The Al-Olofi Seven-Band Hierarchical Brain Model (A7–HBM–ΩΦ) Unveils Sleep Microstate Dynamics Through Oscillatory–Geometric Simulation

The Al-Olofi Seven-Band Hierarchical Brain Model (A7–HBM–ΩΦ) Unveils Sleep Microstate Dynamics Through Oscillatory–Geometric Simulation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article The Al-Olofi Seven-Band Hierarchical Brain Model (A7–HBM–ΩΦ) Unveils Sleep Microstate Dynamics Through Oscillatory–Geometric Simulation Yazeed Mohammed Al-Olofi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8291042/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study applies Al‑Olofi Seven‑Band Hierarchical Brain Model) A7–HBM–ΩΦ( neurogeometric framework to simulate sleep microstates and integrate recent empirical findings from twelve independent studies (2025). The model comprises 28 neural attractors distributed across seven oscillatory layers (δ, θ, α, σ, β, γ, Ω), each associated with specific geometric primitives and dynamical properties. Using a system of coupled nonlinear Stuart–Landau oscillators, phase–amplitude coupling (PAC) is evaluated as the primary regulator of microstate transitions. Simulation results reproduce experimentally observed δ–γ, θ–γ, and δ–β coupling patterns and reveal fine-grained microstate structures consistent with recent EEG/MEG findings (Noh et al., 2025 ; Burlando et al., 2025 ; Niethard, 2025 ). Integration with twelve 2025 studies demonstrates that oscillatory dynamics, cortical geometry, and cognitive function are unified under the A7–HBM–ΩΦ framework, suggesting that the cortex operates as a multi-band geometric computer, generating cognition through lawful transformations of oscillatory–geometric states. These insights may inform the development of neurotechnology applications, sleep disorder diagnostics, and targeted cognitive interventions, highlighting the model’s potential translational impact. Computational Neuroscience A7–HBM–ΩΦ hierarchical brain model neurogeometry sleep microstates phase–amplitude coupling (PAC) cross-frequency coupling (CFC) neural attractors geometric attractors oscillatory–geometric computation multi-band cortical hierarchy sleep architecture computational neuroscience neurodynamic simulation nonlinear oscillators Stuart–Landau networks Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8291042","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":556032359,"identity":"d6e25781-fce4-42d9-9205-7b02fda4eaf6","order_by":0,"name":"Yazeed Mohammed 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(A7–HBM–ΩΦ) Unveils Sleep Microstate Dynamics Through Oscillatory–Geometric Simulation\u003c/strong\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"A7–HBM–ΩΦ, hierarchical brain model, neurogeometry, sleep microstates, phase–amplitude coupling (PAC), cross-frequency coupling (CFC), neural attractors, geometric attractors, oscillatory–geometric computation, multi-band cortical hierarchy, sleep architecture, computational neuroscience, neurodynamic simulation, nonlinear oscillators, Stuart–Landau networks","lastPublishedDoi":"10.21203/rs.3.rs-8291042/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8291042/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study applies Al‑Olofi Seven‑Band Hierarchical Brain Model) A7\u0026ndash;HBM\u0026ndash;ΩΦ( neurogeometric framework to simulate sleep microstates and integrate recent empirical findings from twelve independent studies (2025). The model comprises 28 neural attractors distributed across seven oscillatory layers (δ, θ, α, σ, β, γ, Ω), each associated with specific geometric primitives and dynamical properties. Using a system of coupled nonlinear Stuart\u0026ndash;Landau oscillators, phase\u0026ndash;amplitude coupling (PAC) is evaluated as the primary regulator of microstate transitions.\u003c/p\u003e\u003cp\u003eSimulation results reproduce experimentally observed δ\u0026ndash;γ, θ\u0026ndash;γ, and δ\u0026ndash;β coupling patterns and reveal fine-grained microstate structures consistent with recent EEG/MEG findings (Noh et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Burlando et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Niethard, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Integration with twelve 2025 studies demonstrates that oscillatory dynamics, cortical geometry, and cognitive function are unified under the A7\u0026ndash;HBM\u0026ndash;ΩΦ framework, suggesting that the cortex operates as a multi-band geometric computer, generating cognition through lawful transformations of oscillatory\u0026ndash;geometric states.\u003c/p\u003e\u003cp\u003eThese insights may inform the development of neurotechnology applications, sleep disorder diagnostics, and targeted cognitive interventions, highlighting the model\u0026rsquo;s potential translational impact.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e","manuscriptTitle":"The Al-Olofi Seven-Band Hierarchical Brain Model (A7–HBM–ΩΦ) Unveils Sleep Microstate Dynamics Through Oscillatory–Geometric Simulation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-10 08:48:28","doi":"10.21203/rs.3.rs-8291042/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"d0fd7b2c-fe5f-4f47-9c8d-d10ad6bed5ba","owner":[],"postedDate":"December 10th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":59183557,"name":"Computational Neuroscience"}],"tags":[],"updatedAt":"2025-12-10T08:48:28+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-10 08:48:28","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8291042","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8291042","identity":"rs-8291042","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}