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6 results for “Approximations and bounds”
Coefficients for Tight Logarithmic Approximations and Bounds for Generic Capacity Integrals
<p>This is a supplementary dataset for the publication:</p> <p>I. M. Tanash and T. Riihonen, "Tight Logarithmic Approximations and Bounds for Generic Capacity Integrals and Their Applications to Statistical Analysis of Wireless Systems," in <em>IEEE Transactions on Communications</em>, 2022, doi: 10.1109/TCOMM.2022.3198435.</p> <p>The dataset contains the sets of optimized coefficients for the novel minimax approximations of the Nakagami and lognormal capacity integrals in terms of absolute error. The proposed approximations have the form of a weighted sum of logarithmic functions. The optimized coefficients are found for a wide range of the corresponding fading parameters, namely m for the Nakagami capacity integral and σ (standard deviation) for the lognormal capacity integral. Please note that the optimized coefficients in the provided dataset for the lognormal capacity integral are calculated for σdB (standard deviation in decibels) so σ=0.1 log_e(10) σdB in Eq. 5.</p> <p>The Matlab function (func_extract_coef.m) extracts the required set of optimal coefficients from the provided dataset according to the selected capacity integral, the parameter's value, and the number of terms. See help func_extract_coef for more information.</p> <p>The Matlab script (general_any_func) implements the theory presented in the corresponding journal paper: More specifically, it implements solving Eq. 22 to calculate the optimized coefficients of Eq. 7 for the Nakagami capacity integral. The code also provides general comments on how to generalize it to obtain the optimized coefficients of any communication system in terms of absolute error. Number of supplementary Matlab functions (general_any_func, func_abs_gen_any_func, calc_d_gen, calc_Cappr_gen, calc_d_gen_derivative, calc_Cappr_gen_derivative, Gauss_Laguerre, and peakseek) are provided herein and are used in the main Matlab script.</p> <p>A Matlab script (Example.m) is also provided as an example to illustrate the use of the provided Matlab function (func_extract_coef.m) in extracting the required coefficients from the dataset, to calculate and plot the corresponding absolute error which is shown by figure Example.jpg.</p>
Error bounds for kernel-based approximations of the Koopman operator
<p>This repository contains python scripts and data to re-create the result shown in</p><p>`Error bounds for kernel-based approximations of the Koopman operator, arxiv:2301.08637`</p><p>See README for detailed instructions on how to re-create these data.</p>
Optimized Coefficients for the Generalized Karagiannidis–Lioumpas Approximations and Bounds to the Gaussian Q-Function
<p>This is a supplementary dataset for the publication:</p> <p>I. M. Tanash and T. Riihonen, "Generalized Karagiannidis–Lioumpas Approximations and Bounds to the Gaussian Q-Function with Optimized Coefficients," in<em> IEEE Communications Letters</em>, in press.</p> <p>The dataset contains the sets of the optimized coefficients for the novel GKL minimax approximations and bounds of the Gaussian Q-function, and the optimized coefficients for the GKL approximations in terms of the total error. The corresponding optimized coefficients are found up to 10 terms (N=10) for the two variations of the absolute error and for the relative error in terms of the minimax and the total errors.</p> <p>The Matlab function (func_extract_coef.m) extracts the required set of optimal coefficients from the provided dataset according to the selected optimization_criterion, error_type, number of terms, the bound or approximation type, and the variation. See help func_extract_coef for more information.</p> <p>A Matlab script (Example.m) is also provided as an example to illustrate the use of the provided Matlab function in extracting the required coefficients from the dataset, to calculate and plot the corresponding minimax absolute error function which is shown by figure Example.jpg. Another example is given in the same script to extract the coefficients of the total relative error.<br> </p>
Efficient Approximation Algorithms for the Diameter-Bounded Max-Coverage Group Steiner Tree Problem
<p> It contains all the data used in our experiments, including 5 real graphs (<code>MONDIAL</code>, <code>OpenCyc</code>, <code>LinkedMDB</code>, <code>YAGO</code>, and <code>DBpedia</code>) and 3 synthetic graphs (<code>LUBM-50K</code>, <code>LUBM-500K</code>, and <code>LUBM-5M</code>).</p> <p>Each real KG directory contains 8 files, including:</p> <ul> <li><code>graph.txt</code>: The first value is the number of vertices. Then each line 'u v' means there is an undirected edge between 'u' and 'v'.</li> <li><code>Weightgraph.txt</code>: The first value is the number of vertices. Then each line 'u v w' means there is an undirected edge between 'u' and 'v' weighted by 'w' which is computed by the Informativeness-based Weighting (IW) scheme.</li> <li><code>nodeName.txt</code>: Mapping from vertex ID to vertex name (i.e., entity URI).</li> <li><code>query.txt</code>: Each line is a keyword query containing a set of keyword names.</li> <li><code>kwName.txt</code>: Mapping from keyword ID to keyword name.</li> <li><code>kwMap.txt</code>: Mapping from keyword ID to vertex IDs. The first value of each line is keyword ID, and the rest are vertex IDs.</li> <li><code>UWHBLL.txt</code>: The HBLL index file which was built based on the Unit Weighting.</li> <li><code>IWHBLL.txt</code>: The HBLL index file which was built based on the Informativeness-based Weighting.</li> </ul> <p>Each synthetic directory contains 6 files, including:</p> <ul> <li><code>graph.txt</code>: same as above.</li> <li><code>Weightgraph.txt</code>: same as above.</li> <li><code>nodeName.txt</code>: same as above.</li> <li><code>queryList.txt</code>: Each line contains a set (separated by ',') of sets of vertex IDs.</li> <li><code>UWHBLL.txt</code>: same as above.</li> <li><code>IWHBLL.txt</code>: same as above.</li> </ul> <p>Apart from that, <code>Dbpedia</code> and <code>LUBM-5M</code> also contain a <code>PLLlabel.txt</code> file which was the supplementary file for the HBLL index.</p>
Coefficients for Global Minimax Approximations and Bounds for the Gaussian Q-Function by Sums of Exponentials
<p>This is a supplementary dataset for the publication:</p> <p>I. M. Tanash and T. Riihonen, "Global Minimax Approximations and Bounds for the Gaussian Q-Function by Sums of Exponentials," in <em>IEEE Transactions on Communications</em>, vol. 68, no. 10, pp. 6514-6524, Oct. 2020, doi: 10.1109/TCOMM.2020.3006902.</p> <p>The dataset contains the sets of the optimized coefficients for the novel minimax approximations and bounds of the Gaussian Q-function, its first four integer powers and for the case of average symbol error probability (SEP) in optimal detection of 4-QAM that is actually a polynomial of the Q-function. The proposed approximations and bounds have the form of a weighted sum of exponential functions. The corresponding optimized coefficients are found up to twenty-five exponential terms with the right boundary of the finite interval on the x-axis (x_K+1) ranging from 1 to 10 in steps of 0.1 for the relative error.</p> <p>The Matlab function (func_extract_coef.m) extracts the required set of optimal coefficients from the provided dataset according to the selected error type, variation, number of terms and the right end-point in case of relative error. See help func_extract_coef for more information.</p> <p>A Matlab script (Example.m) is also provided as an example to illustrate the use of the provided Matlab function in extracting the required coefficients from the dataset, to calculate and plot the corresponding relative error which is shown by figure Example.jpg.</p> <p> </p>
Optimizing Within-Distance Queries by Approximating Shapes with Maximal Bounded Boxes - Datasets
<p>Csv and sql files for the underlying data.<br> Figure 9: Calculating the distance between various number and type of shapes, i.e. from polygons, rotated and axis aligned rectangles, to points, polygons, rotated and axis aligned rectangles.<br> Table 1: Calculating distance between shapes of various complexity, i.e. points, lines, quadrilaterals, hexagons, dodecagons, icosagons, pentacontagons.<br> Table 2: Comparing the ordering of the shapes when distance operation is calculated, (a) from polygons to rectangles, (b) from rectangles to polygons.<br> Table 5 & 6: Within-distance and distance queries between (a) actual polygons, (b) their bounded rectangles, (c) actual polygons and points, (d) their bounded rectangles and points.</p>
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