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zenodo44/100

Supporting Movies from: Seismo-acoustic observations of crashing ocean waves: Investigating surf monitoring at Coal Oil Point Reserve, Santa Barbara, California

<div> <div> <div> <p>This repository includes supplementary movies from the manuscript titled, "Seismo-acoustic&nbsp;observations of crashing ocean waves: Investigating&nbsp;surf monitoring at Coal Oil Point Reserve, Santa&nbsp;Barbara, California," submitted to the Journal of Geophysical Research: Solid Earth.</p> <p>&nbsp;</p> <p>Movies S1 and S2. These two movies taken during array deployment 4 on October 20, 2023 show the NW tip of Coal Oil Point at the left of the field of view and Sands Beach northwest of that toward the right. Frames have the same figure layout as Figure 4 of the main text.</p> <p>Movie S3. Same as Movies S1 and S2 but with the NW tip of Coal Oil Point at the right of the field of view and Devereux Beach southeast of that toward the left.</p> </div> </div> </div>

opencc-by-4.0Jun 2024View details →
zenodo44/100

IODP Expedition 360 Magnetic susceptibility (point or contact system)

Magnetic susceptibility was measured on section halves on the Section Half Multisensor Logger (SHMSL) using a Bartington MS2 meter and either a MS2E or MS2K probe. Because all JRSO cores meet minimum size requirements for these two probes, MSPOINT data are corrected for volume and recorded in SI susceptibility units (x10<sup>-5</sup>).

opencc-by-4.0Jan 2017View details →
zenodo44/100

IODP Expedition 397 Magnetic susceptibility (point or contact system)

Magnetic susceptibility was measured on section halves on the Section Half Multisensor Logger (SHMSL) using a Bartington MS2 meter and either a MS2E or MS2K probe. Because all JRSO cores meet minimum size requirements for these two probes, MSPOINT data are corrected for volume and recorded in SI susceptibility units (x10<sup>-5</sup>).

opencc-by-4.0Jun 2024View details →
zenodo44/100

Evaluation of the saturator efficiency of the low frost-point generator INRIM 03 Mark 1

<p>These datasets refers to the evaluation of the&nbsp;saturator efficiency of the low frost-point generator INRIM 03 developed at the Istituto Nazionale di Ricerca Metrologica. Alternating the inlet gas&nbsp;between a dry source and a moist gas source is it possible to&nbsp; test the capability of the generator to saturate the carrier gas (or&nbsp;condensate the excess water) at the corresponding saturation<br>temperature.</p> <p>This work has been carried out within the European Metrology&nbsp;Programme for Innovation and Research (EMPIR) Project&nbsp;&lsquo;PROMETH2O&mdash;Metrology for trace water in ultra-pure process&nbsp;gases&rsquo;.<br>This project (Grant No. 20IND06 PROMETH2O) has&nbsp;received funding from the EMPIR programme co-financed&nbsp;by the Participating States and from the European Union&rsquo;s&nbsp;Horizon 2020 research and innovation programme.</p>

opencc-by-4.0Jul 2024View details →
zenodo44/100

Underwater images collected by an Autonomous Surface Vehicle in Pointe-Des-Aigrettes, Réunion - 2024-07-08

<i>This dataset was collected by an Autonomous Surface Vehicle in Pointe-Des-Aigrettes, Réunion - 2024-07-08.</i> <br> <br><br>Underwater or aerial images collected by scientists or citizens can have a wide variety of use for science, management, or conservation. These images can be annotated and shared to train IA models which can in turn predict the objects on the images. We provide a set of tools (hardware and software) to collect marine data, predict species or habitat, and provide maps.<br><br> This dataset is part of larger collection referencing numerous underwater and aerial images <a href="https://doi.org/10.5281/zenodo.11125847" target="_blank">Seatizen Altas</a>. Methods, tools and scientific objectives are also described in a dedicated data paper.<br> <h2> GPS information: </h2> The data was processed with a PPK workflow to achieve centimeter-level GPS accuracy. <br> Base : Files coming from rtk a GPS-fixed station or any static positioning instrument which can provide with correction frames. <br> Device GPS : Emlid Reach M2 <br> Quality of our data - Q1: 91.26 %, Q2: 2.39 %, Q5: 6.35 % <br> <h2> Bathymetry </h2> The data are collected using a single-beam echosounder <a href="https://www.echologger.com/products/single-frequency-echosounder-deep" target="_blank">ETC 400</a>. <br> We only keep the values which have a GPS correction in Q1.<br> We keep the points that are the waypoints.<br> We keep the raw data where depth was estimated between 3.0 m and 50.0 m deep. <br> The data are first referenced against the WGS84 ellipsoid. Then we apply the local geoid if available.<br> At the end of processing, the data are projected into a homogeneous grid to create a raster and a shapefiles. <br> The size of the grid cells is 0.733 m. <br> The raster and shapefiles are generated by linear interpolation. The 3D reconstruction algorithm is ballpivot. <br> <h2> Generic folder structure </h2> YYYYMMDD_COUNTRYCODE-optionalplace_device_session-number <br> ├── DCIM : folder to store videos and photos depending on the media collected. <br> ├── GPS : folder to store any positioning related file. If any kind of correction is possible on files (e.g. Post-Processed Kinematic thanks to rinex data) then the distinction between device data and base data is made. If, on the other hand, only device position data are present and the files cannot be corrected by post-processing techniques (e.g. gpx files), then the distinction between base and device is not made and the files are placed directly at the root of the GPS folder. <br> │ ├── BASE : files coming from rtk station or any static positioning instrument. <br> │ └── DEVICE : files coming from the device. <br> ├── METADATA : folder with general information files about the session. <br> ├── PROCESSED_DATA : contain all the folders needed to store the results of the data processing of the current session. <br> │ ├── BATHY : output folder for bathymetry raw data extracted from mission logs. <br> │ ├── FRAMES : output folder for georeferenced frames extracted from DCIM videos. <br> │ ├── IA : destination folder for image recognition predictions. <br> │ └── PHOTOGRAMMETRY : destination folder for reconstructed models in photogrammetry. <br> └── SENSORS : folder to store files coming from other sources (bathymetry data from the echosounder, log file from the autopilot, mission plan etc.). <br> <h2> Software </h2> All the raw data was processed using our <a href="https://github.com/SeatizenDOI/plancha-workflow/releases/tag/v1.0.3" target="_blank">worflow</a>. <br>All predictions were generated by our <a href="https://github.com/SeatizenDOI/plancha-inference/releases/tag/v1.0.0" target="_blank">inference pipeline</a>. <br>You can find all the necessary scripts to download this data in this <a href="https://github.com/SeatizenDOI/zenodo-tools" target="_blank">repository</a>. <br>Enjoy your data with <a href="https://github.com/SeatizenDOI" target="_blank">SeatizenDOI</a>! <br>

opencc-by-4.0Jul 2024View details →
zenodo44/100

Datasets for testing the robustness of LiDAR vegetation metrics to varying point densities

<p><span>The calculation of vegetation metrics from LiDAR point clouds might be affected by the available point density of a dataset. Testing how the same LiDAR vegetation metrics differ with different point densities can therefore inform about their robustness for upscaling metrics to other areas or other LiDAR point clouds. The datasets made available here were generated to test the robustness of LiDAR vegetation metrics to varying point densities. A total of 25 LiDAR vegetation metrics representing different aspects of vegetation height, vegetation cover and structural complexity were tested (see metric definition in Kissling et al. 2023, <a href="https://doi.org/10.1016/j.dib.2022.108798">https://doi.org/10.1016/j.dib.2022.108798</a>). The metric calculation was similar to the metric calculation in the Laserchicken software (Meijer et al. 2020, <span><a href="https://doi.org/10.1016/j.softx.2020.100626">https://doi.org/10.1016/j.softx.2020.100626</a>) and the Laserfarm workflow (Kissling et al. 2022, https://doi.org/10.1016/j.ecoinf.2022.101836). The Dutch AHN4 dataset from the years 2020&ndash;2022 with a point density of 20&ndash;30 points/m<sup>2</sup> was used. A number of plots (i.e., squared polygons around centre points) were randomly placed across the Netherlands within Dutch Natura 2000 sites (using shapefiles from the European Environmental Agency). Different Dutch Natura 2000 sites were distinguished based on their dominant habitat type (dunes, grassland, marsh, shrubland, and woodland). About 100 plots were randomly placed in each habitat type. The AHN4 point cloud of each plot was clipped and then randomly downsampled to 1, 2, 5, 10, 15, 20 points per square meter, respectively. This was done for six different spatial resolutions (1, 2, 5, 10, 20 and 30 meter). The clipped points were then used to calculate the 25 LiDAR vegetation metrics for the original point density and for the six down-sampled point densities.</span></span></p>

opencc-by-4.0Jul 2024View details →
zenodo44/100

User Study Data from "Point-and-Shake: Selecting from Levitating Object Displays"

<p>This dataset contains anonymous user study data from the two experiments described in the corresponding CHI 2018 publication.</p>

opencc-by-4.0Apr 2018View details →
zenodo44/100

THOR - point clouds

<p><strong>TH&Ouml;R</strong> is a dataset with human motion trajectory and eye gaze data collected in an indoor environment with accurate ground truth for the position, head orientation, gaze direction, social grouping and goals. TH&Ouml;R contains sensor data collected by a 3D lidar sensor and involves a mobile robot navigating the space. In comparison to other, our dataset has a larger variety in human motion behaviour, is less noisy, and contains annotations at higher frequencies.</p> <p>The dataset includes 9 separate recordings in 3 variations:</p> <ul> <li>``One obstacle&quot; - features one obstacle in the environment and no robot</li> <li>``Moving robot&quot; - features one obstacle in the environment and the moving robot</li> <li>``Three obstacles&quot; - features three obstacles in the environment and no robot</li> </ul> <p><strong>THOR - point clouds </strong>is the part of TH&Ouml;R data set containing bag files with 3D scans collcted during the experiments.</p> <p><strong>Reference:</strong></p> <p>For more details check project website <a href="http://thor.oru.se">thor.oru.se</a> or check our publications:</p> <pre><code>@article{thorDataset2019, title={TH\"OR: Human-Robot Indoor Navigation Experiment and Accurate Motion Trajectories Dataset}, author={Andrey Rudenko and Tomasz P. Kucner and Chittaranjan S. Swaminathan and Ravi T. Chadalavada and Kai O. Arras and Achim J. Lilienthal}, journal={arXiv preprint arXiv:1909.04403}, year={2019} }</code></pre>

opencc-by-4.0Sep 2019View details →
zenodo44/100

Fed4Fire/CDN-X-ALL M3AP, M2AP reference points implementation pcap datatsets for the 3GPP MBMS profile

<p>Following datasets were generated at VICOMTECH (https://www.vicomtech.org) under project/experiment CDN-X-ALL: &quot;CDN edge-cloud computing for efficient cache and reliable streaming aCROSS Aggregated unicast-multicast LinkS&quot;.</p> <p>Project funded by Fed4FIRE+ OC5 (<a href="https://www.fed4fire.eu/">https://www.fed4fire.eu</a>) under grant 732638.</p> <p>The following data provide reference pcap captures that include relevant traces with standardized 3GPP interfaces for the 3GPP MBMS (Multimedia Broadcast Multicast Services) profile.</p> <p>Among others, traces include E-UTRAN and Evolved Packet Core pcap captures with standardized 3GPP M2AP and M3AP interfaces and UE MBMS end to end MAC layer PDUs:</p> <p>1- MBMS_OAI_M3AP_M2AP.pcap</p> <p>- OAI eNB LTE; Evolved Universal Terrestrial Radio Access Network (E-UTRAN); M3 Application Protocol (M3AP) in between an MME (Mobility Management Entity) and MCE (Multicast Control Entity) (3GPP TS 36.444 version 14.1.0 Release 14)</p> <p>- OAI eNB LTE; Evolved Universal Terrestrial Radio Access Network (E-UTRAN); M2 Application Protocol (M2AP) in between an MCE (Multicast Control Entity) and eNB (Evolved NodeB) (3GPP TS 36.443 version 14.0.1 Release 14)</p> <p>2- oai_opt_ue_mbms_SIB13_MTCH_MCCH.pcap</p> <p>- OAI UE side LTE MAC and RRC messages</p> <p>Moreover, the above data can be self-re-generated by downloading and building the original open source code pushed (as part of CDN-X-ALL project) to OpenAirInteface5G gitlab open repository. At the time of publishing these data, the original source code falls under branch (https://gitlab.eurecom.fr/oai/openairinterface5g/tree/fed4fire_fec5_cdn-x-all) and is part of ongoing merge request (https://gitlab.eurecom.fr/oai/openairinterface5g/merge_requests/673)</p>

opencc-by-4.0Sep 2019View details →
zenodo44/100

Official GO FAIR Foundation icons for the Three-Point FAIRification Framework

<p>The official icons for the Three-Point FAIRification Framework (3PFF): Metadata for Machines Workshops, FAIR Implementation Profiles and FAIR Orchestration, created by the GO FAIR Foundation.</p>

opencc-by-sa-4.0Apr 2021View details →
zenodo44/100

UAV-based Lidar point clouds of Experimental Station Britz, Brandenburg, 2024

<p><strong>UAV-based Lidar data of a Experimental Forest Station Britz</strong></p> <ul> <li>Date of acquisition: 09.07.2024</li> <li>Location: Experimental Station Britz, Britz, Brandenburg, Germany</li> <li> <div>DEIMS.iD:&nbsp;<a href="https://deims.org/8ee82a9b-5086-4547-b5aa-4064e3314762">https://deims.org/8ee82a9b-5086-4547-b5aa-4064e3314762</a></div> </li> <li>UAV: DJI M300 RTK with SAPOS connection</li> <li>Flight altitude above ground level: 40 m</li> <li>Line spacing: 7 m</li> <li>Sensor: Yellowscan Mapper Plus</li> <li>EPSG: 25833; GCG2016</li> <li>Data products:&nbsp;<br>&bull; &nbsp; &nbsp;High-resolution point cloud in .laz format<br>&bull; &nbsp; &nbsp;Yellowscan Cloudstation strip adjustment report<br>&bull;&nbsp; &nbsp; Trimble Applanix POSPAC - diagnostic report</li> </ul> <p><br><strong>Acknowledgment</strong></p> <p>Dr. Tanja Sanders</p> <p>Dr. Marco Natkhin</p> <p>Institute of Forest Ecosystems<br>Johann Heinrich von Th&uuml;nen Institute<br>Federal Research Institute for Rural Areas, Forestry and Fisheries</p>

opencc-by-4.0Aug 2024View details →
zenodo44/100

Dataset of Kantorovich-Rubinstein-Wasserstein Polytopes of Metric Spaces on up to 6 Points

<p>We present a complete list of all combinatorial types of generic Kantorovich-Rubinstein-Wasserstein (KRW) polytopes associated with metric spaces on up to 6 points that are generic in the sense of Gordon and Petrov, see [1]. These polytopes and their properties are described in detail in [2].</p> <p>The catalog of KRW polytopes was computed using certain regular triangulations of the full root polytope, see Section 4 in [2]. These regular triangulations were enumerated up to symmetry by J&ouml;rg Rambau using the new <em>topcom</em> package described in [3].</p> <p>The provided data comes in three parts.</p> <ul> <li>The files ending in ".result" contain the original&nbsp;<em>topcom</em> output including the specific regular triangulations of the root polytope.</li> <li>There are <em>julia</em> files that contain these triangulations ("triangulations_x.jl"), one triangulation per line.</li> <li>There is an&nbsp;<em>OSCAR</em> script ("read_triangulations.jl") that reads these triangulations and produces sample metrics associated with each of these triangulations.&nbsp;</li> </ul> <h3>References:</h3> <p>[1] J. Gordon and F. Petrov: Combinatorics of the Lipschitz polytope, 2017, &nbsp;Arnold Math. J. <em>3.2.</em></p> <p>[2] E. Delucchi, L. K&uuml;hne, and L. M&uuml;hlherr: <em>Combinatorial invariants of finite metric spaces and the Wasserstein arrangement</em>, 2024, in preparation.</p> <p>[3] J. Rambau: <em>Symmetric lexicographic subset reverse search for the enumeration of circuits, cocircuits, and triangulations up to symmetry, </em>2023, <a href="https://www.wm.uni-bayreuth.de/de/team/rambau_joerg/TOPCOM/SymLexSubsetRS-2.pdf" target="_blank" rel="noopener">preprint</a>.</p>

opencc-by-4.0Jul 2024View details →
zenodo44/100

NMNH Botany Elevation Data: Single Points

Elevation data from specimens in the collections of the Smithsonian National Museum of Natural History Botany Department.<p></p>

opencc-by-4.0Aug 2024View details →
zenodo44/100

IODP Expedition 398 Magnetic susceptibility (point or contact system)

Magnetic susceptibility was measured on section halves on the Section Half Multisensor Logger (SHMSL) using a Bartington MS2 meter and either a MS2E or MS2K probe. Because all JRSO cores meet minimum size requirements for these two probes, MSPOINT data are corrected for volume and recorded in SI susceptibility units (x10<sup>-5</sup>).

opencc-by-4.0Jul 2024View details →
zenodo44/100

IODP Expedition 355 Magnetic susceptibility (point or contact system)

Magnetic susceptibility was measured on section halves on the Section Half Multisensor Logger (SHMSL) using a Bartington MS2 meter and either a MS2E or MS2K probe. Because all JRSO cores meet minimum size requirements for these two probes, MSPOINT data are corrected for volume and recorded in SI susceptibility units (x10<sup>-5</sup>).

opencc-by-4.0Aug 2016View details →
zenodo44/100

IODP Expedition 356 Magnetic susceptibility (point or contact system)

Magnetic susceptibility was measured on section halves on the Section Half Multisensor Logger (SHMSL) using a Bartington MS2 meter and either a MS2E or MS2K probe. Because all JRSO cores meet minimum size requirements for these two probes, MSPOINT data are corrected for volume and recorded in SI susceptibility units (x10<sup>-5</sup>).

opencc-by-4.0Feb 2017View details →
zenodo44/100

Rational polygons with exactly one interior lattice point

<p>This record contains</p> <ul> <li>maximal \(k\)-rational polygons with exactly one interior lattice point for \(1 \leq k \leq 10\),</li> <li>all \(k\)-rational polygons with exactly one interior lattice point for \(1 \leq k \leq 4\),</li> <li>all Ehrhart quasipolynomials of these polygons for \(1 \leq k \leq 5\).</li> <li>all \(k\)-rational LDP polygons (=almost \(k\)-hollow LDP polygons) for \(1 \leq k \leq 5\).</li> </ul> <p>The maximal polygons are stored as text files with one polygon per line. Each line contains the vertices of the polygon multiplied by \(k\) (so that they are integral). The other polygons as well as the Ehrhart quasipolynomials are stored using the <a href="https://www.hdfgroup.org/solutions/hdf5/">HDF5</a> file format. All polygons and Ehrhart quasipolynomials have been obtained using <a href="https://github.com/justus-springer/RationalPolygons.jl">RationalPolygons.jl</a>.</p> <h3>Structure of the HDF5 files for polygons</h3> <p>In the HDF5 files "all_k&lt;k&gt;.h5", the polygons are split into different datasets according to their normalized area and number of vertices. We use "a" to denote the normalized area (twice the euclidian area) and "n" to denote the number of vertices. For example, the \(3\)-rational polygons with normalized area \(30\) having \(5\) vertices are located in "k3_all.h5" under the dataset "/a30/n5". Each dataset of polygons is one-dimensional with one entry per polygon. A polygon is stored using a compound datatype with \(2 \cdot n\) fields of integers. These integers are the vertices of the polygon multiplied by \(k\), stored in column major layout. For example, a triangle with vertices \((x_1,y_1), (x_2,y_2)\) and \((x_3,y_3)\) is stored as the tuple \((k\cdot x_1,k\cdot y_1,k \cdot x_2,k\cdot y_2,k \cdot x_3,k \cdot y_3)\). Moreover, each file contains the special two-dimensional dataset "numbers_of_polygons" that stores the numbers of polygons for a given normalized volume and number of vertices.</p> <h3>Structure of the HDF5 files for Ehrhart quasipolynomials</h3> <p>In the HDF5 files "ehrhart_k&lt;k&gt;.h5", the Ehrhart quasipolynomials are split into different datasets according to the normalized area of the associated polygon. We use "a" for the normalized area (twice the euclidian area). For example, the Ehrhart quasipolynomials of all \(3\)-rational polygons with normalized area \(30\) are located in "ehrhart_k3.h5" under the dataset "/a30". Each Ehrhart quasipolynomial is stored as a \(3 \times k\) integral matrix. Hence each dataset is three-dimensional, with the first dimension to enumerate the quasipolynomials and the latter two dimensions to store each quasipolynomial itself. For the way Ehrhart quasipolynomials are encoded as \(3 \times k\) integral matrices, we refer to the <a href="https://justus-springer.github.io/RationalPolygons.jl/dev/polygons/#Ehrhart-Theory">relevant documentation of RationalPolygons.jl</a>.</p>

opencc-by-4.0Sep 2024View details →
zenodo44/100

Rational polygons with no interior lattice points

<p>This record contains</p> <ul> <li>maximal \(k\)-rational polygons with no interior lattice points for \(1 \leq k \leq 21\),</li> <li>all \(k\)-rational polygons with no interior lattice points, except those that can be realized in the strip \( \mathbb{R} \times [0,1] \) for \(1 \leq k \leq 6\),</li> <li>all Ehrhart quasipolynomials of these polygons for \(1 \leq k \leq 6\).</li> </ul> <p>The maximal polygons are stored as text files with one polygon per line. Each line contains the vertices of the polygon multiplied by \(k\) (so that they are integral). For \(1 \leq k \leq 6\), the files that contain all polygons as well as the Ehrhart quasipolynomials are stored using the <a href="https://www.hdfgroup.org/solutions/hdf5/">HDF5</a> file format. All polygons and Ehrhart quasipolynomials have been obtained using <a href="https://github.com/justus-springer/RationalPolygons.jl">RationalPolygons.jl</a>.</p> <h3>Structure of the HDF5 files for polygons</h3> <p>In the HDF5 files "all_k&lt;k&gt;.h5", the polygons are split into different datasets according to their normalized area and number of vertices. We use "a" to denote the normalized area (twice the euclidian area) and "n" to denote the number of vertices. For example, the \(3\)-rational polygons with normalized area \(30\) having \(5\) vertices are located in "all_k3.h5" under the dataset "/a30/n5". Each dataset of polygons is one-dimensional with one entry per polygon. A polygon is stored using a compound datatype with \(2 \cdot n\) fields of integers. These integers are the vertices of the polygon multiplied by \(k\), stored in column major layout. For example, a triangle with vertices \((x_1,y_1), (x_2,y_2)\) and \((x_3,y_3)\) is stored as the tuple \((k\cdot x_1,k\cdot y_1,k \cdot x_2,k\cdot y_2,k \cdot x_3,k \cdot y_3)\). Moreover, each file contains the special two-dimensional dataset "numbers_of_polygons" that stores the numbers of polygons for a given normalized volume and number of vertices.</p> <h3>Structure of the HDF5 files for Ehrhart quasipolynomials</h3> <p>In the HDF5 files "ehrhart_k&lt;k&gt;.h5", the Ehrhart quasipolynomials are split into different datasets according to the normalized area of the associated polygon. We use "a" for the normalized area (twice the euclidian area). For example, the Ehrhart quasipolynomials of all \(3\)-rational polygons with normalized area \(30\) are located in "ehrhart_k3.h5" under the dataset "/a30". Each Ehrhart quasipolynomial is stored as a \(3 \times k\) integral matrix. Hence each dataset is three-dimensional, with the first dimension to enumerate the quasipolynomials and the latter two dimensions to store each quasipolynomial itself. For the way Ehrhart quasipolynomials are encoded as \(3 \times k\) integral matrices, we refer to the <a href="https://justus-springer.github.io/RationalPolygons.jl/dev/polygons/#Ehrhart-Theory">relevant documentation of RationalPolygons.jl</a>.</p>

opencc-by-4.0Sep 2024View details →
zenodo44/100

Half-integral polygons with few interior lattice points

<p>This record contains</p> <ul> <li>maximal half-integral polygons with up to 40 interior lattice points,</li> <li>all half-integral polygons with up to 12 interior lattice points,</li> <li>all Ehrhart quasipolynomials of half-integral polygons with up to 16 interior lattice points,</li> <li>all half-integral polygons with up to 15 collinear interior lattice points.</li> </ul> <p>The maximal polygons are stored as text files with one polygon per line. Each line contains the vertices of the polygon multiplied by two (so that they are integral). The other polygons as well as the Ehrhart quasipolynomials are stored using the <a href="https://www.hdfgroup.org/solutions/hdf5/">HDF5</a> file format. All polygons and Ehrhart quasipolynomials have been obtained using <a href="https://github.com/justus-springer/RationalPolygons.jl">RationalPolygons.jl</a>.</p> <h3>Structure of the HDF5 files for polygons</h3> <p>In the HDF5 files "all_i&lt;i&gt;.h5", the polygons are split into different datasets according to their normalized area and number of vertices. We use "a" to denote the normalized area (twice the euclidian area) and "n" to denote the number of vertices. For example, the half-integral polygons with \(8\) interior lattice points having normalized area \(60\) with \(5\) vertices are located in "all_i8.h5" under the dataset "/a60/n5". Each dataset of polygons is one-dimensional with one entry per polygon. A polygon is stored using a compound datatype with \(2 \cdot n\) fields of integers. These integers are the vertices of the polygon multiplied by two, stored in column major layout. For example, a triangle with vertices \((x_1,y_1), (x_2,y_2)\) and \((x_3,y_3)\) is stored as the tuple \((2\cdot x_1,2\cdot y_1,2 \cdot x_2,2\cdot y_2,2 \cdot x_3,2 \cdot y_3)\). Moreover, each file contains the special two-dimensional dataset "numbers_of_polygons" that stores the numbers of polygons for a given normalized volume and number of vertices.</p> <h3>Structure of the HDF5 files for Ehrhart quasipolynomials</h3> <p>In the HDF5 files "ehrhart_k&lt;k&gt;.h5", the Ehrhart quasipolynomials are split into different datasets according to the normalized area of the associated polygon. We use "a" for the normalized area (twice the euclidian area). For example, the Ehrhart quasipolynomials of all half-integral polygons \(8\) interior lattice points having normalized area \(60\) are located in "ehrhart_i8.h5" under the dataset "/a60". Each Ehrhart quasipolynomial is stored as a \(3 \times 2\) integral matrix. Hence each dataset is three-dimensional, with the first dimension to enumerate the quasipolynomials and the latter two dimensions to store each quasipolynomial itself. For the way Ehrhart quasipolynomials are encoded as \(3 \times 2\) integral matrices, we refer to the <a href="https://justus-springer.github.io/RationalPolygons.jl/dev/polygons/#Ehrhart-Theory">relevant documentation of RationalPolygons.jl</a>.</p>

opencc-by-4.0Oct 2024View details →
zenodo44/100

3-rational polygons with few interior lattice points

<p>This record contains</p> <ul> <li>maximal 3-rational polygons with up to 5 interior lattice points,</li> <li>all 3-rational polygons with up to 4 interior lattice points,</li> <li>all Ehrhart quasipolynomials of 3-rational polygons with up to 5 interior lattice points.</li> </ul> <p>The maximal polygons are stored as text files with one polygon per line. Each line contains the vertices of the polygon multiplied by two (so that they are integral). The other polygons as well as the Ehrhart quasipolynomials are stored using the <a href="https://www.hdfgroup.org/solutions/hdf5/">HDF5</a> file format. All polygons and Ehrhart quasipolynomials have been obtained using <a href="https://github.com/justus-springer/RationalPolygons.jl">RationalPolygons.jl</a>.</p> <h3>Structure of the HDF5 files for polygons</h3> <p>In the HDF5 files "all_i&lt;i&gt;.h5", the polygons are split into different datasets according to their normalized area and number of vertices. We use "a" to denote the normalized area (twice the euclidian area) and "n" to denote the number of vertices. For example, the 3-rational polygons with \(8\) interior lattice points having normalized area \(60\) with \(5\) vertices are located in "all_i8.h5" under the dataset "/a60/n5". Each dataset of polygons is one-dimensional with one entry per polygon. A polygon is stored using a compound datatype with \(2 \cdot n\) fields of integers. These integers are the vertices of the polygon multiplied by three, stored in column major layout. For example, a triangle with vertices \((x_1,y_1), (x_2,y_2)\) and \((x_3,y_3)\) is stored as the tuple \((3\cdot x_1,3\cdot y_1,3 \cdot x_2,3\cdot y_2,3 \cdot x_3,3 \cdot y_3)\). Moreover, each file contains the special two-dimensional dataset "numbers_of_polygons" that stores the numbers of polygons for a given normalized volume and number of vertices.</p> <h3>Structure of the HDF5 files for Ehrhart quasipolynomials</h3> <p>In the HDF5 files "ehrhart_k&lt;k&gt;.h5", the Ehrhart quasipolynomials are split into different datasets according to the normalized area of the associated polygon. We use "a" for the normalized area (twice the euclidian area). For example, the Ehrhart quasipolynomials of all 3-rational polygons \(8\) interior lattice points having normalized area \(60\) are located in "ehrhart_i8.h5" under the dataset "/a60". Each Ehrhart quasipolynomial is stored as a \(3 \times 3\) integral matrix. Hence each dataset is three-dimensional, with the first dimension to enumerate the quasipolynomials and the latter two dimensions to store each quasipolynomial itself. For the way Ehrhart quasipolynomials are encoded as \(3 \times 3\) integral matrices, we refer to the <a href="https://justus-springer.github.io/RationalPolygons.jl/dev/polygons/#Ehrhart-Theory">relevant documentation of RationalPolygons.jl</a>.</p>

opencc-by-4.0Oct 2024View details →

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