[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82500-en":3,"doc-seo-82500-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82500,687197100911,"Himbo","https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1782698725881665579",8,"Research & Report","Radial Interaction Tomography Recognizing Non-Transitive Evolutionary Games from One Range-Expansion Image","Colored sectors in microbial range expansion encode more than lineage survival counts. The work formulates a computer-vision inverse problem that reconstructs a radius-indexed pairwise boundary-flow field from a single endpoint image of an accretive multi-type expansion. It tests whether the extracted geometric signal from sector-boundary curves in log-polar coordinates matches a transitive scalar fitness hierarchy or reveals cyclic non-potential flows. Rigorous endpoint observability and stability are proved for frozen fronts, with exact cyclicity testing and Bonferroni-valid interval scanning, supported by deterministic benchmarks and an implementation for active design control via cyclic residuals.","arXiv :2607 .00378v 1 [ cs .CV] 1 Jul 2026  \nRadial Interaction Tomography:  \nRecognizing Non-Transitive Evolutionary Games from One  \nRange-Expansion Image  \nFaruk Alpay∗ Barış Başaran  \nDepartment of Computer Engineering, Bahçeşehir University, Istanbul, Türkiye {faruk.alpay, [baris.basaran}@bahcesehir.edu.tr](baris.basaran}@bahcesehir.edu.tr)  \nAbstract  \nColored sectors in a microbial range expansion encode more than lineage survival counts. We formulate a computer-vision inverse problem: from one endpoint image of an accretive multi-type expansion, recover the radius-indexed pairwise boundary-flow field and test whether the visual pattern is compatible with a transitive scalar fitness hierarchy. The observable is a geometric signal extracted from sector-boundary curves in log-polar coordinates. We prove endpoint observability and stability for frozen fronts, weighted transitive/cyclic decomposition, contact-complete circular design, physical-clock and mechanism non-identifiability, exact Gaussian cyclicity testing, and Bonferroni-valid interval scanning. The benchmark is deterministic:  \nanalytic endpoint images, blurred/noisy pixel round trips, scalar-null stress tests, public-image tracing, multi-resolution mechanistic endpoints, and a non-learning frozen-front simulator. The implementation recovers pairwise edge-flow histories from endpoint images, detects cyclic residuals in a mechanistic four-type expansion, and uses those residuals as forcing signals for a dimensionless active design-control layer covering reaction-diffusion control, phenotype-frontier optimization, protocol synthesis, Monte Carlo robustness, and a downstream population-state bridge.  \n1 Introduction  \nRange-expansion images are a rare case where a final two-dimensional pattern can retain chronological information. In frontier-limited microbial colonies, cells behind the expanding front are approximately frozen, so radius can order material deposition. Prior work exploited this fact to estimate constant relative fitness from sector geometry and to model stochastic boundary wandering [5, 4, 11] . That line of work leaves a harder visual question open: what can one endpoint image say when competition is not a scalar hierarchy?  \nThis paper treats the endpoint colony as a pattern-recognition object. A multi-type sector image induces a visible genotype-contact graph. Each contact boundary is a curve, and the derivative of its unwrapped angle with respect to a deposition coordinate is an oriented pairwise boundary flow. A scalar fitness model constrains these flows to be gradients on the contact graph. Local antagonism, bacteriocin-mediated competition, or cyclic dominance can create non-potential flows, i.e. directed cycle signatures that no scalar ordering can explain [2, 3] .  \nThe main image-level result is a recoverable pairwise-flow history on observed contacts, with uncertainty, in deposition time. Physical time, unobserved pair interactions, isolated front speeds,  \n∗ Corresponding author: [alpay@lightcap.ai](alpay@lightcap.ai)  \nand microscopic mechanism require additional measurements. Separating the geometric observable from those downstream interpretations makes the visual recognition claim falsifiable.  \nContributions.  \n• We formulate radial interaction tomography: a classical computer-vision inverse problem for recognizing radius-indexed transitive and cyclic interaction patterns from one endpoint image.  \n• We separate the observable edge-flow field from biological interpretations, preventing the common but invalid jump from sector geometry to isolated front speed or mechanism.  \n• We give a contact-design theorem: a four-type complete pairwise game requires at least eight circular boundaries in one plate, not six.  \n• We implement a deterministic benchmark with analytic images, pixel-level recovery, scalar-null stress tests, exact cyclicity tests, multi-resolution endpoint tracing, public-image provenance auditing, and mechanistic frozen","cbCaitTy4b2rmMCB","https://ap.wps.com/l/cbCaitTy4b2rmMCB","pdf",1369178,1,17,"English","en",105,"# Abstract\n# Introduction\n# Related work\n## Range-expansion image geometry\n## Local competition is not isolated speed\n## Non-transitive microbial competition\n## Classical vision","[{\"question\":\"What information does a single microbial range-expansion endpoint image contain?\",\"answer\":\"The endpoint image preserves a geometric signal in the sector-boundary curves that can be converted into a radius-indexed pairwise boundary-flow description.\"},{\"question\":\"How does the method determine whether the underlying interaction is transitive or non-transitive?\",\"answer\":\"The approach tests compatibility with a transitive scalar fitness hierarchy by extracting an oriented boundary-flow field and checking for cyclic, non-potential flow signatures.\"},{\"question\":\"What guarantees or validation does the paper provide for the inverse reconstruction?\",\"answer\":\"It proves endpoint observability and stability for frozen fronts, includes exact cyclicity testing, and uses Bonferroni-valid interval scanning within deterministic analytic and benchmark simulations.\"}]",1784180956,43,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"radial-interaction-tomography-recognizing-non-transitive-evolutionary-games-from-one-range-expansion-image","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/radial-interaction-tomography-recognizing-non-transitive-evolutionary-games-from-one-range-expansion-image/82500/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What information does a single microbial range-expansion endpoint image contain?","Question",{"text":75,"@type":76},"The endpoint image preserves a geometric signal in the sector-boundary curves that can be converted into a radius-indexed pairwise boundary-flow description.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the method determine whether the underlying interaction is transitive or non-transitive?",{"text":80,"@type":76},"The approach tests compatibility with a transitive scalar fitness hierarchy by extracting an oriented boundary-flow field and checking for cyclic, non-potential flow signatures.",{"name":82,"@type":73,"acceptedAnswer":83},"What guarantees or validation does the paper provide for the inverse reconstruction?",{"text":84,"@type":76},"It proves endpoint observability and stability for frozen fronts, includes exact cyclicity testing, and uses Bonferroni-valid interval scanning within deterministic analytic and benchmark 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