{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/0-1-laws-for-pattern-occurrences-in","title":"0-1 laws for pattern occurrences in phylogenetic trees and networks","arxiv_id":"2402.04499","date":"2024-02-07","proceeding":null,"authors":["François Bienvenu","Mike Steel"],"abstract":"In a recent paper, the question of determining the fraction of binary trees that contain a fixed pattern known as the snowflake was posed. We show that this fraction goes to 1, providing two very different proofs: a purely combinatorial one that is quantitative and specific to this problem; and a proof using branching process techniques that is less explicit, but also much more general, as it applies to any fixed patterns and can be extended to other trees and networks. In particular, it follows immediately from our second proof that the fraction of $d$-ary trees (resp. level-$k$ networks) that contain a fixed $d$-ary tree (resp. level-$k$ network) tends to $1$ as the number of leaves grows.","url_abs":"https://arxiv.org/abs/2402.04499v2","url_pdf":"https://arxiv.org/pdf/2402.04499v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[],"tasks":[{"task_slug":"10-shot-image-generation","task_name":"10-shot image generation"},{"task_slug":"3d-anomaly-detection-and-segmentation","task_name":"3D Anomaly Detection and Segmentation"},{"task_slug":"3d-face-reconstruction","task_name":"3D Face Reconstruction"},{"task_slug":"articles","task_name":"Articles"},{"task_slug":"automated-theorem-proving","task_name":"Automated Theorem Proving"},{"task_slug":"deepfake-detection","task_name":"DeepFake Detection"},{"task_slug":"face-swapping","task_name":"Face Swapping"},{"task_slug":"informativeness","task_name":"Informativeness"},{"task_slug":"object-detection","task_name":"Object Detection"},{"task_slug":"object-tracking","task_name":"Object Tracking"},{"task_slug":"shadow-removal","task_name":"Shadow Removal"},{"task_slug":"style-transfer","task_name":"Style Transfer"},{"task_slug":"text-to-image-generation","task_name":"Text-to-Image Generation"},{"task_slug":"unconditional-video-generation","task_name":"Unconditional Video Generation"},{"task_slug":"unsupervised-domain-adaptation","task_name":"Unsupervised Domain Adaptation"},{"task_slug":"video-object-detection","task_name":"Video Object Detection"},{"task_slug":"weakly-supervised-semantic-segmentation","task_name":"Weakly-Supervised Semantic Segmentation"},{"task_slug":"zero-shot-3d-point-cloud-classification","task_name":"Zero-shot 3D Point Cloud Classification"}],"methods":[{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":"20 Easy Tricks to Reach Frontier Support Instantly"},{"method_slug":null,"method_name":"20 Quick and Simple Ways to Contact Frontier Support Anytime"},{"method_slug":null,"method_name":"20 Rapid Contact Options for Direct Assistance from Frontier"},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":"5 Ways to Pay Your Spectrum Bill Fast&Free by Phone Call: 5 Quick and Easy"},{"method_slug":null,"method_name":"6 Fast Methods to Access Skyscanner Support"},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":"Comment annuler un billet Etihad sans stress"},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":"Don’t Get Stuck"},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":"Exp.com"},{"method_slug":null,"method_name":"Fast, Live Support"},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":"Human in Seconds"},{"method_slug":null,"method_name":"James David"},{"method_slug":null,"method_name":"Live Support Now"},{"method_slug":null,"method_name":"Liya56"},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":"Props 3D Model"},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":"Quickbooks"},{"method_slug":null,"method_name":"Real Person"},{"method_slug":null,"method_name":"Roobinhood"},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":"STOP the Frustration"},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":"Skip the Bots"},{"method_slug":null,"method_name":"Sp5derHoodiecom"},{"method_slug":null,"method_name":"TAP Air Portugal Support By Phone and Email: Your Complete Guide to Hassle-Free Contact"},{"method_slug":null,"method_name":"TRON"},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":"TrimIQ Dragons Den UK"},{"method_slug":null,"method_name":"TrimIQ UK Review - TrimIQ Customer Reviews | TrimIQ Testimonials."},{"method_slug":null,"method_name":"Trust Wallet"},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":"[[booked on Expedia]]What is a fully refundable ticket on Expedia"},{"method_slug":null,"method_name":"asdcfv"},{"method_slug":null,"method_name":"asfsfs"},{"method_slug":null,"method_name":"contactar con el servicio de atención al cliente de Expedia"},{"method_slug":null,"method_name":"de contactar con el servicio de atención al cliente de Delta"},{"method_slug":null,"method_name":"el servicio de atención al cliente de Aeroméxico"},{"method_slug":null,"method_name":"for Immediate Human"},{"method_slug":null,"method_name":"for Instant Human"},{"method_slug":null,"method_name":"hammondindustries"},{"method_slug":null,"method_name":"https://paperswithcode.com/method/8-easy-options-to-connect-with-booking-com"},{"method_slug":null,"method_name":"official Expedia"},{"method_slug":null,"method_name":"qswdefg"},{"method_slug":null,"method_name":"sdgdgzsd"},{"method_slug":null,"method_name":"test\">"},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null},{"method_slug":null,"method_name":null}],"datasets_introduced":[{"slug":"squad","name":"SQuAD","full_name":"Stanford Question Answering Dataset"}],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}