. The model-based approach facilitates reuse of the L2 diagnostic software; only the model of the system to be diagnosed and telemetry monitoring software has to be rebuilt for a new system or expanded for a growing system. The hierarchical L2 model supports modularity and expendability, and as such is suitable solution for integrated system health management as envisioned for systems-of-systems.

Hayden, Sandra C.↗

Hierarchical Fractional Advection-Dispersion Equation (FADE) to Quantify Anomalous Transport in River Corridor over a Broad Spectrum of Scales: Theory and Applications

Fractional calculus-based differential equations were found by previous studies to be promising tools in simulating local-scale anomalous diffusion for pollutants transport in natural geological media (geomedia), but efficient models are still needed for simulating anomalous transport over a broad spectrum of scales. This study proposed a hierarchical framework of fractional advection-dispersion equations (FADEs) for modeling pollutants moving in the river corridor at a full spectrum of scales. Applications showed that the fixed-index FADE could model bed sediment and manganese transport in streams at the geomorphologic unit scale, whereas the variable-index FADE well fitted bedload snapshots at the reach scale with spatially varying indices. Further analyses revealed that the selection of the FADEs depended on the scale, type of the geomedium (i.e., riverbed, aquifer, or soil), and the type of available observation dataset (i.e., the tracer snapshot or breakthrough curve (BTC)). When the pollutant BTC was used, a single-index FADE with scale-dependent parameters could fit the data by upscaling anomalous transport without mapping the sub-grid, intermediate multi-index anomalous diffusion. Pollutant transport in geomedia, therefore, may exhibit complex anomalous scaling in space (and/or time), and the identification of the FADE’s index for the reach-scale anomalous transport, which links the geomorphologic unit and watershed scales, is the core for reliable applications of fractional calculus in hydrology.

97 MATHEMATICS AND COMPUTING↗