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295 results for “approximation”
Map. The early Gupta kingdom with the approximate location of surrounding powers that offered submission to Samudragupta as recounted in the Allahābād Pillar inscription.
<p>Map. The early Gupta kingdom with the approximate location of surrounding powers that offered submission to Samudragupta as recounted in the <a href="https://siddham.network/object/ob00001/">Allahābād Pillar inscription</a>.</p>
Two-bubble envelope approximation code and results
<p>This deposit contains the code required to carry out the envelope approximation simulations used in the paper with preprint title <em>Vacuum bubble collisions: from microphysics to gravitational waves</em> by Oliver Gould, Satumaaria Sukuvaara, and David Weir.</p> <p>The method and results are based on the following papers:</p> <ul> <li><em>Gravitational Wave Production by Collisions: More Bubbles</em> by Stephan J. Huber and Thomas Konstandin [<a href="https://arxiv.org/abs/0806.1828">arXiv:0806.1828</a>].</li> <li><em>Gravitational radiation from colliding vacuum bubbles: envelope approximation to many bubble collisions</em> by Arthur Kosowsky and Michael S. Turner [<a href="https://arxiv.org/abs/astro-ph/9211004">arXiv:astro-ph/9211004</a>].</li> <li><em>Gravitational radiation from colliding vacuum bubbles </em>by Arthur Kosowsky, Michael S. Turner and Richard Watkins<em> </em>[<a href="https://inspirehep.net/literature/324187">Inspire</a>].</li> </ul> <p>In the latter paper the envelope approximation is introduced in Appendix C.</p> <p>There are two files:</p> <ul> <li><strong>dweir-envelope-b2842c4827ad.zip</strong> is a snapshot of the <a href="https://bitbucket.org/dweir/envelope/">Bitbucket-hosted Git repository for the simulation code</a>, corresponding to <a href="https://bitbucket.org/dweir/envelope/src/v1.1.0/">the commit tagged <em>v1.1.0</em></a>. Later versions of the code may exist. The snapshot was generated by the Bitbucket service and does not include the Git metadata.</li> <li><strong>two-bubbles-envelope-data.tar.gz </strong>is an archive of the simulation results used to generate the envelope approximation results seen in the preprint, as well as numerical tests and some additional numerical explorations. While the results were generated with a slightly earlier version of the code than the tagged release in this deposit, they have been confirmed to be reproducible with the code provided.</li> </ul> <p>Both archives contain README.md files with further information.</p>
Values, distributions and approximations of the empirical liquidity cost function for various futures contracts.
<p>The figures presents the values, distributions and approximations of the empirical liquidity cost function for various futures contracts. The raw data was obtained from the LOB snapshots for the cash-settled futures contracts on the RTS index (RI), on Brent oil (BR) and FX-rate of US dollar versus Russian ruble (Si). The data corresponds to the period from 05 May 2020 to 26 Feb 2021. The tables summarize the results.</p>
One qubit as a universal approximant
<p>In this repository one can find all the code used to generate the figures in the paper <em>One qubit as a Universal Approximant</em>, <a href="https://arxiv.org/abs/2102.04032">arXiv:2102.04032</a> including the original data sets.</p>
An approximation of the spectral gap for the Laplace operator on SAut(F₅)
<p>This is the dataset accompanying <em>Aut(𝔽₅) has property (T)</em> paper (https://arxiv.org/abs/1712.07167). See Section 4 thereof for a detailed description of the content of the included files:</p> <blockquote> <p><code>tar --list -f ./oSAutF5_r2.tar.xz</code></p> <p><br> <code>oSAutF5_r2/<br> oSAutF5_r2/1.3/<br> oSAutF5_r2/1.3/full_2018-01-26T12:29:58.143.log<br> oSAutF5_r2/1.3/solver_2018-01-26T12:29:58.143.log<br> oSAutF5_r2/1.3/SDPmatrix.jld<br> oSAutF5_r2/1.3/lambda.jld<br> oSAutF5_r2/U_pis.jld<br> oSAutF5_r2/pm.jld<br> oSAutF5_r2/delta.jld<br> oSAutF5_r2/orbits.jld<br> oSAutF5_r2/preps.jld</code></p> </blockquote> <p>To replicate the computation of the spectral gap clone <code>1712.07167</code> repository first</p> <blockquote> <p><code>git clone https://git.wmi.amu.edu.pl/kalmar/1712.07167.git</code></p> </blockquote> <p>Then unpack the content of <code>oSAutF5_r2.tar.xz</code> into <code>1712.07167</code> folder.</p> <p>You need <code>julia-1.1.0</code> or above. In <code>julia</code>s REPL run</p> <blockquote> <p><code>using Pkg<br> Pkg.activate("1712.07167")<br> Pkg.instantiate()<br> Pkg.test("PropertyT")</code></p> </blockquote> <p>Finally, to verify that the Laplace operator on <em>SAut(𝔽₅)</em> (associated to the standard generating set) has spectral gap of at least <code>1.3</code> run from within <code>1712.07167</code> folder</p> <blockquote> <p><code>julia check_SAutF5.jl</code></p> </blockquote> <p>If You want to generate the multiplication table and other files on Your own delete all <code>*.jld</code> files from the <code>oSAutF5_r2</code> folder (but the ones in <code>1.3</code> folder) and run the same command again. Note: You need at least <code>20</code>GB of RAM and spare a few hours of Your CPU.</p> <p>We reproduce the content of <code>check_SAutF5.jl</code> script below.</p> <blockquote> <p><code>using Pkg<br> Pkg.activate(".")<br> using Groups<br> using GroupRings<br> using PropertyT<br> using SparseArrays<br> using LinearAlgebra<br> using IntervalArithmetic<br> using JLD</code></p> <p><code>@show Threads.nthreads()<br> BLAS.set_num_threads(Threads.nthreads());</code></p> <p><code>G = SAut(FreeGroup(5))<br> pm = load("oSAutF5_r2/pm.jld", "pm");<br> RG = GroupRing(G, pm)<br> @info RG</code></p> <p><code>S_size = 80<br> # due to technical problems we are no longer able to load delta.jl on julia-1.0<br> Δ_coeff = SparseVector(maximum(pm), collect(1:(1+S_size)), [S_size; -ones(S_size)])<br> Δ = GroupRingElem(Δ_coeff, RG);<br> Δ² = Δ^2;</code></p> <p><code>@info "Loading solution"<br> λ₀ = load("oSAutF5_r2/1.3/lambda.jld", "λ")<br> P₀ = load("oSAutF5_r2/1.3/SDPmatrix.jld", "P");</code></p> <p><code>@info "Taking square root of P"<br> @time Q = real(sqrt(P₀));</code></p> <p><code>Q_aug, check_columns_augmentation = PropertyT.augIdproj(Interval, Q);<br> @show check_columns_augmentation<br> if !check_columns_augmentation<br> @warn "Columns of Q are not guaranteed to represent elements of the augmentation ideal!"<br> end</code></p> <p><code>@info "Computing SOS decomposition"<br> @time sos = PropertyT.compute_SOS(RG, Q_aug);</code></p> <p><code>residual = Δ² - @interval(λ₀)*Δ - sos;<br> @show norm(residual, 1)</code></p> </blockquote> <p> </p> <p>This research was supported in part by</p> <ul> <li>PL-Grid Infrastructure,</li> <li>grant 2015/19/B/ST1/01458, National Science Center, Poland</li> <li>grant 2017/26/D/ST1/00103, National Science Center, Poland.</li> </ul>
Dataset of the article "A new and almost perfectly accurate approximation of the eigenvalue effective population size of a dioecious population: comparisons with other estimates and detailed proofs"
<p>Dataset of the article "A new and almost perfectly accurate approximation of the eigenvalue effective population size of a dioecious population: comparisons with other estimates and detailed proofs" (https://doi.org/10.5281/zenodo.7927968), recommended by PCI Evol Biol (https://evolbiol.peercommunityin.org/articles/rec?id=651)</p>
Project's repository for: Co-immersion in Audio Augmented Virtuality: the Case Study of a Static and Approximated Late Reverberation Algorithm
<p>Repository of the VR scene and the audio data used for the experiment reported in the publication <a href="https://ieeexplore.ieee.org/document/10269056" target="_blank" rel="noopener">available in Open Access</a>:</p> <blockquote> <p>Davide Fantini, Giorgio Presti, Michele Geronazzo, Riccardo Bona, Alessandro Giuseppe Privitera and Federico Avanzini (2023) "Co-immersion in Audio Augmented Virtuality: the Case Study of a Static and Approximated Late Reverberation Algorithm" in <em>IEEE Transactions on Visualization and Computer Graphics (ISMAR special issue)</em></p> </blockquote> <p>The file <a href="../api/files/06c374e2-c54d-40f1-ae23-c4c7afbfba5b/README.md">README.md</a> includes some instructions to use the data in this repository.</p> <p> </p> <p><strong>AUDIO</strong></p> <p>The file <a href="../api/files/06c374e2-c54d-40f1-ae23-c4c7afbfba5b/audio.zip">audio.zip</a> includes the Reaper's projects and audio files used in the experiment to provide the auditory stimuli (simultaneous reverberated speeches) to the participants. Each subfolder corresponds to a different Virtual Acoustics Environment (VAE):</p> <ul> <li><<em>LivingRoom</em>|<em>MARCo</em>|<em>METU</em>> <ul> <li><<em>Living Room</em>|<em>MARCo</em>|<em>METU</em>><em>.rpp</em>: Reaper's project for the VAE</li> <li><em>Bin</em>: folder including the speech data convolved with the late reverberation part of the reverb condition \(B\) for each source position in the VAE</li> <li><em>Freeverb</em>: folder including the speech data convolved with the late reverberation part of the reverb condition \(F_\text{d}\) for each source position in the VAE</li> <li><em>HOA</em>: <ul> <li><em>ER</em>: folder including the speech data convolved with the early reflections part (HOA in A-format) of the reference reverb condition \(H\) for each source position in the VAE</li> <li><em>Ref</em>: folder including the speech data convolved with the entire reference reverb condition \(H\) (HOA in A-format) for each source position in the VAE</li> </ul> </li> </ul> </li> </ul> <p>The reverberated speech data in the <a href="../api/files/06c374e2-c54d-40f1-ae23-c4c7afbfba5b/audio.zip">audio.zip</a> file are obtained using third-party datasets:</p> <ul> <li>The anechoic speech data are retrieved from four speakers (F2, F5, M3, M6) of the <a href="https://doi.org/10.5281/zenodo.6257551">ACE challenge corpus</a></li> <li>The Room Impulse Responses (RIR) in High-Order Ambisonics (HOA) format used to reverberate the speeches are retrieved from: <ul> <li><a href="https://doi.org/10.5281/zenodo.5747753">Living Room</a></li> <li><a href="https://doi.org/10.5281/zenodo.3477602">Concert hall (MARCo)</a></li> <li><a href="https://doi.org/10.5281/zenodo.2635758">Classroom (METU)</a></li> </ul> </li> </ul> <p> </p> <p><strong>VR SCENE</strong></p> <p>The file <a href="../api/files/06c374e2-c54d-40f1-ae23-c4c7afbfba5b/VRscene.zip">VRscene.zip</a> includes the Virtual Reality (VR) scene provided to the participants during the experiment via an Oculus Quest 2. This file includes two subfolders:</p> <ul> <li><em>UDPServer</em>: C# code for the UDP server used for sending the OSC messages for head tracking <ul> <li><em>external/SharpOSC.dll</em>: external library (<a href="https://github.com/ValdemarOrn/SharpOSC">SharpOSC</a>) used to interact with the OSC protocol</li> </ul> </li> <li><em>VR_Headtracking</em>: folder including the Unity project with the VR scene</li> </ul> <p> </p>
Tree ring widths from 1974-2003 for approximately 10 trees/site for 82 sites located in the 2004 burns off the Steese, Taylor, and Dalton Highways, and for the 2005 burn near Eagle Plains, Yukon.
This dataset contains annual raw ring width measurements from 1975-2003 for 793 black spruce trees in 84 sites. Ring widths were measured using WinDendro (resolution 0.001 mm) on two radii per stem disk collected 1.3 m along stem. Data is the average of the two radii measurments in each year for each tree. Accuracy of ring width dates were checked by crossdating using COFECHA.
Aerial view of part of the Bisti badlands from an elevation of approximately 8500 feet. Exposed here are the Upper Cretaceous Fruitland and Kirtland Formations. Photograph taken the morning of 13 April 1992. Copyright © Paul L. Sealey. 1992. in Stratigraphy, paleontology and age of the Fruitland and Kirtland Formations (upper Cretaceous), San Juan Basin, New Mexico
Aerial view of part of the Bisti badlands from an elevation of approximately 8500 feet. Exposed here are the Upper Cretaceous Fruitland and Kirtland Formations. Photograph taken the morning of 13 April 1992. Copyright © Paul L. Sealey. 1992.
Datasets from Approximate equality of character strings and its application to record linkage in metadata of scientific publications thesis
<p>The datasets were produced in my thesis project. The thesis (in Czech language) explores the application of approximate string matching in scientific publication record linkage process. An introduction to record matching along with five commonly used metrics for string distance (Levenshtein, Jaro, Jaro-Winkler, Cosine distances and Jaccard coefficient) are provided. These metrics are applied on publication metadata from V3S current research information system of the Czech Technical University in Prague. Based on the findings, optimal thresholds in the F1, F2 and F3-measures are determined for each metric.</p> <p>Thesis citation:<br> DOBIÁŠOVSKÝ, Jan. <em>Approximate equality of character strings and its application to record linkage in metadata of scientific publications</em> [online]. Praha, 2020 [cit. 2020-05-04]. Masters thesis. Charles University. Faculty of Arts. Institute of Information Studies and Librarianship.</p> <p> </p>
FIGURE 1. Chiridota heheva new species. Approximately 4 in Chiridota heheva, new species, from Western Atlantic deepsea cold seeps and anthropogenic habitats (Echinodermata: Holothuroidea: Apodida)
FIGURE 1. Chiridota heheva new species. Approximately 4 individuals in situ near whitish bacterial mats (?) at Florida Escarpment seep site, eastern Gulf of Mexico, 3,270 meters. Alvin Dive 1343. Approximate diameter of body 5 mm. Photo, S. Golubic.
Generalized Approximate Message Passing Practical 2D Phase Transition Simulations Dataset
<p>This deposition contains the results from a simulation of phase transitions for various practical 2D problem suites when using the Generalised Approximate Message Passing (GAMP) reconstruction algorithm.</p> <p>The deposition consists of:</p> <ol> <li>Five HDF5 databases containing the results from the phase transition simulations (<em>gamp_practical_2d_phase_transitions_ID_[0-4]_of_5.hdf5</em>).</li> <li>The Python script which was used to create the databases (<em>gamp_practical_2d_phase_transitions.py</em>).</li> <li>A Python module with tools needed to run the simulations (<em>gamp_pt_tools.py</em>).</li> <li>MD5 and SHA256 checksums of the databases and Python scripts (<em>gamp_practical_2d_phase_transitions.MD5SUMS / gamp_practical_2d_phase_transitions.SHA256SUMS</em>).</li> </ol> <p>The HDF5 databases are licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/) . Since the CC BY 4.0 license is not well suited for source code, the Python scripts are licensed under the BSD 2-Clause license (http://opensource.org/licenses/BSD-2-Clause) .</p> <p><strong>The files are provided as-is with no warranty as detailed in the above mentioned licenses.</strong></p>
Generalized Approximate Message Passing Practical 2D Phase Transition Simulations Dataset 2
<p>This deposition contains the results from a simulation of phase transitions for various practical 2D and 3D problem suites when using the Generalised Approximate Message Passing (GAMP) reconstruction algorithm.</p> <p>The deposition consists of:</p> <ol> <li>Five HDF5 databases containing the results from the phase transition simulations (<em>gamp_practical_2d_phase_transitions_ID_[0-4]_of_5.hdf5</em>).</li> <li>The Python script which was used to create the databases (<em>gamp_practical_2d_phase_transitions.py</em>).</li> <li>A Python module with tools needed to run the simulations (<em>gamp_pt_tools.py</em>).</li> <li>MD5 and SHA256 checksums of the databases and Python scripts (<em>gamp_practical_2d_phase_transitions.MD5SUMS / gamp_practical_2d_phase_transitions.SHA256SUMS</em>).</li> </ol> <p>The HDF5 databases are licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/) . Since the CC BY 4.0 license is not well suited for source code, the Python scripts are licensed under the BSD 2-Clause license (http://opensource.org/licenses/BSD-2-Clause) .</p> <p><strong>The files are provided as-is with no warranty as detailed in the above mentioned licenses.</strong></p>
Replication data for An Empirical Approximation of the Effects of Trade Sanctions with an Application to Russia
<p>This is the dataset to replicate all the tables and figures in the paper <a href="https://doi.org/10.1093/epolic/eiad027">"An Empirical Approximation of the Effects of Trade Sanctions with an Application to Russia"</a>, published in <i>Economic Policy</i>, 2023, by Jean Imbs and Laurent Pauwels. All data manipulations and programming are detailed on the GitHub site:<a href="https://github.com/laurentpauwels/sanctionpaper"> https://github.com/laurentpauwels/sanctionpaper</a>. The raw and processed data are in this <i>sanctionpaperdata_v1/matlab/data folder. </i>For convenience the simulation output <i>(simulationoutput.txt) </i>required to build the scatter plots in Figure 1 with STATA is available in<i> sanctionpaperdata</i>_v1<i>/matlab/output</i>.</p><p><strong>Instructions</strong> </p><p> If you clone the GitHub repository:</p><p>1. Place the downloaded <i>data</i> folder (located in <i>sanctionpaperdata_v1/matlab/)</i> in the <i>matlab</i> folder of the GitHub repository. </p><p>2. Place the downloaded <i>simulation_output.txt</i> I(located in <i>sanctionpaperdata_v1/matlab/output/) </i>in the <i>matlab/output </i>folder of the GitHub repository if you do not want to run the simulations as detailed on GitHub.</p><p><strong>Description</strong></p><p>The <i>matlab/data/raw</i> folder contains an <i>ICIO21</i> folder with the ICIO21 data, and a <i>WIOD</i> folder with the SEA16 data (in <i>data/raw/WIOD/SEA16</i>) and the WIOT16 data in CSV format (in <i>data/raw/WIOD/WIOT16</i>).</p><p>NOTE: WIOD provides the data in XLSB format. The XLSB WIOD data is in the <i>WIOT_in_EXCEL.zip</i> located in the <i>matlab/data/raw/WIOD/</i>. Python is used to convert XLSB into CSV files. See python code in GitHub repository for unzipping and conversion to CSV. The converted CSV files are provided for convenience.</p><p>The parsed and pre-processed ICIO21, SEA16, and WIOT16 data are stored in the <i>/matlab/data/processed</i> folder into three separate .mat structure files:</p><p><i>icio21_strc.mat</i> contains:</p><ul><li>the meta data (<i>icio21_text</i>), i.e., the information about the structure of the numerical data such as lists of countrycode, countries, industrycode, industries, isic_rev4 codes, years covered, name of final categories, etc.</li><li>the numerical data (<i>icio21_data</i>):<ul><li>Z (<i>icio21_data.Z</i>), the intermediate IO data for the listed industries (R), countries (N), and years (T). Its structure is 3-dimensionsal: (NxR)x(NxR)xT.</li><li>F (<i>icio21_data.F</i>), the final demand data for the same countries, industries and years. Its structure is 3-dimension: (NxR)x(NxC)xT. The columns are NxC where C are the number of final demand categories.</li></ul></li></ul><p><br><i>wiod16_strc.mat</i> has the same structure as <i>icio21_strc.ma</i>t with the meta data in <i>wiot16_text</i> and the numerical data in <i>wiot16_data</i>.</p><p><i>sea16_strc.mat</i> has the meta data in <i>sea16_text</i> and the numerical data in <i>sea16_data</i>. SEA16 contains 16 variables instead of Input-Output type data. The country, industry, and year coverage is not the same as ICIO21.</p><p>NOTE: <i>matlab/scripts/convertMatlabStruc2data.m</i> in the GitHub repository converts <i>MATLAB v7.3 </i>format ("structure data") to an updated format without structure so that it is more easily compatible with other software. All data parsing and preprocessing are done with MATLAB, see GitHub repository for details.</p><p><strong>Sources</strong></p><p>The raw data come from these sources:</p><p>1. OECD Inter-Country Input-Output (ICIO) data November 2021 release (downloaded on 2 July 2023)</p><p>- Source: OECD-ICIO 2021 release data is available at <a href="http://oe.cd/icio">http://oe.cd/icio</a></p><p>2. WIOD Socio-Economic Accounts (SEA) data 2016 release (downloaded on 30 May 2023)</p><p>- Source: <a href="https://www.rug.nl/ggdc/valuechain/wiod/wiod-2016-release">https://www.rug.nl/ggdc/valuechain/wiod/wiod-2016-release</a></p><p>3. WIOD World Input-Output Tables (WIOT) data November 2016 (downloaded on 23 June 2023)</p><p>- Source: <a href="https://www.rug.nl/ggdc/valuechain/wiod/wiod-2016-release">https://www.rug.nl/ggdc/valuechain/wiod/wiod-2016-release</a> </p>
Approximations of derivatives by finite differences
<p>As supplementary material of the paper, it follows many of the approximations of derivatives by finite differences in PDF and text format, following the table model proposed in the paper to store the finite difference equations.</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>
Exponential approximation of the coherence contribution to the thermal conductivity of complex clathrate-type crystals
<p>The low-temperature properties of guest-host crystals, such as clathrates and skutterudites, offer a rich playground for discovering novel physical phenomena and developing new materials with unique properties. The temperature dependence of thermal conductivity in these materials can exhibit both crystal-like and glass-like behavior, which reflects the properties of the phonon excitations and various scattering mechanisms. The ultra-low thermal conductivity of clathrate crystals is closely related to the concept of minimal thermal conductivity, which is determined by the intrinsic phonon scattering in the material. In this work, the temperature dependence of thermal conductivity for both crystal-like and glass-like behavior of different structural types of clathrates and skutterudites was analyzed using the ”Unified theory of thermal transport in crystals and glasses” of M. Simoncelli, N. Marzari & F. Mauri. A method was proposed and tested for the coherence contribution related to wave-like tunneling and loss of coherence between different vibrational eigenstates. The temperature dependence of the coherence contribution to thermal conductivity was approximated by the exponential function of an Arrhenius type with characteristic energy <em>E</em> and characteristic minimal thermal conductivity parameter <em>κ</em><sub>0</sub>. The coherence contribution is intertwined with other phonon scattering mechanisms, and over a wide temperature range, its temperature dependence is universal with parameters depending on the crystal structure, positional disorder, and impurity doping. This work provides insights into the temperature dependence of thermal conductivity in guest-host materials and its importance for designing and optimizing their properties for various applications, such as thermoelectric generators</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>
РИС. 2. Скульптура постЭмбриональных оборотов раковины крымских Clausiliidae. A. Cochlodina laminata. B. Mentissa canalifera. C. Balea perversa. D. Mentissa gracilicosta. E. Macrogastra plicatula. F–I. Устье и ЗатылочнаЯ область раковины Balea perversa с г. Демерджи (Крым, РоссиЯ). Все иЗображениЯ приблиЗительно в одном масШтабе. FIG. 2. Sculpture of postembryonic whorls of the Crimean Clausiliidae shells. A. Cochlodina laminata. B. Mentissa canalifera. C. Balea perversa. D. Mentissa gracilicosta. E. Macrogastra plicatula. F–I. Mouth and cervical area of the Balea perversa shell from Demerdzhi mountain (Crimea, Russia). All images are approximately at the same scale. in О достоверности находок Balea perversa (Gastropoda: Pulmonata: Clausiliidae) в Крыму
РИС. 2. Скульптура постЭмбриональных оборотов раковины крымских Clausiliidae. A. Cochlodina laminata. B. Mentissa canalifera. C. Balea perversa. D. Mentissa gracilicosta. E. Macrogastra plicatula. F–I. Устье и ЗатылочнаЯ область раковины Balea perversa с г. Демерджи (Крым, РоссиЯ). Все иЗображениЯ приблиЗительно в одном масШтабе. FIG. 2. Sculpture of postembryonic whorls of the Crimean Clausiliidae shells. A. Cochlodina laminata. B. Mentissa canalifera. C. Balea perversa. D. Mentissa gracilicosta. E. Macrogastra plicatula. F–I. Mouth and cervical area of the Balea perversa shell from Demerdzhi mountain (Crimea, Russia). All images are approximately at the same scale.
Fig. 3. Amphinema turrida, bell height approximately 6 in Hydromedusae observed during night dives in the Gulf Stream
Fig. 3. Amphinema turrida, bell height approximately 6 mm. (A) Lateral view. (B-D) Oblique views from oral side, note the presence of thin cirri.
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