Find research datasets worth reusing
Search datasets from major research repositories and use ShareScore to quickly assess how well each record supports discovery, access, and reuse.
206
datasets available to search
ShareScore release 0.9.0
Dataset results
206 results for “Rationality”
Data for: Rational Approximation of Golden Angles: Accelerated Reconstructions for Radial MRI
<p>Magnetic Resonance Imaging data used in the work "Rational Approximation of Golden Angles: Accelerated Reconstructions for Radial MRI". The data is provided in a file format used by the BART toolbox (DOI: <a href="http://doi.org/10.5281/zenodo.592960">10.5281/zenodo.592960</a>).</p> <p> </p> <p>The *_ind.{cfl,hdr} files store the indices of the different spokes of the corresponding datasets:</p> <p> </p> <p><strong>data_res_S{1597,0987,0377,0233,0089,0055,0021}</strong></p> <p>Type: Radial Dataset</p> <p>Object: Single-slice of T1 sphere of the NIST phantom (Model 106)</p> <p>Sequence: FLASH</p> <p>TR|TE [ms]: 3.2|2.04</p> <p>FA [deg]: 8</p> <p>T_RF [ms]: 0.4</p> <p>BWTP: 1.6</p> <p>FOV [mm]: 200</p> <p>Spoke Angle: 2\psi_{16,15,13,12,10,9,7}^1</p> <p>Sampling: RAGA</p> <p><br> </p> <p><strong>data_bin_raga, data_bin_ga</strong></p> <p>Type: Radial Single-Shot Dataset</p> <p>Object: Single-slice of T1 sphere of the NIST phantom (Model 106)</p> <p>Sequence: IR FLASH</p> <p>TR|TE [ms]: 2.9|1.77</p> <p>FA [deg]: 8</p> <p>T_RF [ms]: 0.4</p> <p>BWTP: 1.6</p> <p>FOV [mm]: 200</p> <p>Spoke Angle: 2\psi_{13}^1, 2\psi^1</p> <p>Sampling: RAGA</p> <p><br> </p> <p><strong>data_bin_ga</strong></p> <p>Type: Radial Single-Shot Dataset</p> <p>Object: Single-slice of T1 sphere of the NIST phantom (Model 106)</p> <p>Sequence: IR FLASH</p> <p>TR|TE [ms]: 2.9|1.77</p> <p>FA [deg]: 8</p> <p>T_RF [ms]: 0.4</p> <p>BWTP: 1.6</p> <p>FOV [mm]: 200</p> <p>Spoke Angle: 2\psi^1</p> <p>Sampling: GA</p> <p><br><br> </p> <p><strong>data_invivo_ga</strong></p> <p>Type: Radial Dataset</p> <p>Object: Single-slice cardiac short-axis</p> <p>Sequence: FLASH</p> <p>TR|TE [ms]: 2.9|1.77</p> <p>FA [deg]: 8</p> <p>T_RF [ms]: 0.4</p> <p>BWTP: 1.6</p> <p>FOV [mm]: 320</p> <p>Spoke Angle: \psi^1</p> <p>Sampling: Golden-Ratio</p> <p><br> </p> <p> </p> <p><strong>data_invivo_raga</strong></p> <p>Type: Radial Dataset</p> <p>Object: Single-slice cardiac short-axis</p> <p>Sequence: FLASH</p> <p>TR|TE [ms]: 2.9|1.77</p> <p>FA [deg]: 8</p> <p>T_RF [ms]: 0.4</p> <p>BWTP: 1.6</p> <p>FOV [mm]: 320</p> <p>Spoke Angle: \psi_{13}^1</p> <p>Sampling: RAGA</p> <p><br> </p>
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<k>.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<k>.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>
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<k>.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<k>.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>
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<i>.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<k>.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>
Guidelines for the rational design and engineering of 3D manufactured solid oxide fuel cell composite electrodes
<p>This file contains the data reported in the paper:</p> <p>A Bertei, F Tariq, V Yufit, E Ruiz-Trejo, N P Brandon, <em>Guidelines for the rational design and engineering of 3D manufactured solid oxide fuel cell composite electrodes</em>, <strong>Journal of the Electrochemical Society</strong> (2016)</p> <p>All the data here reported can be reproduced by solving the equations reported in the manuscript with the corresponding parameters.</p>
Corrected Diophantine Rational Sextuples List
<p>Phillip E. Gibbs published a list of 644 Diophantine Sextuples in <a href="https://www.researchgate.net/profile/Philip-Gibbs-2/publication/309429323_A_Survey_of_Rational_Diophantine_Sextuples_of_Low_Height/links/581099ae08aef2ef97b28ed8/A-Survey-of-Rational-Diophantine-Sextuples-of-Low-Height.pdf">https://www.researchgate.net/profile/Philip-GiA Survey of Rational Diophantine Sextuples of Low Height</a> in Annex A.</p> <p>Unfortunately the indexing was incorrect. The downloaded file has made corrections to his original list, and carefully followed the index scheme which he used as much as possible.</p>
Source code and simulation results: Efficient rational approximation of optical response functions with the AAA algorithm
<p>This publication provides data published in the article "Efficient rational approximation of optical response functions with the AAA algorithm" [1] in tabulated form along with the Matlab scripts that have been used to produce them. These scripts interface the finite element method solver JCMsuite [2,3]. The article presents rational approximations of optical response functions based on an extended version of the AAA algorithm [4] that allows to efficiently reconstruct sensitivty spectra and gives access to sensitivities of poles, residues, and zeros. Furthermore, the rational approximation of a scalar observalbe is used to construct solutions of the source free Maxwell's equation, i.e., a nonlinear eigenvalue problem. </p> <p><strong>The physical Structure</strong></p> <p>The example is based on the chiral metasurface introduced in [5]. For the sake of simplicity we added infinite layers of SiO\(_2\) to the top and the bottom of the structure. The original structure has a SiO\(_2\) substrate and a layer of PMMA polymethyl methacrylate (PMMA) deposited on top. PMMA can be modelled with the same refractive index of 1.45 as SiO\(_2\). Furthermore, our simulations include the 13 nm indium tin oxide (ITO) coating which drastically reduces the Q-factor as it is slightly absorbing. The accuracy of the discrete model is verified by assessing reflection, transmission, and absorption at 241 evenly spaced points within the specified range. Energy conservation requires that the discrepancy between their sum and the energy entering the system is zero. The numerical discretization is chosen such that the maximum relative error is less than \(3\times10^{−5}\).</p> <p><strong>Dispersion</strong></p> <p>Tabulated data for ITO has been taken from the <a href="https://refractiveindex.info/?shelf=other&book=In2O3-SnO2&page=Konig">refractiveindex.info</a> database (T. A. F. König et al., 2014, https://doi.org/10.1021/nn501601e) and the data for TiO2 was kindly provided the authors of [5]. The permittivity \(\varepsilon = (n+ik)^2\) is locally approximated as a rational function, i.e., only data in a vicinity of the frequency range of interest is considered. As we aim for a function with the symmetry \(f^\ast(\omega) = f(-\omega^\ast)\) we add the complex conjugated data at negative frequencies and enforce the symmetry in a second step. The partial fraction decomposition of the required function is of the form: \(\varepsilon(\omega) = \varepsilon_\infty + \sum_{j=1}^{4}a_j/(\omega-\omega_j) - a_j^\ast/(\omega+\omega_j^\ast)\) with the residues \(a_j\) and the poles \(\omega_j\). We expect 4 pairs of poles to sufficiently approximate the data within the range of interest (4 with positive and 4 with negative real parts).</p> <h4><strong>Requirements</strong></h4> <ul> <li>JCMsuite (at least 6.2.0)</li> <li>MATLAB (tested with version R2023b)</li> </ul> <p>In order to run the simulations with JCMsuite you must replace corresponding place holders with a path to your installation of JCMsuite. Free trial licenses are available, please refer to the homepage of <a href="https://jcmwave.com/">JCMwave</a>.</p> <p><strong>Usage</strong></p> <p>With the content of 'spectra.zip' you can reproduce results presented in the paper. Running the script 'plots.m' will not start any expensive simulation but use the provided data. With 'dispersion.m' the fits to the material data can be reproduced. Additionally, tabulated data is contained in 'data/ascii'. The archive 'eigenmodes.zip' must be extracted in the same directory as 'spectra.zip'.</p> <p><strong>References</strong></p> <p>[1] Fridtjof Betz, Martin Hammerschmidt, Lin Zschiedrich, Sven Burger, Felix Binkowski: Efficient rational approximation of optical response functions<br>with the AAA algorithm, https://doi.org/10.48550/arXiv.2403.19404.</p> <p>[2] Jan Pomplun, Sven Burger, Lin Zschiedrich, Frank Schmidt, Adaptive finite element method for simulation of optical nano structures, Physica Status Solidi B <strong>244</strong>, 3419 (2007), http://dx.doi.org/10.1002/pssb.200743192.</p> <p>[3] Fridtjof Betz, Felix Binkowski, Sven Burger, RPExpand: Software for Riesz projection expansion of resonance phenomena, SoftwareX <strong>15</strong>, 100763 (2021), https://doi.org/10.1016/j.softx.2021.100763.</p> <p>[4] Y. Nakatsukasa, O. Sète, and L. N. Trefethen, The AAA Algorithm for Rational Approximation, SIAM Journal on Scientific Computing <strong>40</strong>, A1494 (2018), http://dx.doi.org/10.1137/16M1106122.</p> <p>[5] X. Zhang, Y. Liu, J. Han, Y. Kivshar, and Q. Song, Chiral emission from resonant metasurfaces, Science <strong>377</strong>, 1215 (2022), http://dx.doi.org/%2010.1126/science.abq7870.</p>
FEX3-ECG/Charts01: Least Squares Approximation of ECG Signals with Rational Functions
<p> </p> <p> We introduce a new algorithm for "Least Squares Approximation of ECG Signals with Rational Functions". Detailed description here: <a href="https://doi.org/10.5281/zenodo.7628747">https://doi.org/10.5281/zenodo.7628747</a> . The following is one result of the approximations and its charts.</p> <p><br> The original ECG signals:<br> DOI: <a href="https://doi.org/10.13026/C28C71">https://doi.org/10.13026/C28C71</a><br> License: Open Data Commons Attribution License v1.0</p> <p>We approached the following signal from the database above:<br> Patient009, the file: S0035_RE.XYZ, vy(Frank lead system)<br> The location of the QRS: 8669th point (8.669 sec)</p> <p>That is:<br> The approximated signal (P QRS T) section: 1:1139, the location of the QRS 371<br> The first signal point = 8299th data point.<br> Detailes:<br> locations of data points : 8299 8300 8301 .. 8669 .. 9437<br> indexes of signal points : 1 2 3 .. 371 .. 1139<br> values of signal points : 291 282 307 .. 352</p> <p>The signal described above is approximated by the following parameters of rational function in the example_1a.m short program.</p> <p><em>The </em><em>grids of charts:</em><br> X axis: 40ms (The sampling rate is 1000Hz)<br> Y axis: 0.1mV (200 A/D units)<br> This is on the original medical ECG paper: 1mm x 1mm.</p> <p> </p> <p><strong>FILES of Charts01.zip:<br> example_1a.m</strong> This file contains a short script of charts.(GNU Octave or MATLAB?)<br> Input: no. <strong><em>The parameters are in this</em></strong><strong><em> short</em></strong><strong><em> program.</em></strong><br> Output: Figure_b_1 and Figure_b_2<br> <strong>PQRST_sgnl_a.m</strong> Subroutine (of example_1a.m)</p> <p><strong>Figure_b_1.jpg</strong> First output chart of the example_1a.m<br> blue An approximation of the P wave<br> red An approximation of the QRS wave<br> yellow An approximation of the T wave<br> magenta An approximation of the Ta wave</p> <p><strong>Figure_b_2.jpg</strong> Second output chart of the example_1a.m<br> blue An approximation of all the waves (the sum of the above)</p> <p><strong>data_a_c.csv</strong> Result spreadsheet of the approximation program (decimal comma)<br> <strong>data_a_</strong><strong>p</strong><strong>.csv</strong> Result spreadsheet of the approximation program (decimal point)<br> Columns:<br> R relative QRS relative indexing<br> Original The original ECG signal<br> Approx An approximation of the ECG signal<br> Err220128 Error and noise (+date: yymmdd)<br> BL174355 Baseline (+time: hhmmss)<br> P(+Ta) An approximation of the P wave (+Ta wave)<br> QRS An approximation of the QRS wave<br> T An approximation of the T wave<br> V__idy 4 The length of the ECG vector (normalized, max. = 1mV)</p> <p><strong>image_a_</strong><strong>1</strong><strong>.gif</strong> First chart of the columns in the data_a_?.csv (MS Excel)<br> Original<br> Approx<br> Err220128<br> BL174355</p> <p><strong>image_a_</strong><strong>2</strong><strong>.gif</strong> Second chart of the columns in the data_a_?.csv (MS Excel)<br> P(+Ta)<br> QRS<br> T</p> <p> Kobzos, Laszlo<br> Location: HU (Budapest)<br> email: zehu.kola.ci@gmail.com</p> <p> </p>
Ehrhart series coefficients and quasi-period for random rational polytopes
<p><strong>Ehrhart series coefficients and quasi-period for random rational polytopes</strong></p> <p>A dataset of Ehrhart data for 84000 randomly generated rational polytopes, in dimensions 2 to 4, with quasi-periods 2 to 15.</p> <p>The polytopes used to generate this data were produced by the following algorithm:</p> <ol> <li>Fix <span class="math-tex">\(d\)</span> a positive integer in <span class="math-tex">\(\{2,3,4\}\)</span>.</li> <li>Choose <span class="math-tex">\(r\in\{2,\ldots,15\}\)</span> uniformly at random.</li> <li>Choose <span class="math-tex">\(d + k\)</span> lattice points <span class="math-tex">\(\{v_1,\ldots,v_{d+k}\}\)</span> uniformly at random in a box <span class="math-tex">\([-5r,5r]^d\)</span>, where <span class="math-tex">\(k\)</span> is chosen uniformly at random in <span class="math-tex">\(\{1,\ldots,5\}\)</span>.</li> <li>Set <span class="math-tex">\(P := \mathrm{conv}\{v_1,\ldots,v_{d+k}\}\)</span>. If <span class="math-tex">\(\mathrm{dim}(P)\)</span> is not equal to <span class="math-tex">\(d\)</span> then return to step 3.</li> <li>Choose a lattice point <span class="math-tex">\(v\in P \cap \mathbb{Z}^d\)</span> uniformly at random and replace <span class="math-tex">\(P\)</span> with the translation <span class="math-tex">\(P-v\)</span>.</li> <li>Replace <span class="math-tex">\(P\)</span> with the dilation <span class="math-tex">\(P/r\)</span>.</li> </ol> <p>The final dataset was produced by first removing duplicate records, and then downsampling to a subset with 2000 datapoints for each pair <span class="math-tex">\((d,q)\)</span>, where <span class="math-tex">\(d\)</span> is the dimension of <span class="math-tex">\(P\)</span> and <span class="math-tex">\(q\)</span> is the quasi-period of <span class="math-tex">\(P\)</span>, with <span class="math-tex">\(d\in\{2,3,4\}\)</span> and <span class="math-tex">\(q\in\{2,\ldots,15\}\)</span>.</p> <p>For details, see the paper:</p> <p> <em>Machine Learning the Dimension of a Polytope</em>, Tom Coates, Johannes Hofscheier, and Alexander M. Kasprzyk, 2022.</p> <p>If you make use of this data, please cite the above paper and the DOI for this data:</p> <p> doi:10.5281/zenodo.6614829</p> <p><strong>quasiperiod.txt.gz</strong><br> The file "quasiperiod.txt.gz" is a gzip-compressed plain text file containing key:value records with keys and values as described below, where each record is separated by a blank line. There are 84000 records in the file.</p> <p><strong>Example record</strong><br> ULID: 01G57JBYP2ZW825E0NT4Q9JQNQ<br> Dimension: 2<br> Quasiperiod: 2<br> Volume: 97<br> EhrhartDelta: [1,50,195,289,192,49]<br> Ehrhart: [1,50,198,...]<br> LogEhrhart: [0.000000000000000000000000000000,3.91202300542814605861875078791,5.28826703069453523626966617327,...]</p> <p>(The values for Ehrhart and LogEhrhart in the example have been truncated.)</p> <p>For each polytope <span class="math-tex">\(P\)</span> of dimension <span class="math-tex">\(d\)</span> and quasi-period <span class="math-tex">\(q\)</span> we record the following keys and values in the dataset:</p> <p>ULID: A randomly generated string identifier for this record.<br> Dimension: A positive integer. The dimension <span class="math-tex">\(2 \leq d \leq 4\)</span> of the polytope <span class="math-tex">\(P\)</span>.<br> Quasiperiod: A positive integer. The quasi-period <span class="math-tex">\(2 \leq q \leq 15\)</span> of the polytope <span class="math-tex">\(P\)</span>.<br> Volume: A positive rational number. The lattice-normalised volume <span class="math-tex">\(\mathrm{Vol}(P)\)</span> of the polytope <span class="math-tex">\(P\)</span>.<br> EhrhartDelta: A sequence <span class="math-tex">\([1,a_1,a_2,\ldots,a_N]\)</span> of integers of length <span class="math-tex">\(N + 1\)</span>, where <span class="math-tex">\(N := q(d + 1) - 1\)</span>. This is the Ehrhart <span class="math-tex">\(\delta\)</span>-vector (or <span class="math-tex">\(h^*\)</span>-vector) of <span class="math-tex">\(P\)</span>. The Ehrhart series <span class="math-tex">\(\mathrm{Ehr}(P)\)</span> of <span class="math-tex">\(P\)</span> is given by the power-series expansion of <span class="math-tex">\((1 + a_1t + a_2t^2 + \ldots + a_Nt^N) / (1 - t^q)^{d+1}\)</span>.<br> Ehrhart: A sequence <span class="math-tex">\([1,c_1,c_2,\ldots,c_{1100}]\)</span> of positive integers. The value <span class="math-tex">\(c_i\)</span> is equal to the number of lattice points in the <span class="math-tex">\(i\)</span>-th dilation of <span class="math-tex">\(P\)</span>, that is, <span class="math-tex">\(c_i = \#(iP \cap \mathbb{Z}^d)\)</span>. Equivalently, <span class="math-tex">\(c_i\)</span> is the coefficient of <span class="math-tex">\(t^i\)</span> in <span class="math-tex">\(\mathrm{Ehr}(P) = 1 + c_1t + c_2t^2 + \ldots = (1 + a_1t + a_2t^2 + \ldots + a_Nt^N) / (1 - t^q)^{d+1}\)</span>.<br> LogEhrhart: A sequence <span class="math-tex">\([0,y_1,y_2,\ldots,y_{1100}]\)</span> of non-negative floating point numbers. Here <span class="math-tex">\(y_i := \log c_i\)</span>.</p>
Resource-Rational Lossy-Context Surprisal (Model Predictions)
<p>Resource-Rational Lossy-Context Surprisal is a computationally implemented model of how humans process language, predicting at what points in complex sentences they experience comprehension difficulty. It unifies the memory-based and expectation-based paradigms in psycholinguistics, and provides a more refined account of when hierarchical structure is difficult to comprehend for humans.</p> <p>This repository contains output of the model on a battery of test sentences exhibiting iterated recursive structure, described in associated publications on Resource-Rational Lossy-Context Surprisal. The filenames are referred to in the source code, to be published together with a forthcoming journal publication on the model.</p> <p>The model was first described in the following publication:</p> <p><em>Lexical Effects in Structural Forgetting: Evidence for Experience-Based Accounts and a Neural Network Model</em></p> <p>(Michael Hahn, Richard Futrell, Edward Gibson), 33rd Annual CUNY Human Sentence Processing Conference, 2020</p>
Figure 2 in The impact of wheat resistance and bio-rational insecticides toxicity against cherry-oat aphid, Rhopalosiphum padi L. (Hemiptera: Aphididae)
Figure 2: Trichomes density on mm 2 leaf area of various wheat varieties. Each value is the mean of five replications. *Mean followed by the same letter do not differ significantly at p = 0.05
Figure 3 in The impact of wheat resistance and bio-rational insecticides toxicity against cherry-oat aphid, Rhopalosiphum padi L. (Hemiptera: Aphididae)
Figure 3. Effect of IGR's and plant extracts application on the population of Rhopalosiphum padi. A. After the first spray, B. After the second spray DBT (day before treatment), DAT (day after treatment).
Figure 1 in The impact of wheat resistance and bio-rational insecticides toxicity against cherry-oat aphid, Rhopalosiphum padi L. (Hemiptera: Aphididae)
Figure 1: Rhopalosiphum padi preference at various time intervals and varieties. Each value is the mean of five replications. *Mean followed by the same letter do not differ significantly at p = 0.05
Fig 6 in Reproductive biology of the main fish species in lakes Taabo, Kossou and Faé (Côte d'Ivoire) with a view to rational fishing
Fig 6: Non-metric multidimensional scaling (nMDS) plot of months of reproduction of fish species in Lakes Taabo, Kossou and Faé Table 1: List of fish species studied in the three lakes
Racionální užití léků ve stáří (rational use of drugs in geriaric age- EU COST Action IS1402 and EUROAGEISM H2020 project)
<p>During the EU COST Action IS1402 video presentations, the information on ageism in medication use, ageist approaches at regulatory level, at the level of service provision and in rationality of drug prescribing in older adults have been emphasized, as well as main aims of FIP7 project in the EUROAGEISM H2020 (FIP project is entitled "Inappropriate prescribing and availability of medication safety and medication management services in older patients in Europe and other countries"). Video presentation is in national language- Czech. </p>
FEX3-ECG/Charts02: Least Squares Approximation of ECG Signals with Rational Functions
<p><br> We introduce a new algorithm for "Least Squares Approximation of ECG Signals with Rational Functions". Detailed description here: <a href="https://doi.org/10.5281/zenodo.7628747">https://doi.org/10.5281/zenodo.7628747</a> . The following figures show the results of some of the approximations.<br> <br> The original ECG signals:<br> DOI: <a href="https://doi.org/10.13026/C28C71">https://doi.org/10.13026/C28C71</a><br> License: Open Data Commons Attribution License v1.0</p> <p><strong><em>Notes:</em></strong></p> <p>- We refer to the database records as follows: s.... = serial number, p... = patient. For example: <strong>s0508_p269</strong>. If we want to specify the location more precisely within the record, we also indicate the lead and the time of the QRS. For example: <strong>s0508_p269, vy, 6689</strong> (Where "vy" is one of the Frank leads.).</p> <p>- The figures were created with Microsoft Excel (gif, non-animated). In addition to the figures, data files of the results are usually also included. In the text files, we used a decimal point (for GNU Octave) or a decimal comma (for Excel). Any text editor can be used to transform them, replacing all commas with points or vice versa.</p> <p>- In some ppaarraamm.txt files, we have written the location and values of the parameters of each approximation (in Hungarian). The starting point of the time coordinate is now the first point of the ECG signal drawing. For the quadratic parameters of the numerator, the values of the two real roots or the conjugate complex root are placed one after the other. Similarly, the quadratic parameters of the denominator have the values of the conjugate complex root one after the other. The data from <strong>example_1a.m </strong>in <a href="https://doi.org/10.5281/zenodo.6479410">https://doi.org/10.5281/zenodo.6479410</a> is from <strong>From_series\s0035_p009\vy\ppaarraamm.txt</strong> also found below.<br> <em>Mini <strong>Hu==>En dictionary</strong>: </em>ha==>if; nincs==>there is none; számláló==>numerator; nevező==>denominator; a pontok száma==>the number of points; nullad- és elsőfokú==>zeroth and first degree; másodfokú==>second degree; hely_bazis==>location base (the origin of the drawings).</p> <p>- Below, the meaning of the two numbers after the wave letter is related to the number of approximation parameters. For example: P35 means: P wave, 3 is the number of parameters of the numerator (including the main coefficient <strong>d</strong>), while 5 is the number of pole <strong>pairs</strong> (factors) of the denominator. So the number of approximation parameters is 3 + 2×5=13.<br> The meaning of Ta here: the approximation includes the Ta wave.</p> <p>- Below is the meaning of the 2×6 digit number, for example in filename: <br> <em>yymmdd hhmmss</em>: year month day hour minute second (time stamp).<br> <br> <strong><em>Notes on pole-zero representation:</em></strong></p> <p>- In the figures, the poles are marked with <strong>x</strong> and the zeros with <strong>o</strong>.</p> <p>- In the figures, only one of the two conjugated complex roots was shown, namely always the one falling towards the momentary value of the signal.</p> <p>- The pole of the Ta wave was not marked.</p> <p>- In the<strong> older figures</strong>, only the poles are visible, the zeros are not indicated. When the poles are drawn in the diagram shared with the signs, their location (coordinate <strong>t</strong>) is good, but the imaginary part was taken into account in a different way at that time.</p> <p>- Drawing the imaginary values of the roots on the same diagram as the signs on the <strong>newer figures</strong>, we multiplied them by 50, 100 and 10 for the P, QRS and T waves, respectively.<br> <br> <strong><em>The grids of charts </em></strong>(on the original medical ECG paper: "small squares" = 1mm x 1mm):<br> X axis: 40ms (The sampling rate is 1000Hz)<br> Y axis: 0.1mV (200 A/D units)</p> <p>=====================================================================================</p> <p><strong>Unid-Alte\</strong></p> <p>Diagram of two multipliers.<br> Here, the imaginary part of the poles and zeros is multiplied by 0.3.<br> It can be seen that the pole and zero locations do not coincide with the extremum locations on the alternating direction diagram.<br> <br> <strong>Histogram\</strong></p> <p>All 125 periods of the <strong>s0177_p050</strong> signal were approximated (<strong>vx, vy, vz</strong>). The figure is a histogram of one of the parameters of the T wave of <strong>vz</strong> lead (excluding the 2 extreme values).<br> <br> <strong>s0021_p005-vy\</strong></p> <p>These figures are the steps for approximating a QRS (<strong>s0021_p005, vy, 6810</strong>).<br> <em>Mini <strong>Hu==>En dictionary</strong>:</em> kozelito==>approximate; err......==>discrepancy; kend volt==>this had to be approached</p> <p>rajz-r-y-002---1.gif result of QRS11<br> rajz-r-y-002---2.gif result of QRS12<br> rajz-r-y-002---3.gif result of QRS13<br> The approximation of the small wave on the right side of the QRS is still missing. The approximation below the left side of the QRS is not yet good enough. We entered 2 zeros and multiplied the denominator by a complex conjugate root pairs.<br> rajz-r-y-002---4.gif result of QRS34<br> rajz-r-y-002---5.gif result of QRS35 Acceptable.<br> </p> <p>rajz-r-y-002---6.gif after a later approximation, we compared the results of the new QRS77 and QRS35.</p> <p>rajz-y-002-221022_201157_1.gif The final results of this new approximation (indicating the poles and zeros).<br> rajz-y-002-221022_201157_2.gif</p> <p><em>Mini <strong>Hu==>En dictionary</strong></em>: R.hely==>the relative <strong>t</strong> coordinate calculated from the origin; Eredeti==>raw; Approx==>approximate; Err......==>discrepancy, BL......==>baseline<br> <br> <strong>Shapes\</strong></p> <p>Approximation of some important shape types.<br> <em>Mini <strong>Hu==>En dictionary</strong></em>: R.hely==>the relative <strong>t</strong> coordinate calculated from the origin; Eredet==>raw; Approx==>approximate; Err......==>discrepancy, BL......==>baseline; pólusok==>poles</p> <p>s0025_p005 V3 7009 Dome Ta P32 T34 QRS34<br> s0047_p015 II 2758 Digitalis P22 T33 QRS34 One pair of poles of QRS and T coincide in the drawing (<strong>t</strong>=32).<br> s0146_p044 V4 3725 Coronaria T Ta P22 T22 QRS23<br> s0508_p269 aVR 5019 Block Ta P12 T12 QRS24<br> s0542_p283 vz 2581 QRS W-shaped P__ T22 QRS34 There is no P wave in any of the leads. (Atrial fibrillation)<br> <br> <strong>From_series\</strong></p> <p> <em>Mini <strong>Hu==>En dictionary</strong></em>: R.hely==>the relative <strong>t</strong> coordinate calculated from the origin; Eredet==>raw; Approx==>approximate; Err......==>discrepancy, BL......==>baseline; pólusok==>poles</p> <table> <tbody> <tr> <td>s.... = S/N, p... = patient:</td> <td> s0001_p119</td> <td>s0002_p196</td> <td>s0034_p163</td> <td>s0035_p009</td> </tr> <tr> <td> QRS_location:</td> <td>6938 10291</td> <td>9067</td> <td>7580</td> <td>8669</td> </tr> <tr> <td><strong>vx</strong></td> <td>Ta Ta</td> <td>Ta</td> <td> </td> <td>Ta</td> </tr> <tr> <td> </td> <td>P12 P12</td> <td>P12</td> <td>P65</td> <td>P13</td> </tr> <tr> <td> </td> <td>T23 T34</td> <td>T25</td> <td>T35</td> <td>T34</td> </tr> <tr> <td> </td> <td>QRS24 QRS24</td> <td>QRS15</td> <td>QRS89</td> <td>QRS57</td> </tr> <tr> <td><strong>vy</strong></td> <td>Ta</td> <td> </td> <td>Ta</td> <td>Ta</td> </tr> <tr> <td> </td> <td>P24</td> <td>P55</td> <td>P34</td> <td>P13</td> </tr> <tr> <td> </td> <td>T54</td> <td>T24</td> <td>T26</td> <td>T13</td> </tr> <tr> <td> </td> <td>QRS55</td> <td>QRS25</td> <td>QRS47</td> <td>QRS48</td> </tr> <tr> <td><strong>vz</strong></td> <td> </td> <td> </td> <td>Ta</td> <td>Ta</td> </tr> <tr> <td> </td> <td>P65</td> <td>P43</td> <td>P23</td> <td>P11</td> </tr> <tr> <td> </td> <td>T14</td> <td>T33</td> <td>T24</td> <td>T44</td> </tr> <tr> <td> </td> <td>QRS25</td> <td>QRS25</td> <td>QRS27</td> <td>QRS26</td> </tr> </tbody> </table> <p>The s0001_p119\vy\rajz-y-001-190918_210304_vlc.gif image has been expanded with the length of the vector ("V__idy 1"). The origin of the <strong>t</strong> axis (vx, vy, vz) is determined from the curve of the vector length.</p> <p>The figures for <strong>s0001_p119, vx, 10291</strong> are in the s0001_p119_U\vx directory. This is from the same <strong>vx</strong> signal as the previous one (6938), just 4 periods later. There is a U wave in it, T34 was needed instead of T23 to approximate it. The image Rajz-001-005a.gif is in the same directory. On this, we enlarged the part between the T and the next P wave at two periods (Data<strong>1</strong> 6938 and Data<strong>5</strong> 10291) of the vx signal.</p> <p>The figures of <strong>s0002_p196,</strong> <strong>vx, vy, vz, 9067</strong> show that the approximation on the left side of the QRS should be improved, probably by increasing the degree of the denominator.</p> <p>The figures for <strong>s0034_p163, vx, 7580</strong> are in the s0034_p163\vx\ directory. In the figure "rajz-x-003-221031_174534_2.gif" at t=-128, a pole and a zero coincide in the drawing, so we have enlarged this part (around P and QRS) :<br> rajz-x-003-221031_174534_2-zoom.gif.</p> <p>The figures for <strong>s0035_p009, vy, 8669</strong> are in the s0035_p009\vy\ directory. In the figure "rajz-y-004-221031_114914_2.gif" at t=-21, a pole and a zero almost coincide in the drawing.<br> As already written above, the data of example_1a.m (Octave, Matlab) on <a href="https://doi.org/10.5281/zenodo.6479410">https://doi.org/10.5281/zenodo.6479410</a> comes from the file ppaarraamm.txt in the same directory.</p> <p> Kobzos, Laszlo<br> Location: HU (Budapest)<br> email: zehu.kola.ci@gmail.com</p>
Datasets of the manuscript "Rational design of profile HMMs for sensitive and specific sequence detection with case studies applied to viruses, bacteriophages, and casposons"
<p><strong>DATASETS</strong></p> <p>Rational design of profile HMMs for sensitive and specific sequence detection with case studies applied to viruses, bacteriophages, and casposons</p> <p>Liliane S. Oliveira, Alejandro Reyes, Bas E. Dutilh and Arthur Gruber<sup>*</sup></p> <p>* Correspondence: <a href="mailto:argruber@usp.br">argruber@usp.br</a> (AG); Tel. +55 11 3091 7274</p> <p> </p> <p>Here we provide different data of <em>Microviridae</em>, <em>Flavivirus</em> and casposons used throughout the work:</p> <ul> <li>Microviridae folder <ul> <li>conserved_HMMs – profile HMMs constructed with TABAJARA in Conservation mode for <em>Microviridae</em></li> <li>discriminative_HMMs – profile HMMs constructed with TABAJARA in Discrimination mode for <em>Microviridae</em></li> <li>sequences – different sequence datasets and respective multiple sequence alignments <ul> <li>Microviridae_113-seq_training_set.fasta - 113 VP1 sequences covering diversity of the <em>Microviridae</em> family</li> <li>Microviridae_113-seq.aln – multiple sequence alignment of the 113-protein dataset</li> <li>Microviridae_1836-seq_testset.fasta - 1,836 sequence dataset covering 1,836 sequences of the major capsid protein (VP1) comprising 501 <em>Alpavirinae</em> sequences, 1,040 <em>Gokushovirinae</em> sequences and 295 <em>Pichovirinae</em> sequences</li> <li>Microviridae_1866-seq.aln - multiple sequence alignment of the 1,866-protein <em>Microviridae</em> dataset used in the experiment of Figure 4</li> </ul> </li> </ul> </li> <li>Flavivirus folder <ul> <li>conserved_HMMs – profile HMMs constructed with TABAJARA in Conservation mode for <em>Flavivirus</em></li> <li>discriminative_HMMs – profile HMMs constructed with TABAJARA in Discrimination mode for <em>Flavivirus</em> <ul> <li>full-length – models constructed from full-length protein sequences</li> <li>short - models constructed from selected short alignment blocks of the protein sequences</li> </ul> </li> <li>sequences – different sequence datasets and respective multiple sequence alignments <ul> <li>Flavivirus_127-seq_training_set.fasta - 127 polyprotein sequences covering species diversity of the genus <em>Flavivirus</em></li> <li>Flavivirus_127-seq.aln – multiple sequence alignment of the 127-protein dataset</li> <li>Flavivirus_6364-seq_testset.fasta - 6,364 sequence dataset covering species diversity of <em>Flavivirus</em>, including 3,919 of dengue virus (DENV), 327 of Zika virus (ZIKV), 63 of yellow fever virus (YFV), and the remaining 2,055 sequences covering other available flaviviruses</li> <li>Flavivirus_6364-seq.aln - multiple sequence alignment of the 6,364-protein <em>Flavivirus</em> dataset</li> </ul> </li> </ul> </li> <li>Casposons folder <ul> <li>casposon_generic_HMMs – profile HMMs constructed with TABAJARA in Discrimination mode for the generic detection of all casposons and discrimination from CRISPRs.</li> <li>casposon_family_discriminative_HMMs – profile HMMs constructed with TABAJARA in Discrimination mode for the specific discrimination among casposon families and from CRISPRs.</li> <li>sequences – different sequence datasets and respective multiple sequence alignments <ul> <li>casposons_crisprs.fasta – 106 Cas1 <em>bona fide</em> sequences derived from 52 CRISPRs and 54 casposons</li> <li>casposon_family_discrimination.aln - multiple sequence alignment of 52 <em>bona fide</em> CRISPR and 54 casposon sequences, with appropriate nomenclature to run TABAJARA for the discrimination of each casposon family.</li> <li>casposons_crisprs_discrimination.aln - multiple sequence alignment of 52 <em>bona fide</em> CRISPR and 54 casposon sequences, with appropriate nomenclature to run TABAJARA for discrimination of CRISPRs and casposons.</li> </ul> </li> </ul> </li> </ul>
Exposure to sugar rationing in the first 1000 days of life protected against chronic disease
Open the record for dataset details and reuse information.
Much or More? Experiments of Rationality and Spite with School Children - Data Set
<p>Much or More? Experiments of Rationality and Spite with School Children Original Data set.</p> <p>Data was collected as a binary choice coded in the following way:</p> <p>0 - played <em>min</em> ; 1 - played <em>max</em></p> <p>Each row represents player A and B of each game and each column represents treatment; the 5 rounds of the game; payoff for each round; total payoff of the 5 rounds; age of the player, school year of the player and school of the player. Name of schools are coded inside the file.</p> <p>See original article for references on how data was collected and analysed.</p>
Molecular dynamics trajectories, GROMACS input files, and analysis code from "Rational optimization of a transcription factor activation domain inhibitor" by Basu et. al, Nature Structural & Molecular Biology, 2023
<p>Molecular dynamics trajectories, GROMACS input files, and analysis code from "Rational optimization of a transcription factor activation domain inhibitor" by Basu et. al, Nature Structural & Molecular Biology, 2023</p> <p> </p> <p> </p>
ScienceDex guides
Understand access before you commit
These curated guides explain access requirements, typical timelines, costs, and reuse considerations for widely used research datasets.
Allen Brain Atlas
Allen Brain Atlas is an Allen Institute collection of brain map atlases, datasets, APIs, and analysis tools covering mouse, human, and non-human primate brain resources.
Annotated Behaviour and Observability Dataset (ABODe)
ABODe is a University of Edinburgh DataShare dataset for behavior classification in group-housed mice using home-cage video, identities, bounding boxes, ground-plate positions, and annotator labels.
DANDI Archive for NWB datasets
DANDI is a BRAIN Initiative archive for publishing and sharing neurophysiology data, including electrophysiology, optophysiology, and behavioral data packaged as NWB and related standards.
International Brain Laboratory public data
The International Brain Laboratory public data releases expose standardized mouse decision-making experiments, including Neuropixels recordings, widefield calcium imaging, behavior, and session metadata accessed through the ONE API.
OpenNeuro
OpenNeuro is a free, open platform for sharing neuroimaging datasets, with public search, dataset pages, and download paths for web, S3, DataLad, and the OpenNeuro CLI.