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is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2503.13512">arXiv:2503.13512</a> <span> [<a href="https://arxiv.org/pdf/2503.13512">pdf</a>, <a href="https://arxiv.org/format/2503.13512">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Machine Learning">stat.ML</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Discrete Mathematics">cs.DM</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Symbolic Computation">cs.SC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Positivity sets of hinge functions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/stat?searchtype=author&query=Schicho%2C+J">Josef Schicho</a>, <a href="/search/stat?searchtype=author&query=Tewari%2C+A+K">Ayush Kumar Tewari</a>, <a href="/search/stat?searchtype=author&query=Warren%2C+A">Audie Warren</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="2503.13512v1-abstract-short" style="display: inline;"> In this paper we investigate which subsets of the real plane are realisable as the set of points on which a one-layer ReLU neural network takes a positive value. In the case of cones we give a full characterisation of such sets. Furthermore, we give a necessary condition for any subset of $\mathbb R^d$. We give various examples of such one-layer neural networks. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.13512v1-abstract-full" style="display: none;"> In this paper we investigate which subsets of the real plane are realisable as the set of points on which a one-layer ReLU neural network takes a positive value. In the case of cones we give a full characterisation of such sets. Furthermore, we give a necessary condition for any subset of $\mathbb R^d$. We give various examples of such one-layer neural networks. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.13512v1-abstract-full').style.display = 'none'; document.getElementById('2503.13512v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2410.22729">arXiv:2410.22729</a> <span> [<a href="https://arxiv.org/pdf/2410.22729">pdf</a>, <a href="https://arxiv.org/format/2410.22729">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Machine Learning">stat.ML</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistics Theory">math.ST</span> </div> </div> <p class="title is-5 mathjax"> Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshots </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/stat?searchtype=author&query=Guan%2C+V">Vincent Guan</a>, <a href="/search/stat?searchtype=author&query=Janssen%2C+J">Joseph Janssen</a>, <a href="/search/stat?searchtype=author&query=Rahmani%2C+H">Hossein Rahmani</a>, <a href="/search/stat?searchtype=author&query=Warren%2C+A">Andrew Warren</a>, <a href="/search/stat?searchtype=author&query=Zhang%2C+S">Stephen Zhang</a>, <a href="/search/stat?searchtype=author&query=Robeva%2C+E">Elina Robeva</a>, <a href="/search/stat?searchtype=author&query=Schiebinger%2C+G">Geoffrey Schiebinger</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="2410.22729v2-abstract-short" style="display: inline;"> Stochastic differential equations (SDEs) are a fundamental tool for modelling dynamic processes, including gene regulatory networks (GRNs), contaminant transport, financial markets, and image generation. However, learning the underlying SDE from data is a challenging task, especially if individual trajectories are not observable. Motivated by burgeoning research in single-cell datasets, we present… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.22729v2-abstract-full').style.display = 'inline'; document.getElementById('2410.22729v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2410.22729v2-abstract-full" style="display: none;"> Stochastic differential equations (SDEs) are a fundamental tool for modelling dynamic processes, including gene regulatory networks (GRNs), contaminant transport, financial markets, and image generation. However, learning the underlying SDE from data is a challenging task, especially if individual trajectories are not observable. Motivated by burgeoning research in single-cell datasets, we present the first comprehensive approach for jointly identifying the drift and diffusion of an SDE from its temporal marginals. Assuming linear drift and additive diffusion, we prove that these parameters are identifiable from marginals if and only if the initial distribution lacks any generalized rotational symmetries. We further prove that the causal graph of any SDE with additive diffusion can be recovered from the SDE parameters. To complement this theory, we adapt entropy-regularized optimal transport to handle anisotropic diffusion, and introduce APPEX (Alternating Projection Parameter Estimation from $X_0$), an iterative algorithm designed to estimate the drift, diffusion, and causal graph of an additive noise SDE, solely from temporal marginals. We show that APPEX iteratively decreases Kullback-Leibler divergence to the true solution, and demonstrate its effectiveness on simulated data from linear additive noise SDEs. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.22729v2-abstract-full').style.display = 'none'; document.getElementById('2410.22729v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 30 October, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2406.02840">arXiv:2406.02840</a> <span> [<a href="https://arxiv.org/pdf/2406.02840">pdf</a>, <a href="https://arxiv.org/format/2406.02840">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Methodology">stat.ME</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistics Theory">math.ST</span> </div> </div> <p class="title is-5 mathjax"> Statistical inference of convex order by Wasserstein projection </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/stat?searchtype=author&query=Kim%2C+J">Jakwang Kim</a>, <a href="/search/stat?searchtype=author&query=Kim%2C+Y">Young-Heon Kim</a>, <a href="/search/stat?searchtype=author&query=Ruan%2C+Y">Yuanlong Ruan</a>, <a href="/search/stat?searchtype=author&query=Warren%2C+A">Andrew Warren</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="2406.02840v3-abstract-short" style="display: inline;"> Ranking distributions according to a stochastic order has wide applications in diverse areas. Although stochastic dominance has received much attention, convex order, particularly in general dimensions, has yet to be investigated from a statistical point of view. This article addresses this gap by introducing a simple statistical test for convex order based on the Wasserstein projection distance.… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.02840v3-abstract-full').style.display = 'inline'; document.getElementById('2406.02840v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2406.02840v3-abstract-full" style="display: none;"> Ranking distributions according to a stochastic order has wide applications in diverse areas. Although stochastic dominance has received much attention, convex order, particularly in general dimensions, has yet to be investigated from a statistical point of view. This article addresses this gap by introducing a simple statistical test for convex order based on the Wasserstein projection distance. This projection distance not only encodes whether two distributions are indeed in convex order, but also quantifies the deviation from the desired convex order and produces an optimal convex order approximation. Lipschitz stability of the backward and forward Wasserstein projection distance is proved, which leads to elegant consistency and concentration results of the estimator we employ as our test statistic. Combining these with state of the art results regarding the convergence rate of empirical distributions, we also derive upper bounds for the $p$-value and type I error of our test statistic, as well as upper bounds on the type II error for an appropriate class of strict alternatives. With proper choices of families of distributions, we further attain that the power of the proposed test increases to one as the number of samples grows to infinity. Lastly, we provide an efficient numerical scheme for our test statistic, by way of an entropic Frank-Wolfe algorithm. Experiments based on synthetic data sets illuminate the success of our approach. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.02840v3-abstract-full').style.display = 'none'; document.getElementById('2406.02840v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 January, 2025; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 4 June, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2024. </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">31 pages, 3 figures, Add previous literature about the Wasserstein projection (Aurelien Alfonsi, Jacopo Corbetta and Benjamin Jourdain (2020)), and the stability of the projection measure in one dimension (Benjamin Jourdain, William Margheriti and Gudmund Pammer(2023))</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> PIMS-20240605-PRN01 <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 62G99; 49Q22 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2403.15291">arXiv:2403.15291</a> <span> [<a href="https://arxiv.org/pdf/2403.15291">pdf</a>, <a href="https://arxiv.org/format/2403.15291">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Applications">stat.AP</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Physics and Society">physics.soc-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Populations and Evolution">q-bio.PE</span> </div> </div> <p class="title is-5 mathjax"> Wastewater-based Epidemiology for COVID-19 Surveillance and Beyond: A Survey </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/stat?searchtype=author&query=Chen%2C+C">Chen Chen</a>, <a href="/search/stat?searchtype=author&query=Wang%2C+Y">Yunfan Wang</a>, <a href="/search/stat?searchtype=author&query=Kaur%2C+G">Gursharn Kaur</a>, <a href="/search/stat?searchtype=author&query=Adiga%2C+A">Aniruddha Adiga</a>, <a href="/search/stat?searchtype=author&query=Espinoza%2C+B">Baltazar Espinoza</a>, <a href="/search/stat?searchtype=author&query=Venkatramanan%2C+S">Srinivasan Venkatramanan</a>, <a href="/search/stat?searchtype=author&query=Warren%2C+A">Andrew Warren</a>, <a href="/search/stat?searchtype=author&query=Lewis%2C+B">Bryan Lewis</a>, <a href="/search/stat?searchtype=author&query=Crow%2C+J">Justin Crow</a>, <a href="/search/stat?searchtype=author&query=Singh%2C+R">Rekha Singh</a>, <a href="/search/stat?searchtype=author&query=Lorentz%2C+A">Alexandra Lorentz</a>, <a href="/search/stat?searchtype=author&query=Toney%2C+D">Denise Toney</a>, <a href="/search/stat?searchtype=author&query=Marathe%2C+M">Madhav Marathe</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="2403.15291v2-abstract-short" style="display: inline;"> The pandemic of COVID-19 has imposed tremendous pressure on public health systems and social economic ecosystems over the past years. To alleviate its social impact, it is important to proactively track the prevalence of COVID-19 within communities. The traditional way to estimate the disease prevalence is to estimate from reported clinical test data or surveys. However, the coverage of clinical t… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.15291v2-abstract-full').style.display = 'inline'; document.getElementById('2403.15291v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2403.15291v2-abstract-full" style="display: none;"> The pandemic of COVID-19 has imposed tremendous pressure on public health systems and social economic ecosystems over the past years. To alleviate its social impact, it is important to proactively track the prevalence of COVID-19 within communities. The traditional way to estimate the disease prevalence is to estimate from reported clinical test data or surveys. However, the coverage of clinical tests is often limited and the tests can be labor-intensive, requires reliable and timely results, and consistent diagnostic and reporting criteria. Recent studies revealed that patients who are diagnosed with COVID-19 often undergo fecal shedding of SARS-CoV-2 virus into wastewater, which makes wastewater-based epidemiology for COVID-19 surveillance a promising approach to complement traditional clinical testing. In this paper, we survey the existing literature regarding wastewater-based epidemiology for COVID-19 surveillance and summarize the current advances in the area. Specifically, we have covered the key aspects of wastewater sampling, sample testing, and presented a comprehensive and organized summary of wastewater data analytical methods. Finally, we provide the open challenges on current wastewater-based COVID-19 surveillance studies, aiming to encourage new ideas to advance the development of effective wastewater-based surveillance systems for general infectious diseases. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.15291v2-abstract-full').style.display = 'none'; document.getElementById('2403.15291v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 September, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 March, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1902.10754">arXiv:1902.10754</a> <span> [<a href="https://arxiv.org/pdf/1902.10754">pdf</a>, <a href="https://arxiv.org/format/1902.10754">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">stat.ML</span> </div> </div> <p class="title is-5 mathjax"> Introspection Learning </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/stat?searchtype=author&query=Serrano%2C+C+R">Chris R. Serrano</a>, <a href="/search/stat?searchtype=author&query=Warren%2C+M+A">Michael A. Warren</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="1902.10754v1-abstract-short" style="display: inline;"> Traditional reinforcement learning agents learn from experience, past or present, gained through interaction with their environment. Our approach synthesizes experience, without requiring an agent to interact with their environment, by asking the policy directly "Are there situations X, Y, and Z, such that in these situations you would select actions A, B, and C?" In this paper we present Introspe… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.10754v1-abstract-full').style.display = 'inline'; document.getElementById('1902.10754v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1902.10754v1-abstract-full" style="display: none;"> Traditional reinforcement learning agents learn from experience, past or present, gained through interaction with their environment. Our approach synthesizes experience, without requiring an agent to interact with their environment, by asking the policy directly "Are there situations X, Y, and Z, such that in these situations you would select actions A, B, and C?" In this paper we present Introspection Learning, an algorithm that allows for the asking of these types of questions of neural network policies. Introspection Learning is reinforcement learning algorithm agnostic and the states returned may be used as an indicator of the health of the policy or to shape the policy in a myriad of ways. We demonstrate the usefulness of this algorithm both in the context of speeding up training and improving robustness with respect to safety constraints. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.10754v1-abstract-full').style.display = 'none'; document.getElementById('1902.10754v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 February, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2019. </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">8 pages. Submitted to 2019 AAAI Spring Symposium on Verification of Neural Networks</span> </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> <a href="https://info.arxiv.org/help/contact.html"> Contact</a> </li> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"/></svg> <a href="https://info.arxiv.org/help/subscribe"> Subscribe</a> </li> </ul> </div> </div> </div>   <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/license/index.html">Copyright</a></li> <li><a href="https://info.arxiv.org/help/policies/privacy_policy.html">Privacy Policy</a></li> </ul> </div> <div class="column sorry-app-links"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/web_accessibility.html">Web Accessibility Assistance</a></li> <li> <p class="help"> <a class="a11y-main-link" href="https://status.arxiv.org" target="_blank">arXiv Operational Status <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 256 512" class="icon filter-dark_grey" role="presentation"><path d="M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z"/></svg></a><br> Get status notifications via <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/email/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg>email</a> or <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/slack/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512" class="icon filter-black" role="presentation"><path d="M94.12 315.1c0 25.9-21.16 47.06-47.06 47.06S0 341 0 315.1c0-25.9 21.16-47.06 47.06-47.06h47.06v47.06zm23.72 0c0-25.9 21.16-47.06 47.06-47.06s47.06 21.16 47.06 47.06v117.84c0 25.9-21.16 47.06-47.06 47.06s-47.06-21.16-47.06-47.06V315.1zm47.06-188.98c-25.9 0-47.06-21.16-47.06-47.06S139 32 164.9 32s47.06 21.16 47.06 47.06v47.06H164.9zm0 23.72c25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06H47.06C21.16 243.96 0 222.8 0 196.9s21.16-47.06 47.06-47.06H164.9zm188.98 47.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06h-47.06V196.9zm-23.72 0c0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06V79.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06V196.9zM283.1 385.88c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06v-47.06h47.06zm0-23.72c-25.9 0-47.06-21.16-47.06-47.06 0-25.9 21.16-47.06 47.06-47.06h117.84c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06H283.1z"/></svg>slack</a> </p> </li> </ul> </div> </div> </div>  </div> </footer> <script src="https://static.arxiv.org/static/base/1.0.0a5/js/member_acknowledgement.js"></script> </body> </html>

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