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name="searchtype"><option value="all">All fields</option><option value="title">Title</option><option selected value="author">Author(s)</option><option value="abstract">Abstract</option><option value="comments">Comments</option><option value="journal_ref">Journal reference</option><option value="acm_class">ACM classification</option><option value="msc_class">MSC classification</option><option value="report_num">Report number</option><option value="paper_id">arXiv identifier</option><option value="doi">DOI</option><option value="orcid">ORCID</option><option value="license">License (URI)</option><option value="author_id">arXiv author ID</option><option value="help">Help pages</option><option value="full_text">Full text</option></select> <input id="query" name="query" type="text" value="Imrie, C"> <ul id="abstracts"><li><input checked id="abstracts-0" name="abstracts" type="radio" value="show"> <label for="abstracts-0">Show abstracts</label></li><li><input id="abstracts-1" name="abstracts" 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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/2405.18180">arXiv:2405.18180</a> <span> [<a href="https://arxiv.org/pdf/2405.18180">pdf</a>, <a href="https://arxiv.org/format/2405.18180">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> </div> </div> <p class="title is-5 mathjax"> Safe Reinforcement Learning in Black-Box Environments via Adaptive Shielding </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Bethell%2C+D">Daniel Bethell</a>, <a href="/search/cs?searchtype=author&query=Gerasimou%2C+S">Simos Gerasimou</a>, <a href="/search/cs?searchtype=author&query=Calinescu%2C+R">Radu Calinescu</a>, <a href="/search/cs?searchtype=author&query=Imrie%2C+C">Calum Imrie</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="2405.18180v1-abstract-short" style="display: inline;"> Empowering safe exploration of reinforcement learning (RL) agents during training is a critical impediment towards deploying RL agents in many real-world scenarios. Training RL agents in unknown, black-box environments poses an even greater safety risk when prior knowledge of the domain/task is unavailable. We introduce ADVICE (Adaptive Shielding with a Contrastive Autoencoder), a novel post-shiel… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.18180v1-abstract-full').style.display = 'inline'; document.getElementById('2405.18180v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2405.18180v1-abstract-full" style="display: none;"> Empowering safe exploration of reinforcement learning (RL) agents during training is a critical impediment towards deploying RL agents in many real-world scenarios. Training RL agents in unknown, black-box environments poses an even greater safety risk when prior knowledge of the domain/task is unavailable. We introduce ADVICE (Adaptive Shielding with a Contrastive Autoencoder), a novel post-shielding technique that distinguishes safe and unsafe features of state-action pairs during training, thus protecting the RL agent from executing actions that yield potentially hazardous outcomes. Our comprehensive experimental evaluation against state-of-the-art safe RL exploration techniques demonstrates how ADVICE can significantly reduce safety violations during training while maintaining a competitive outcome reward. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.18180v1-abstract-full').style.display = 'none'; document.getElementById('2405.18180v1-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> 28 May, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2401.17187">arXiv:2401.17187</a> <span> [<a href="https://arxiv.org/pdf/2401.17187">pdf</a>, <a href="https://arxiv.org/format/2401.17187">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Software Engineering">cs.SE</span> </div> </div> <p class="title is-5 mathjax"> Formal Synthesis of Uncertainty Reduction Controllers </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Carwehl%2C+M">Marc Carwehl</a>, <a href="/search/cs?searchtype=author&query=Imrie%2C+C">Calum Imrie</a>, <a href="/search/cs?searchtype=author&query=Vogel%2C+T">Thomas Vogel</a>, <a href="/search/cs?searchtype=author&query=Rodrigues%2C+G">Gena铆na Rodrigues</a>, <a href="/search/cs?searchtype=author&query=Calinescu%2C+R">Radu Calinescu</a>, <a href="/search/cs?searchtype=author&query=Grunske%2C+L">Lars Grunske</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="2401.17187v2-abstract-short" style="display: inline;"> In its quest for approaches to taming uncertainty in self-adaptive systems (SAS), the research community has largely focused on solutions that adapt the SAS architecture or behaviour in response to uncertainty. By comparison, solutions that reduce the uncertainty affecting SAS (other than through the blanket monitoring of their components and environment) remain underexplored. Our paper proposes a… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.17187v2-abstract-full').style.display = 'inline'; document.getElementById('2401.17187v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2401.17187v2-abstract-full" style="display: none;"> In its quest for approaches to taming uncertainty in self-adaptive systems (SAS), the research community has largely focused on solutions that adapt the SAS architecture or behaviour in response to uncertainty. By comparison, solutions that reduce the uncertainty affecting SAS (other than through the blanket monitoring of their components and environment) remain underexplored. Our paper proposes a more nuanced, adaptive approach to SAS uncertainty reduction. To that end, we introduce a SAS architecture comprising an uncertainty reduction controller that drives the adaptive acquisition of new information within the SAS adaptation loop, and a tool-supported method that uses probabilistic model checking to synthesise such controllers. The controllers generated by our method deliver optimal trade-offs between SAS uncertainty reduction benefits and new information acquisition costs. We illustrate the use and evaluate the effectiveness of our approach for mobile robot navigation and server infrastructure management SAS. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.17187v2-abstract-full').style.display = 'none'; document.getElementById('2401.17187v2-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> 1 February, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 30 January, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2401.05673">arXiv:2401.05673</a> <span> [<a href="https://arxiv.org/pdf/2401.05673">pdf</a>, <a href="https://arxiv.org/format/2401.05673">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Software Engineering">cs.SE</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/10.1145/3597503.3639093">10.1145/3597503.3639093 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Analyzing and Debugging Normative Requirements via Satisfiability Checking </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Feng%2C+N">Nick Feng</a>, <a href="/search/cs?searchtype=author&query=Marsso%2C+L">Lina Marsso</a>, <a href="/search/cs?searchtype=author&query=Yaman%2C+S+G">Sinem Getir Yaman</a>, <a href="/search/cs?searchtype=author&query=Baatartogtokh%2C+Y">Yesugen Baatartogtokh</a>, <a href="/search/cs?searchtype=author&query=Ayad%2C+R">Reem Ayad</a>, <a href="/search/cs?searchtype=author&query=de+Mello%2C+V+O">Vict贸ria Oldemburgo de Mello</a>, <a href="/search/cs?searchtype=author&query=Townsend%2C+B">Beverley Townsend</a>, <a href="/search/cs?searchtype=author&query=Standen%2C+I">Isobel Standen</a>, <a href="/search/cs?searchtype=author&query=Stefanakos%2C+I">Ioannis Stefanakos</a>, <a href="/search/cs?searchtype=author&query=Imrie%2C+C">Calum Imrie</a>, <a href="/search/cs?searchtype=author&query=Rodrigues%2C+G+N">Gena铆na Nunes Rodrigues</a>, <a href="/search/cs?searchtype=author&query=Cavalcanti%2C+A">Ana Cavalcanti</a>, <a href="/search/cs?searchtype=author&query=Calinescu%2C+R">Radu Calinescu</a>, <a href="/search/cs?searchtype=author&query=Chechik%2C+M">Marsha Chechik</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="2401.05673v1-abstract-short" style="display: inline;"> As software systems increasingly interact with humans in application domains such as transportation and healthcare, they raise concerns related to the social, legal, ethical, empathetic, and cultural (SLEEC) norms and values of their stakeholders. Normative non-functional requirements (N-NFRs) are used to capture these concerns by setting SLEEC-relevant boundaries for system behavior. Since N-NFRs… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.05673v1-abstract-full').style.display = 'inline'; document.getElementById('2401.05673v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2401.05673v1-abstract-full" style="display: none;"> As software systems increasingly interact with humans in application domains such as transportation and healthcare, they raise concerns related to the social, legal, ethical, empathetic, and cultural (SLEEC) norms and values of their stakeholders. Normative non-functional requirements (N-NFRs) are used to capture these concerns by setting SLEEC-relevant boundaries for system behavior. Since N-NFRs need to be specified by multiple stakeholders with widely different, non-technical expertise (ethicists, lawyers, regulators, end users, etc.), N-NFR elicitation is very challenging. To address this challenge, we introduce N-Check, a novel tool-supported formal approach to N-NFR analysis and debugging. N-Check employs satisfiability checking to identify a broad spectrum of N-NFR well-formedness issues (WFI), such as conflicts, redundancy, restrictiveness, insufficiency, yielding diagnostics which pinpoint their causes in a user-friendly way that enables non-technical stakeholders to understand and fix them. We show the effectiveness and usability of our approach through nine case studies in which teams of ethicists, lawyers, philosophers, psychologists, safety analysts, and engineers used N-Check to analyse and debug 233 N-NFRs comprising 62 issues for the software underpinning the operation of systems ranging from assistive-care robots and tree-disease detection drones to manufacturing collaborative robots. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.05673v1-abstract-full').style.display = 'none'; document.getElementById('2401.05673v1-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> 11 January, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2303.08476">arXiv:2303.08476</a> <span> [<a href="https://arxiv.org/pdf/2303.08476">pdf</a>, <a href="https://arxiv.org/format/2303.08476">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Robotics">cs.RO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Bayesian Learning for the Robust Verification of Autonomous Robots </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Zhao%2C+X">Xingyu Zhao</a>, <a href="/search/cs?searchtype=author&query=Gerasimou%2C+S">Simos Gerasimou</a>, <a href="/search/cs?searchtype=author&query=Calinescu%2C+R">Radu Calinescu</a>, <a href="/search/cs?searchtype=author&query=Imrie%2C+C">Calum Imrie</a>, <a href="/search/cs?searchtype=author&query=Robu%2C+V">Valentin Robu</a>, <a href="/search/cs?searchtype=author&query=Flynn%2C+D">David Flynn</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="2303.08476v2-abstract-short" style="display: inline;"> Autonomous robots used in infrastructure inspection, space exploration and other critical missions operate in highly dynamic environments. As such, they must continually verify their ability to complete the tasks associated with these missions safely and effectively. Here we present a Bayesian learning framework that enables this runtime verification of autonomous robots. The framework uses prior… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.08476v2-abstract-full').style.display = 'inline'; document.getElementById('2303.08476v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2303.08476v2-abstract-full" style="display: none;"> Autonomous robots used in infrastructure inspection, space exploration and other critical missions operate in highly dynamic environments. As such, they must continually verify their ability to complete the tasks associated with these missions safely and effectively. Here we present a Bayesian learning framework that enables this runtime verification of autonomous robots. The framework uses prior knowledge and observations of the verified robot to learn expected ranges for the occurrence rates of regular and singular (e.g., catastrophic failure) events. Interval continuous-time Markov models defined using these ranges are then analysed to obtain expected intervals of variation for system properties such as mission duration and success probability. We apply the framework to an autonomous robotic mission for underwater infrastructure inspection and repair. The formal proofs and experiments presented in the paper show that our framework produces results that reflect the uncertainty intrinsic to many real-world systems, enabling the robust verification of their quantitative properties under parametric uncertainty. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.08476v2-abstract-full').style.display = 'none'; document.getElementById('2303.08476v2-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> 11 December, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 15 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2023. </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">Accepted by Communications Engineering</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2302.04634">arXiv:2302.04634</a> <span> [<a href="https://arxiv.org/pdf/2302.04634">pdf</a>, <a href="https://arxiv.org/format/2302.04634">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Computer Vision and Pattern Recognition">cs.CV</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Formal Languages and Automata Theory">cs.FL</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> </div> </div> <p class="title is-5 mathjax"> Closed-loop Analysis of Vision-based Autonomous Systems: A Case Study </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Pasareanu%2C+C+S">Corina S. Pasareanu</a>, <a href="/search/cs?searchtype=author&query=Mangal%2C+R">Ravi Mangal</a>, <a href="/search/cs?searchtype=author&query=Gopinath%2C+D">Divya Gopinath</a>, <a href="/search/cs?searchtype=author&query=Yaman%2C+S+G">Sinem Getir Yaman</a>, <a href="/search/cs?searchtype=author&query=Imrie%2C+C">Calum Imrie</a>, <a href="/search/cs?searchtype=author&query=Calinescu%2C+R">Radu Calinescu</a>, <a href="/search/cs?searchtype=author&query=Yu%2C+H">Huafeng Yu</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="2302.04634v1-abstract-short" style="display: inline;"> Deep neural networks (DNNs) are increasingly used in safety-critical autonomous systems as perception components processing high-dimensional image data. Formal analysis of these systems is particularly challenging due to the complexity of the perception DNNs, the sensors (cameras), and the environment conditions. We present a case study applying formal probabilistic analysis techniques to an exper… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2302.04634v1-abstract-full').style.display = 'inline'; document.getElementById('2302.04634v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2302.04634v1-abstract-full" style="display: none;"> Deep neural networks (DNNs) are increasingly used in safety-critical autonomous systems as perception components processing high-dimensional image data. Formal analysis of these systems is particularly challenging due to the complexity of the perception DNNs, the sensors (cameras), and the environment conditions. We present a case study applying formal probabilistic analysis techniques to an experimental autonomous system that guides airplanes on taxiways using a perception DNN. We address the above challenges by replacing the camera and the network with a compact probabilistic abstraction built from the confusion matrices computed for the DNN on a representative image data set. We also show how to leverage local, DNN-specific analyses as run-time guards to increase the safety of the overall system. Our findings are applicable to other autonomous systems that use complex DNNs for perception. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2302.04634v1-abstract-full').style.display = 'none'; document.getElementById('2302.04634v1-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> 6 February, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2202.03360">arXiv:2202.03360</a> <span> [<a href="https://arxiv.org/pdf/2202.03360">pdf</a>, <a href="https://arxiv.org/format/2202.03360">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> </div> </div> <p class="title is-5 mathjax"> Discrete-Event Controller Synthesis for Autonomous Systems with Deep-Learning Perception Components </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Calinescu%2C+R">Radu Calinescu</a>, <a href="/search/cs?searchtype=author&query=Imrie%2C+C">Calum Imrie</a>, <a href="/search/cs?searchtype=author&query=Mangal%2C+R">Ravi Mangal</a>, <a href="/search/cs?searchtype=author&query=Rodrigues%2C+G+N">Gena铆na Nunes Rodrigues</a>, <a href="/search/cs?searchtype=author&query=P%C4%83s%C4%83reanu%2C+C">Corina P膬s膬reanu</a>, <a href="/search/cs?searchtype=author&query=Santana%2C+M+A">Misael Alpizar Santana</a>, <a href="/search/cs?searchtype=author&query=V%C3%A1zquez%2C+G">Gricel V谩zquez</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="2202.03360v2-abstract-short" style="display: inline;"> We present DeepDECS, a new method for the synthesis of correct-by-construction discrete-event controllers for autonomous systems that use deep neural network (DNN) classifiers for the perception step of their decision-making processes. Despite major advances in deep learning in recent years, providing safety guarantees for these systems remains very challenging. Our controller synthesis method add… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2202.03360v2-abstract-full').style.display = 'inline'; document.getElementById('2202.03360v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2202.03360v2-abstract-full" style="display: none;"> We present DeepDECS, a new method for the synthesis of correct-by-construction discrete-event controllers for autonomous systems that use deep neural network (DNN) classifiers for the perception step of their decision-making processes. Despite major advances in deep learning in recent years, providing safety guarantees for these systems remains very challenging. Our controller synthesis method addresses this challenge by integrating DNN verification with the synthesis of verified Markov models. The synthesised models correspond to discrete-event controllers guaranteed to satisfy the safety, dependability and performance requirements of the autonomous system, and to be Pareto optimal with respect to a set of optimisation objectives. We use the method in simulation to synthesise controllers for mobile-robot collision mitigation and for maintaining driver attentiveness in shared-control autonomous driving. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2202.03360v2-abstract-full').style.display = 'none'; document.getElementById('2202.03360v2-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 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 7 February, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2022. </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">18 pages 6 Figures 2 Tables</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">ACM Class:</span> D.2.2; D.2.4; G.3; I.2.0; I.2.6 </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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