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is-small is-grey tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Biological Physics">physics.bio-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Data Analysis, Statistics and Probability">physics.data-an</span> </div> </div> <p class="title is-5 mathjax"> Continuous Diffraction of Molecules and Disordered Molecular Crystals </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/physics?searchtype=author&amp;query=Chapman%2C+H+N">Henry N. Chapman</a>, <a href="/search/physics?searchtype=author&amp;query=Yefanov%2C+O+M">Oleksandr M. Yefanov</a>, <a href="/search/physics?searchtype=author&amp;query=Ayyer%2C+K">Kartik Ayyer</a>, <a href="/search/physics?searchtype=author&amp;query=White%2C+T+A">Thomas A. White</a>, <a href="/search/physics?searchtype=author&amp;query=Barty%2C+A">Anton Barty</a>, <a href="/search/physics?searchtype=author&amp;query=Morgan%2C+A">Andrew Morgan</a>, <a href="/search/physics?searchtype=author&amp;query=Mariani%2C+V">Valerio Mariani</a>, <a href="/search/physics?searchtype=author&amp;query=Oberthuer%2C+D">Dominik Oberthuer</a>, <a href="/search/physics?searchtype=author&amp;query=Pande%2C+K">Kanupriya Pande</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1705.05173v1-abstract-short" style="display: inline;"> The diffraction pattern of a single non-periodic compact object, such as a molecule, is continuous and is proportional to the square modulus of the Fourier transform of that object. When arrayed in a crystal, the coherent sum of the continuous diffracted wave-fields from all objects gives rise to strong Bragg peaks that modulate the single-object transform. Wilson statistics describe the distribut&hellip; <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1705.05173v1-abstract-full').style.display = 'inline'; document.getElementById('1705.05173v1-abstract-short').style.display = 'none';">&#9661; More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1705.05173v1-abstract-full" style="display: none;"> The diffraction pattern of a single non-periodic compact object, such as a molecule, is continuous and is proportional to the square modulus of the Fourier transform of that object. When arrayed in a crystal, the coherent sum of the continuous diffracted wave-fields from all objects gives rise to strong Bragg peaks that modulate the single-object transform. Wilson statistics describe the distribution of continuous diffraction intensities to the same extent that they apply to Bragg diffraction. The continuous diffraction obtained from translationally-disordered molecular crystals consists of the incoherent sum of the wave-fields from the individual rigid units (such as molecules) in the crystal, which is proportional to the incoherent sum of the diffraction from the rigid units in each of their crystallographic orientations. This sum over orientations modifies the statistics in a similar way that crystal twinning modifies the distribution of Bragg intensities. These statistics are applied to determine parameters of continuous diffraction such as its scaling, the beam coherence, and the number of independent wave-fields or object orientations contributing. Continuous diffraction is generally much weaker than Bragg diffraction and may be accompanied by a background that far exceeds the strength of the signal. Instead of just relying upon the smallest measured intensities to guide the subtraction of the background it is shown how all measured values can be utilised to estimate the background, noise, and signal, by employing a modified &#34;noisy Wilson&#34; distribution that explicitly includes the background. Parameters relating to the background and signal quantities can be estimated from the moments of the measured intensities. The analysis method is demonstrated on previously-published continuous diffraction data measured from imperfect crystals of photosystem II. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1705.05173v1-abstract-full').style.display = 'none'; document.getElementById('1705.05173v1-abstract-short').style.display = 'inline';">&#9651; Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 May, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">34 pages, 11 figures, 2 appendices</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1402.6135">arXiv:1402.6135</a> <span>&nbsp;[<a href="https://arxiv.org/pdf/1402.6135">pdf</a>, <a href="https://arxiv.org/format/1402.6135">other</a>]&nbsp;</span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1107/S1600577514006857">10.1107/S1600577514006857 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Characterization of Spatial Coherence of Synchrotron Radiation with Non-Redundant Arrays of Apertures </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/physics?searchtype=author&amp;query=Skopintsev%2C+P">P. Skopintsev</a>, <a href="/search/physics?searchtype=author&amp;query=Singer%2C+A">A. Singer</a>, <a href="/search/physics?searchtype=author&amp;query=Bach%2C+J">J. Bach</a>, <a href="/search/physics?searchtype=author&amp;query=M%7Fuller%2C+L">L. Muller</a>, <a href="/search/physics?searchtype=author&amp;query=Beyersdorf%2C+B">B. Beyersdorf</a>, <a href="/search/physics?searchtype=author&amp;query=Schleitzer%2C+S">S. Schleitzer</a>, <a href="/search/physics?searchtype=author&amp;query=Gorobtsov%2C+O">O. Gorobtsov</a>, <a href="/search/physics?searchtype=author&amp;query=Shabalin%2C+A">A. Shabalin</a>, <a href="/search/physics?searchtype=author&amp;query=Kurta%2C+R">R. Kurta</a>, <a href="/search/physics?searchtype=author&amp;query=Dzhigaev%2C+D">D. Dzhigaev</a>, <a href="/search/physics?searchtype=author&amp;query=Yefanov%2C+O+M">O. M. Yefanov</a>, <a href="/search/physics?searchtype=author&amp;query=Glaser%2C+L">L. Glaser</a>, <a href="/search/physics?searchtype=author&amp;query=Sakdinawat%2C+A">A. Sakdinawat</a>, <a href="/search/physics?searchtype=author&amp;query=Liu%2C+Y">Y. Liu</a>, <a href="/search/physics?searchtype=author&amp;query=Gr%7Fubel%2C+G">G. Grubel</a>, <a href="/search/physics?searchtype=author&amp;query=Fr%7Fomter%2C+R">R. Fromter</a>, <a href="/search/physics?searchtype=author&amp;query=Oepen%2C+H+P">H. P. Oepen</a>, <a href="/search/physics?searchtype=author&amp;query=Viefhaus%2C+J">J. Viefhaus</a>, <a href="/search/physics?searchtype=author&amp;query=Vartanyants%2C+I+A">I. A. Vartanyants</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1402.6135v1-abstract-short" style="display: inline;"> We present a method to characterize the spatial coherence of soft X-ray radiation from a single diffraction pattern. The technique is based on scattering from non-redundant arrays (NRA) of slits and records the degree of spatial coherence at several relative separations from one to 15 microns, simultaneously. Using NRAs we measured the transverse coherence of the X-ray beam at the XUV X-ray beamli&hellip; <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1402.6135v1-abstract-full').style.display = 'inline'; document.getElementById('1402.6135v1-abstract-short').style.display = 'none';">&#9661; More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1402.6135v1-abstract-full" style="display: none;"> We present a method to characterize the spatial coherence of soft X-ray radiation from a single diffraction pattern. The technique is based on scattering from non-redundant arrays (NRA) of slits and records the degree of spatial coherence at several relative separations from one to 15 microns, simultaneously. Using NRAs we measured the transverse coherence of the X-ray beam at the XUV X-ray beamline P04 of the PETRA III synchrotron storage ring as a function of different beam parameters. To verify the results obtained with the NRAs additional Young&#39;s double pinhole experiments were conducted and show good agreement. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1402.6135v1-abstract-full').style.display = 'none'; document.getElementById('1402.6135v1-abstract-short').style.display = 'inline';">&#9651; Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 February, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15 pages, 6 figures, 2 tables, 42 references</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. Synchrotron Rad. 21 Part 4, pages 722-728. (2014) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1302.5730">arXiv:1302.5730</a> <span>&nbsp;[<a href="https://arxiv.org/pdf/1302.5730">pdf</a>, <a href="https://arxiv.org/format/1302.5730">other</a>]&nbsp;</span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Biological Physics">physics.bio-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Soft Condensed Matter">cond-mat.soft</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/0953-4075/46/16/164013">10.1088/0953-4075/46/16/164013 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Orientation Determination in Single Particle X-ray Coherent Diffraction Imaging Experiments </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/physics?searchtype=author&amp;query=Yefanov%2C+O+M">O. M. Yefanov</a>, <a href="/search/physics?searchtype=author&amp;query=Vartanyants%2C+I+A">I. A. Vartanyants</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1302.5730v1-abstract-short" style="display: inline;"> Single particle diffraction imaging experiments at free-electron lasers (FEL) have a great potential for structure determination of reproducible biological specimens that can not be crystallized. One of the challenges in processing the data from such an experiment is to determine correct orientation of each diffraction pattern from samples randomly injected in the FEL beam. We propose an algorithm&hellip; <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.5730v1-abstract-full').style.display = 'inline'; document.getElementById('1302.5730v1-abstract-short').style.display = 'none';">&#9661; More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1302.5730v1-abstract-full" style="display: none;"> Single particle diffraction imaging experiments at free-electron lasers (FEL) have a great potential for structure determination of reproducible biological specimens that can not be crystallized. One of the challenges in processing the data from such an experiment is to determine correct orientation of each diffraction pattern from samples randomly injected in the FEL beam. We propose an algorithm (see also O. Yefanov et al., Photon Science - HASYLAB Annual Report 2010) that can solve this problem and can be applied to samples from tens of nanometers to microns in size, measured with sub-nanometer resolution in the presence of noise. This is achieved by the simultaneous analysis of a large number of diffraction patterns corresponding to different orientations of the particles. The algorithms efficiency is demonstrated for two biological samples, an artificial protein structure without any symmetry and a virus with icosahedral symmetry. Both structures are few tens of nanometers in size and consist of more than 100 000 non-hydrogen atoms. More than 10 000 diffraction patterns with Poisson noise were simulated and analyzed for each structure. Our simulations indicate the possibility to achieve resolution of about 3.3 脜 at 3 脜 wavelength and incoming flux of 10^{12} photons per pulse focused to 100\times 100 nm^2. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.5730v1-abstract-full').style.display = 'none'; document.getElementById('1302.5730v1-abstract-short').style.display = 'inline';">&#9651; Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 February, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">23 pages, 10 figures, 40 references</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. Phys. B: At. Mol. Opt. Phys. v. 46, 164013 (2013) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1301.6654">arXiv:1301.6654</a> <span>&nbsp;[<a href="https://arxiv.org/pdf/1301.6654">pdf</a>, <a href="https://arxiv.org/ps/1301.6654">ps</a>, <a href="https://arxiv.org/format/1301.6654">other</a>]&nbsp;</span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.111.034802">10.1103/PhysRevLett.111.034802 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Hanbury Brown and Twiss interferometry at a free-electron laser </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/physics?searchtype=author&amp;query=Singer%2C+A">A. Singer</a>, <a href="/search/physics?searchtype=author&amp;query=Lorenz%2C+U">U. Lorenz</a>, <a href="/search/physics?searchtype=author&amp;query=Sorgenfrei%2C+F">F. Sorgenfrei</a>, <a href="/search/physics?searchtype=author&amp;query=Gerasimova%2C+N">N. Gerasimova</a>, <a href="/search/physics?searchtype=author&amp;query=Gulden%2C+J">J. Gulden</a>, <a href="/search/physics?searchtype=author&amp;query=Yefanov%2C+O+M">O. M. Yefanov</a>, <a href="/search/physics?searchtype=author&amp;query=Kurta%2C+R+P">R. P. Kurta</a>, <a href="/search/physics?searchtype=author&amp;query=Shabalin%2C+A">A. Shabalin</a>, <a href="/search/physics?searchtype=author&amp;query=Dronyak%2C+R">R. Dronyak</a>, <a href="/search/physics?searchtype=author&amp;query=Treusch%2C+R">R. Treusch</a>, <a href="/search/physics?searchtype=author&amp;query=Kocharyan%2C+V">V. Kocharyan</a>, <a href="/search/physics?searchtype=author&amp;query=Weckert%2C+E">E. Weckert</a>, <a href="/search/physics?searchtype=author&amp;query=Wurth%2C+W">W. Wurth</a>, <a href="/search/physics?searchtype=author&amp;query=Vartanyants%2C+I+A">I. A. Vartanyants</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1301.6654v1-abstract-short" style="display: inline;"> We present measurements of second- and higher-order intensity correlation functions (so-called Hanbury Brown and Twiss experiment) performed at the free-electron laser (FEL) FLASH in the non-linear regime of its operation. We demonstrate the high transverse coherence properties of the FEL beam with a degree of transverse coherence of about 80% and degeneracy parameter of the order 10^9 that makes&hellip; <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1301.6654v1-abstract-full').style.display = 'inline'; document.getElementById('1301.6654v1-abstract-short').style.display = 'none';">&#9661; More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1301.6654v1-abstract-full" style="display: none;"> We present measurements of second- and higher-order intensity correlation functions (so-called Hanbury Brown and Twiss experiment) performed at the free-electron laser (FEL) FLASH in the non-linear regime of its operation. We demonstrate the high transverse coherence properties of the FEL beam with a degree of transverse coherence of about 80% and degeneracy parameter of the order 10^9 that makes it similar to laser sources. Intensity correlation measurements in spatial and frequency domain gave an estimate of the FEL average pulse duration of 50 fs. Our measurements of the higher-order correlation functions indicate that FEL radiation obeys Gaussian statistics, which is characteristic to chaotic sources. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1301.6654v1-abstract-full').style.display = 'none'; document.getElementById('1301.6654v1-abstract-short').style.display = 'inline';">&#9651; Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 28 January, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">19 pages, 6 figures, 1 table, 40 references</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. v. 111, 034802 (2013) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1206.1091">arXiv:1206.1091</a> <span>&nbsp;[<a href="https://arxiv.org/pdf/1206.1091">pdf</a>, <a href="https://arxiv.org/ps/1206.1091">ps</a>, <a href="https://arxiv.org/format/1206.1091">other</a>]&nbsp;</span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1364/OE.20.017480">10.1364/OE.20.017480 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Spatial and temporal coherence properties of single free-electron laser pulses </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/physics?searchtype=author&amp;query=Singer%2C+A">A. Singer</a>, <a href="/search/physics?searchtype=author&amp;query=Sorgenfrei%2C+F">F. Sorgenfrei</a>, <a href="/search/physics?searchtype=author&amp;query=Mancuso%2C+A+P">A. P. Mancuso</a>, <a href="/search/physics?searchtype=author&amp;query=Gerasimova%2C+N">N. Gerasimova</a>, <a href="/search/physics?searchtype=author&amp;query=Yefanov%2C+O+M">O. M. Yefanov</a>, <a href="/search/physics?searchtype=author&amp;query=Gulden%2C+J">J. Gulden</a>, <a href="/search/physics?searchtype=author&amp;query=Gorniak%2C+T">T. Gorniak</a>, <a href="/search/physics?searchtype=author&amp;query=Senkbeil%2C+T">T. Senkbeil</a>, <a href="/search/physics?searchtype=author&amp;query=Sakdinawat%2C+A">A. Sakdinawat</a>, <a href="/search/physics?searchtype=author&amp;query=Liu%2C+Y">Y. Liu</a>, <a href="/search/physics?searchtype=author&amp;query=Attwood%2C+D">D. Attwood</a>, <a href="/search/physics?searchtype=author&amp;query=Dziarzhytski%2C+S">S. Dziarzhytski</a>, <a href="/search/physics?searchtype=author&amp;query=Mai%2C+D+D">D. D. Mai</a>, <a href="/search/physics?searchtype=author&amp;query=Treusch%2C+R">R. Treusch</a>, <a href="/search/physics?searchtype=author&amp;query=Weckert%2C+E">E. Weckert</a>, <a href="/search/physics?searchtype=author&amp;query=Salditt%2C+T">T. Salditt</a>, <a href="/search/physics?searchtype=author&amp;query=Rosenhahn%2C+A">A. Rosenhahn</a>, <a href="/search/physics?searchtype=author&amp;query=Wurth%2C+W">W. Wurth</a>, <a href="/search/physics?searchtype=author&amp;query=Vartanyants%2C+I+A">I. A. Vartanyants</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1206.1091v1-abstract-short" style="display: inline;"> The experimental characterization of the spatial and temporal coherence properties of the free-electron laser in Hamburg (FLASH) at a wavelength of 8.0 nm is presented. Double pinhole diffraction patterns of single femtosecond pulses focused to a size of about 10 microns by 10 microns were measured. A transverse coherence length of 6.2 microns in the horizontal and 8.7 microns in the vertical dire&hellip; <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1206.1091v1-abstract-full').style.display = 'inline'; document.getElementById('1206.1091v1-abstract-short').style.display = 'none';">&#9661; More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1206.1091v1-abstract-full" style="display: none;"> The experimental characterization of the spatial and temporal coherence properties of the free-electron laser in Hamburg (FLASH) at a wavelength of 8.0 nm is presented. Double pinhole diffraction patterns of single femtosecond pulses focused to a size of about 10 microns by 10 microns were measured. A transverse coherence length of 6.2 microns in the horizontal and 8.7 microns in the vertical direction was determined from the most coherent pulses. Using a split and delay unit the coherence time of the pulses produced in the same operation conditions of FLASH was measured to be 1.75 fs. From our experiment we estimated the degeneracy parameter of the FLASH beam to be on the order of $10^{10}$ to $10^{11}$, which exceeds the values of this parameter at any other source in the same energy range by many orders of magnitude. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1206.1091v1-abstract-full').style.display = 'none'; document.getElementById('1206.1091v1-abstract-short').style.display = 'inline';">&#9651; Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 5 June, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">16 pages, 7 figures, 1 table</span> </p> </li> </ol> <div class="is-hidden-tablet"> <!-- feedback for mobile only --> <span class="help" style="display: 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