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At least 397 records · Page 22

An optimized FM-index library for nucleotide and amino acid search

Abstract Background Pattern matching is a key step in a variety of biological sequence analysis pipelines. The FM-index is a compressed data structure for pattern matching, with search run time that is independent of the length of the database text. Implementation of the FM-index is reasonably complicated, so that increased adoption will be aided by the availability of a fast and flexible FM-index library. Results We present AvxWindowedFMindex (AWFM-index), a lightweight, open-source, thread-parallel FM-index library written in C that is optimized for indexing nucleotide and amino acid sequences. AWFM-index introduces a new approach to storing FM-index data in a strided bit-vector format that enables extremely efficient computation of the FM-index occurrence function via AVX2 bitwise instructions, and combines this with optional on-disk storage of the index’s suffix array and a cache-efficient lookup table for partial k-mer searches. The AWFM-index performs exact match count and locate queries faster than SeqAn3’s FM-index implementation across a range of comparable memory footprints. When optimized for speed, AWFM-index is $$\sim $$ ∼ 2–4x faster than SeqAn3 for nucleotide search, and $$\sim $$ ∼ 2–6x faster for amino acid search; it is also $$\sim $$ ∼ 4x faster with similar memory footprint when storing the suffix array in on-disk SSD storage. Conclusions AWFM-index is easy to incorporate into bioinformatics software, offers run-time performance parameterization, and provides clients with FM-index functionality at both a high-level (count or locate all instances of a query string) and low-level (step-wise control of the FM-index backward-search process). The open-source library is available for download at https://github.com/TravisWheelerLab/AvxWindowFmIndex.

59 BASIC BIOLOGICAL SCIENCES↗

SMC 2021 : Analyzing Resource Utilization and User Behavior on Titan Supercomputer

Resource utilization statistics of submitted jobs on a supercomputer can help us understand how users from various scientific domains use HPC platforms and better design a job scheduler. We explore to generate insight regarding workload distribution and usage pattern domains from job scheduler trace, GPU failure information, and project-specific information collected from Titan supercomputer. Furthermore, we want to know how the scheduler performance varies over time and how the users' scheduling behavior changes following a system failure. These observations have the potential to provide valuable insight, which is helpful to prepare for system failures. These practices will help us develop and apply novel machine learning algorithms in understanding system behavior, requirement, and better scheduling of HPC systems. There are two datasets, RUR and GPU. RUR: This dataset is the job scheduler traces collected from the Titan supercomputerfrom 01/01/2015 to 07/31/2019 (2015.csv - 2019.csv). These were collected usingResource Utilization Report (RUR), a Cray-developed resource-usage data collectionand reporting system. It contains the usage information of its critical resources (CPU,Memory, GPU, and I/O) of each running job on Titan during that period [2]. ProjectAreas: Every job is associated with a project ID. TheProjectAreas.csvdatasetprovides a mapping of the project ID to its domain science. GPU: There have been some hardware-related issues in the GPUs in Titan that caused some GPUs to fail, sometimes irrecoverably during some job runs. This dataset provides information regarding these failures during the execution of the submitted jobs. GPUs on Titan are uniquely identified by a serial number (SN), and they are installed in a location. A GPU can be installed in a location, then removed from that location following a failure, and then re-installed in a different location after fixing the problem. If the failure can't be recovered, the GPU might be removed entirely from Titan. There are two prominent types of failures that resulted in the removal of GPUs from Titan: Double Bit Error (DBE) and Out of the Bus (OTB). The dataset (gc_full.csv) has the following fields: 1. SN : Serial number of a GPU 2. location : The location where it is installed 3. insert : The time when it was inserted into that location 4. remove : The time when it was removed from that location 5. duration : Amount of time the GPU spent in this location 6. out : If the device was taken out entirely w/o a re-installment into a new location. 7. event : If the GPU was taken out entirely, the reason for its removal. To learn more about this dataset, please refer to the git repositoryhttps://github.com/olcf/TitanGPULifeand the related publication [1]. References [1] George Ostrouchov, Don Maxwell, Rizwan A Ashraf, Christian Engelmann, MallikarjunShankar, and James H Rogers. Gpu lifetimes on titan supercomputer: Survival analysisand reliability. InSC20: International Conference for High Performance Computing,Networking, Storage and Analysis, pages 1-14. IEEE, 2020. [2] Feiyi Wang, Sarp Oral, Satyabrata Sen, and Neena Imam. Learning from five-yearresource-utilization data of titan system. In2019 IEEE International Conference onCluster Computing (CLUSTER), pages 1-6. IEEE, 2019.

42 ENGINEERING↗

SMC 2021 Data Challenge: Analyzing Resource Utilization and User Behavior on Titan Supercomputer

Resource utilization statistics of submitted jobs on a supercomputer can help us understand how users from various scientific domains use HPC platforms and better design a job scheduler. We explore to generate insight regarding workload distribution and usage pattern domains from job scheduler trace, GPU failure information, and project-specific information collected from Titan supercomputer. Furthermore, we want to know how the scheduler performance varies over time and how the users' scheduling behavior changes following a system failure. These observations have the potential to provide valuable insight, which is helpful to prepare for system failures. These practices will help us develop and apply novel machine learning algorithms in understanding system behavior, requirement, and better scheduling of HPC systems. There are two datasets, RUR and GPU: RUR dataset is the job scheduler traces collected from the Titan supercomputer from 01/01/2015 to 07/31/2019 (2015.csv - 2019.csv). These were collected using resource Utilization Report (RUR), a Cray-developed resource-usage data collection and reporting system. It contains the usage information of its critical resources (CPU, Memory, GPU, and I/O) of each running job on Titan during that period (https://ieeexplore.ieee.org/abstract/document/8891001). It includes ProjectAreas as additional information, every job is associated with a project ID. TheProjectAreas.csv dataset provides a mapping of the project ID to its domain science. GPU dataset has information regarding GPU failure on Titan. There have been some hardware-related issues in the GPUs in Titan that caused some GPUs to fail, sometimes irrecoverably during some job runs. This dataset provides information regarding these failures during the execution of the submitted jobs. GPUs on Titan are uniquely identified by a serial number (SN), and they are installed in a location. A GPU can be installed in a location, then removed from that location following a failure, and then re-installed in a different location after fixing the problem. If the failure can't be recovered, the GPU might be removed entirely from Titan. There are two prominent types of failures that resulted in the removal of GPUs from Titan: Double Bit Error (DBE) and Out of the Bus (OTB). The dataset (gc_full.csv) has seven attributes, we provided a short description of these attributes in the ReadMe file. To learn more about this dataset, please refer to the git repository https://github.com/olcf/TitanGPULife and the related publication (https://ieeexplore.ieee.org/abstract/document/9355319).

42 ENGINEERING↗

SST-TG-P1F4R3200: Decaying Stably-Stratified Turbulence (SST), Initialized Using Taylor-Green Vortices (TG) at Prandtl Number Pr=1, Froude Number Fr=4, Reynolds Number Re=3200

This dataset comprises direct numerical simulations (DNS) of decaying stably-stratified turbulence influenced by a linear background density gradient, initialized using an array of Taylor-Green vortices, as described in [Riley & de Bruyn Kops (2003)](https://doi.org/10.1063/1.1578077). The initial Prandtl, Froude, and Reynolds numbers are (Pr, Fr, Re) = (1, 4, 3200). A total of 15,000 snapshots are recorded at uniform time intervals, each with a spatial resolution of 512x512x256 grid points. Four flow variables are associated with each snapshot: the three velocity components (u,v,w) and the perturbed density field (rho) away from the background gradient. All fields are stored in binary format (32-bit little-endian), each with a size of 255 MB, yielding a total dataset size of 15.3 TB. Further details are referenced in the attached README file, and a current list of publications and associated analysis tools are provided at https://stratified-turbulence.github.io/web/.

42 ENGINEERING↗

SST-TG-P50F4R3200: Decaying Stably-Stratified Turbulence (SST), Initialized Using Taylor-Green Vortices (TG) at Prandtl Number Pr=50, Froude Number Fr=4, Reynolds Number Re=3200

This dataset comprises direct numerical simulations (DNS) of decaying stably-stratified turbulence influenced by a linear background density gradient, initialized using an array of Taylor-Green vortices, extending the Pr=1 simulations performed in [Riley and de Bruyn Kops (2003)](https://doi.org/10.1063/1.1578077). The initial Prandtl, Froude, and Reynolds numbers are (Pr, Fr, Re) = (50, 4, 3200). A total of 1,680 snapshots are recorded at uniform time intervals, each with a spatial resolution of 3584x3584x1792 grid points. Four flow variables are associated with each snapshot: the three velocity components (u,v,w) and the perturbed density field (rho) away from the background gradient. All fields are stored in binary format (32-bit little-endian), each with a size of 85.8 GB, yielding a total dataset size of 577 TB. Further details are referenced in the attached README file, and a current list of publications and associated analysis tools are provided at https://stratified-turbulence.github.io/web/.

42 ENGINEERING↗

SST-TG-P7F4R3200: Decaying Stably-Stratified Turbulence (SST), Initialized Using Taylor-Green Vortices (TG) at Prandtl Number Pr=7, Froude Number Fr=4, Reynolds Number Re=3200

This dataset comprises direct numerical simulations (DNS) of decaying stably-stratified turbulence influenced by a linear background density gradient, initialized using an array of Taylor-Green vortices, extending the Pr=1 simulations performed in [Riley and de Bruyn Kops (2003)](https://doi.org/10.1063/1.1578077). The initial Prandtl, Froude, and Reynolds numbers are (Pr, Fr, Re) = (7, 4, 3200). A total of 15,250 snapshots are recorded at uniform time intervals, each with a spatial resolution of 1280x1280x640 grid points. Four flow variables are associated with each snapshot: the three velocity components (u,v,w) and the perturbed density field (rho) away from the background gradient. All fields are stored in binary format (32-bit little-endian), each with a size of 4 GB, yielding a total dataset size of 244 TB. Further details are referenced in the attached README file, and a current list of publications and associated analysis tools are provided at https://stratified-turbulence.github.io/web/.

42 ENGINEERING↗

Structural Models and Sequence Alignment Results of the Desulfovibrio vulgaris Proteome

This dataset contains the structural models for the primary transcripts of the Desulfovibrio vulgaris proteome as well as sequence alignment results for a subset of the encoded proteins. For each protein, the five models inferred from AlphaFold 2 are provided. The largest pTM-scoring model for each protein was energy minimized; this minimized structure as well as its AlphaFold pickle output file are also provided. This set of structures represent an alternate source of models for the D. vulgaris proteome to those available in the AlphaFold Protein Structure Database (AFDB). This is a bit more complicated since the proteins reporting in the AFDB originate from an outdated form of the D. vulgaris sequence. The different versions of the D. vulgaris gene annotation are collected in the Chronology subdirectory; further consideration of these changes on the structural space of the proteome are currently underway. For proteins that have been annotated as hypothetical, sequence alignment results from the HHblits and SAdLSA alignment methods are provided. These methods are often more capable to resolve sequence homology than other methods. Therefore, the results from both HHblits and SAdLSA are provided to identify possible homologs for these challenging proteins. Numerous sequence databases are utilized for these alignments. References AlphaFold v2 Multimer: https://doi.org/10.1101/2021.10.04.463034. References HHblits: hhtps://doi.org/10.1186/s12859-019-3019-7. References SAdLSA: hhtps://doi.org/10.3389/fbinf.2021.689960.

59 BASIC BIOLOGICAL SCIENCES↗

Cryogenic C-band wavelength division multiplexing system using an AIM Photonics Foundry process design kit

Cryogenic environments make superconducting computing possible by reducing thermal noise, electrical resistance and heat dissipation. Heat generated by the electronics and thermal conductivity of electrical transmission lines to the outside world constitute two main sources of thermal load in such systems. As a result, higher data rates require additional transmission lines which come at an increasingly higher cooling power cost. Hybrid or monolithic integration of silicon photonics with the electronics can be the key to higher data rates and lower power costs in these systems. We present a 4-channel wavelength division multiplexing photonic integrated circuit (PIC) built from modulators in the AIM Photonics process development kit (PDK) that operate at 25 Gbps at room temperature and 10 Gbps at 40 K. We further demonstrate 2-channel operation for 20 Gbps aggregate data rate at 40 K using two different modulators/wavelengths, with the potential for higher aggregate bit rates by utilizing additional channels.

42 ENGINEERING↗

Optimal resource allocation for flexible-grid entanglement distribution networks

We use a genetic algorithm (GA) as a design aid for determining the optimal provisioning of entangled photon spectrum in flex-grid quantum networks with arbitrary numbers of channels and users. After introducing a general model for entanglement distribution based on frequency-polarization hyperentangled biphotons, we derive upper bounds on fidelity and entangled bit rate for networks comprising one-to-one user connections. Simple conditions based on user detector quality and link efficiencies are found that determine whether entanglement is possible. We successfully apply a GA to find optimal resource allocations in four different representative network scenarios and validate features of our model experimentally in a quantum local area network in deployed fiber. Our results show promise for the rapid design of large-scale entanglement distribution networks.

97 MATHEMATICS AND COMPUTING↗

Entanglement-based quantum digital signatures over a deployed campus network

The quantum digital signature protocol offers a replacement for most aspects of public-key digital signatures ubiquitous in today’s digital world. A major advantage of a quantum-digital-signatures protocol is that it can have information-theoretic security, whereas public-key cryptography cannot. Here we demonstrate and characterize hardware to implement entanglement-based quantum digital signatures over our campus network. Over 25 hours, we collect measurements on our campus network, where we measure sufficiently low quantum bit error rates (<5% in most cases) which in principle enable quantum digital signatures at over 50 km as shown through rigorous simulation accompanied by a noise model developed specifically for our implementation. These results show quantum digital signatures can be successfully employed over deployed fiber. Moreover, our reported method provides great flexibility in the number of users, but with reduced entanglement rate per user. Finally, while the current implementation of our entanglement-based approach has a low signature rate, feasible upgrades would significantly increase the signature rate.

97 MATHEMATICS AND COMPUTING↗

Strain-concentration for fast, compact photonic modulation and non-volatile memory

A critical figure of merit (FoM) for electro-optic (EO) modulators is the transmission change per voltage, d T / d V . Conventional approaches in wave-guided modulators maximize d T / d V via a high EO coefficient or longer light-material interaction lengths but are ultimately limited by material losses and nonlinearities. Optical and RF resonances improve d T / d V at the cost of spectral non-uniformity, especially for high- Q optical cavity resonances. Here, we introduce an EO modulator based on piezo-strain-concentration of a photonic crystal cavity to address both trade-offs: (i) it eliminates the trade-off between d T / d V and waveguide loss—i.e., enhancement of the resonance tuning efficiency d v c / d V for the fixed EO coefficient, waveguide length, and cavity Q —and (ii) at high DC strains it exhibits a non-volatile (NV) cavity tuning Δ v c ,NV for passive memory and programming of multiple devices into resonance despite fabrication variations. The device is fabricated on a scalable silicon nitride-on-aluminum nitride platform. We measure d v c / d V =177±1MHz/V, corresponding to Δ v c =40±0.32GHz for a voltage spanning ±120V with an energy consumption of δ U /Δ v c =0.17nW/GHz. The modulation bandwidth is flat up to ω BW,3dB /2 π =3.2±0.07MHz for broadband DC-AC and 142±17MHz for resonant operation near a 2.8 GHz mechanical resonance. Optical extinction up to 25 dB is obtained via Fano-type interference. Strain-induced beam-buckling modes are programmable under a “read-write” protocol with a continuous, repeatable tuning range of 5±0.25GHz, allowing for storage and retrieval, which we quantify with mutual information of 2.4 bits and a maximum non-volatile excursion of 8 GHz. Using a full piezo-optical finite-element-model (FEM) we identify key design principles for optimizing strain-based modulators and chart a path towards achieving performance comparable to lithium niobate-based modulators and the study of high strain physics on-chip.

Wen, Y. Henry (ORCID:0009000685423628)↗

Spatio-spectral quantum state estimation of photon pairs from optical fiber using stimulated emission

Developing a quantum light source that carries more than one bit per photon is pivotal for expanding quantum information applications. Characterizing a high-dimensional multiple-degree-of-freedom source at the single-photon level is challenging due to the large parameter space as well as limited emission rates and detection efficiencies. Here, we characterize photon pairs generated in optical fiber in the transverse-mode and frequency degrees of freedom by applying stimulated emission in both degrees of freedom while detecting in one of them at a time. This method may be useful in the quantum state estimation and optimization of various photon-pair source platforms in which complicated correlations across multiple degrees of freedom may be present.

Kim, Dong Beom (ORCID:0000000346887375)↗

Utah FORGE Downhole Geophone Seismic Data (August 2022)

This is a link to downhole geophone data collected by Schlumberger. These data were collected in the Utah FORGE deep seismic monitoring wells 58-32 and 56-32. The format is a standard SEGY and the units are bits. To convert to acceleration (m/s2) multiply by 2.333 x 10-7. Use one of the scripts linked below to use wget commands to pull the data.

15 GEOTHERMAL ENERGY↗

Underwater Target Detection Software Demonstration on the RivGen Turbine

This repository contains data and processing scripts necessary to train the object detection models utilized in the underwater target detection software demonstration on the RivGen turbine project and to produce performance metrics (precision, recall, mAP50, mAP50-95). - Contents - Data consist of "images" and "labels". Each image has an associated label, both share the same time string in its file name (e.g., 2024_05_25_09_01_57.98.jpg and 2024_05_25_09_01_57.98.txt). Time strings have the format %yyyy_%mm_%dd_%HH_%MM_%SS.%3f. Images and labels were curated from 2021 and 2024 smolt outmigration periods at the project site in Igiugig, AK. Images are monochrome 8-bit images of objects (smolt, debris, and other) passing through the field of view of the deployed cameras during various operational stages of the RivGen turbine. Labels are text files indicating the class and bounding polygon of each object in an image. The provided labels use the "YOLO" label format. - Requirements - Python3.8+ is required to install and run the train and validation script. The README.md provides instruction for installing the requirements from the requirements.py file. - Instructions - The "example_train.py" file ingests the provided data, trains a model, and produces model performance metrics at completion. NOTE: model performance metrics will vary from run to run as a consequence of the random selection of training and validation data.

16 TIDAL AND WAVE POWER↗

Sap Velocity Data for Urban Trees in Chicago, Illinois (2024-2025)

This dataset contains uncorrected sap velocity measurements using the heat ratio method (HRM) collected using ICT International SFM1x sensors at five urban sites in Chicago, Illinois, as part of the DOE CROCUS project. The data includes continuous monitoring of sap velocity from various tree species, including Maples (Acer spp.): Sugar Maple (Acer saccharum), Silver Maple (Acer saccharinum), and Red Maple (Acer rubrum); Oaks (Quercus spp.): Swamp White Oak (Quercus bicolor); American Elm (Ulmus americana); Honey Locust (Gleditsia triacanthos); Cottonwood (Populus deltoides); and Tree of Heaven (Ailanthus altissima) across Chicago State University (CSU), Northeastern Illinois University (NEIU), Northwestern University (NU), University of Illinois Chicago (UIC), and West Woodlawn "Blacks in Green" (BIG). These include both street trees and those in urban park locations. Measurements were collected at 15-20 minute intervals, depending on the sensor, and transmitted via Long Range Wide Area Network (LoRaWAN) protocols. The wireless data was collected by Sage Network (https://sagecontinuum.org/) nodes. The dataset includes sensor ID, Global Positioning System (GPS) coordinates, tree species (common and scientific names), tree identification number, diameter at breast height (DBH in cm), uncorrected sap velocity measurements (cm/hr) from both inner and outer probes, and Sage Node identifiers so the data can be mapped to related variables such as air quality and wind speed that were collected on the Sage nodes. All timestamps are in local Chicago time (CDT/CST). Quality control flags are provided using a 3-bit binary system indicating physical range violations (< -10 or > 60 cm/hr), step spikes (absolute difference > 36 cm/hr), and stuck sensor conditions (> 10 consecutive identical values). These are raw data, not corrected for wood anatomy or species-specific characteristics. Data is provided in comma separated (CSV) format. This dataset is part of a larger collection of CROCUS environmental monitoring data, including linked datasets from Air Quality Transmitter (AQT) sensors, Weather Transmitter (WXT) sensors, and Multi-Function Research LoRaWAN (MFR) Nodes. DOIs for the supporting data are provided as part of this data package.

Chicago↗

A network of soil moisture, soil temperature, air temperature, net radiation, ground heat flux and ground water for Chicago, Illinois

This dataset contains environmental monitoring data collected using solar-powered Multi-Function Research (MFR) Long Range Wide Area (LoRaWAN)-enabled nodes at 11 sites in Chicago, Illinois, as part of the DOE Urban Integrated Field Lab CROCUS project. The MFR node system consists of an Input/Output Digital Input Module (IB8) interface box (ICT International) providing wired connections for environmental sensors and an MFR-Node-L data logger that manages power, data processing, and LoRaWAN communication. The wireless data are ingested via Sage network (https://sagecontinuum.org/) nodes that contain LoRaWAN antennae. Measurements were collected from 11 MFR nodes deployed across Chicago State University (CSU), Northeastern Illinois University (NEIU), Northwestern University (NU), University of Illinois Chicago (UIC), West Woodlawn "Blacks in Green" (BIG), and Indian Boundary Prairies (IBP). Each MFR node supports a consistent suite of sensors measuring atmospheric, soil, and hydrological variables. Atmospheric measurements include 2m air temperature (°C), 2m vapor pressure deficit (kPa), and 2m shortwave/longwave radiation (incoming and outgoing, W/m²) measured using ATH-VPD and Apogee SN500 sensors. Soil measurements include volumetric water content (VWC, %) and temperature (°C) at four depths (15, 30, 45, and 60 cm below surface) using Meter Teros54 sensors, and heat flux (W/m²) at 10 cm depth using Huske HFP01-05 sensors. At selected locations, Meter Hydros21 sensors measure groundwater depth (mm), specific conductivity (dS/m), and temperature (°C). The dataset includes timestamps, site identifiers with location names, device IDs, Global Positioning System (GPS) coordinates, variable names with units, measurement depths, values, sensor names, and Sage node identifiers. All timestamps are in local Chicago time (CDT/CST). Quality control flags are provided using a 6-bit binary system indicating physical range violations, step spikes, 24-hour flat-line conditions, 6-hour jitter, 7-day ultra-low variance, and persistent high offset. Data is provided in CSV and CF-compliant NetCDF formats. This dataset is part of a larger collection of CROCUS environmental monitoring data, including linked datasets from Air Quality Transmitter (AQT) sensors, Weather Transmitter (WXT) sensors, and Sap Flow Meter (SFM1x) sensors.

Chicago↗

Materials science for quantum information science and technology

Quantum computing, sensing, and communications are emerging technologies that may circumvent known limitations of their existing traditional counterparts. While the promises of these technologies are currently narrow in scope, it is possible that they will broadly impact our lives by revolutionizing the capabilities of data centers and medical diagnostics, for example. At the heart of these technologies is the use of a quantum object to contain information, called a quantum bit or qubit. Current realizations of qubits exist in a broad variety of material systems, including individual spins in semiconductors or insulators, superconducting circuits, and trapped ions. Further advancement of qubits requires significant contributions from materials science in areas of materials selection, synthesis, fabrication, simulation and characterization. In this paper, we discuss some of the needs and opportunities for contributions to advance the fundamental understanding of materials used in quantum information applications.

36 MATERIALS SCIENCE↗

Crustal Strain Rates in the Western United States and Their Relationship with Earthquake Rates

Abstract We present a suite of strain rate models for the western United States based on geologic and geodetic data. The geologic data consist of Quaternary fault-slip rates and the geodetic data consists of a new compilation of Global Positioning System (GPS) velocities derived from continuous, semicontinuous, and campaign measurements. We remove postseismic deformation from the GPS time series in order for our geodetic strain rate model to best capture the interseismic strain accumulation rate. We present models based on either geologic or geodetic data, but also create a hybrid model. Although there are some differences between the models, the large-scale features are the same, with the noticeable exception for the Pacific Northwest where interseismic strain is naturally more distributed than the long-term strain release. We also present a map of earthquake rate densities based on mainshocks, and the result has similar spatial features similar to the strain rate models (at least in the southwestern United States). We perform a general correlation analysis between strain rate and seismicity rate (south of Cascadia) and find a change in linearity between seismicity and strain rates from slow to faster deforming areas with seismicity rates relatively lower for the latter. The extent of that change depends a bit on assumptions made on the declustering and completeness of the catalog, but the finding of a change in slope is robust across the different strain rate models. Linearity for all areas is only expected when Gutenberg–Richter parameters and parameters involved in the conversion from strain to moment rate are uniform across the study area. We discuss these qualifications, but find no single satisfactory explanation for our observation. Moreover, when considering a rather short time and space, theoretical considerations of sampling from a power-law distribution actually predict there to be a power law instead of a linear relationship, generally consistent with our observation.

Geochemistry & Geophysics↗