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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>MLKN.lab — Multi-Layered Knowledge Network</title>
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<meta name="keywords" content="metascience, science of science, computational epistemology, network science, systems science, interdisciplinary research, interdisciplinarity, knowledge network, hierarchy, complex systems, research mapping, knowledge diffusion, cognitive science, human-machine interaction, human-ai interaction, unified theory of knowledge, graph topology, multilayer networks, hypergraphs, semantic web, collective intelligence, data science, knowledge graph, knowledge network graph, data visualization, interactive visualization, scientometrics, bibliometrics, polyhierarchy, epistemology, ontology, taxonomy, knowledge organization systems, scholarly knowledge graph, OpenAlex, SKOS, Frascati Classification, FAIR principles, D3.js, Python, NetworkX, open science, open source, open data, open education">
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<!-- Top Navigation Bar (a unified version) -->
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<a>Home</a>
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<li><a href="research/research.html">Research Focus</a></li>
<li><a href="model/model.html">MLKN.model</a></li>
<li><a href="model/model-mathematical-foundations.html">Mathematical Foundations</a></li>
<li><a href="method/method.html">Method</a></li>
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<a>Knowledge Network</a>
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<li><a href="polyhierarchy/polyhierarchy.html">Polyhierarchy</a></li>
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<li><a href="data/data.html">Data</a></li>
</ul>
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<li class="has-dropdown">
<a>Knowledge Library</a>
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<li><a href="references/references.html">Scientific References</a></li>
<li><a href="monographs/monographs.html">Open Access Monographs</a></li>
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<p class="hero-eyebrow">MLKN.lab — Multi-Layered Knowledge Network Ideas Laboratory</p>
<h1 class="hero-title" id="hero-title"><em>MLKN.lab</em></h1>
<p class="hero-subtitle">
A <strong>computational metascience platform</strong> mapping the <strong>structural topology of human knowledge</strong>
through a <strong>polyhierarchical, data-driven framework</strong>.
</p>
<!-- Stats with Colored Circles -->
<div class="hero-stats">
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<div class="hstat-num">6</div>
<div class="hstat-lbl">Core Domains</div>
</div>
<div>
<div class="stat-circle" style="background: #4A90E2;"></div>
<div class="hstat-num">25</div>
<div class="hstat-lbl">Disciplines</div>
</div>
<div>
<div class="stat-circle" style="background: #50C878;"></div>
<div class="hstat-num">235</div>
<div class="hstat-lbl">Subdisciplines</div>
</div>
<div>
<div class="stat-circle" style="background: #FFD700;"></div>
<div class="hstat-num">320K+</div>
<div class="hstat-lbl">Connections</div>
</div>
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Select any node subtitle below to see an overview. Follow the corresponding arrow to open the dedicated page.
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<h3 class="nav-grid-case-title">Knowledge Network</h3>
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<a href="#polyhierarchy">Polyhierarchy</a>
</div>
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<a href="polyhierarchy/polyhierarchy.html" class="nav-arrow" aria-label="Go to Polyhierarchy page">↗</a>
</div>
</li>
<li>
<div class="text-container">
<a href="#hypergraph">MLKN.hypergraph</a>
</div>
<div class="arrow-container">
<a href="knowledge_network/MLKN-hypergraph.html" class="nav-arrow" aria-label="Go to MLKN.hypergraph page">↗</a>
</div>
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<li>
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<a href="#data">Data</a>
</div>
<div class="arrow-container">
<a href="data/data.html" class="nav-arrow" aria-label="Go to Data page">↗</a>
</div>
</li>
</ul>
</div>
<!-- Case 4: Knowledge Library (Middle Right) -->
<div class="nav-grid-case">
<h3 class="nav-grid-case-title">Knowledge Library</h3>
<ul class="nav-grid-list">
<li>
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</div>
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<a href="#normativereferences">Normative References</a>
</div>
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<a href="normative_references/normative-references.html" class="nav-arrow" aria-label="Go to Normative References page">↗</a>
</div>
</li>
</ul>
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<h3 class="nav-grid-case-title">Applications</h3>
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<br>
</section>
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<a href="#research">Research</a>
<a href="#model">MLKN.model</a>
<a href="#mathematical-foundations">Mathematical Foundations</a>
<a href="#method">Method</a>
<a href="#polyhierarchy">Polyhierarchy</a>
<a href="#hypergraph">MLKN.hypergraph</a>
<a href="#data">Data</a>
<a href="#references">Scientific References</a>
<a href="#monographs">Open Access Monographs</a>
<a href="#applications">Applications</a>
<a href="#essays">Essays & Explorations</a>
<a href="#about">About</a>
<a href="#inspirations">Inspirations</a>
<a href="#normative">Normative Foundations</a>
</div>
<br>
</section>
<!-- Website Overview -->
<section id="overview" class="section" aria-labelledby="overview-title">
<br>
<h2 class="sec-h" id="overview-title">Overview</h2>
<p class="sec-sub">A Polyhierarchical Framework for Computational Epistemology</p>
<p>
MLKN.lab is a <strong>computational metascience initiative</strong> dedicated to <strong>mapping, modeling, and quantifying</strong>
the <strong>epistemic topology of global scientific discovery</strong>. By treating knowledge as a
<strong>dynamic, multi-layered hypergraph</strong>, we reveal hidden structures, bridges, and gaps across disciplines—
enabling researchers to <strong>navigate, analyze, and predict</strong> the evolution of science itself.
</p>
<br>
<p>
Built from <strong>bibliometric analysis of large-scale scholarly metadata</strong> (OpenAlex, Scopus, MeSH, IEEE Thesaurus),
MLKN.lab operationalizes a <strong>polyhierarchical framework</strong> across:
</p>
<ul class="discipline-list" style="margin-top: 15px;">
<li><span class="discipline-square" style="background: #1A6BAA;"></span> <strong>5 Ontological Layers</strong> (Core Domains → Concepts).</li>
<li><span class="discipline-square" style="background: #2ECC71;"></span> <strong>6 Epistemological Core Domains</strong> (Formal Sciences, Natural Sciences, etc.).</li>
<li><span class="discipline-square" style="background: #FF6347;"></span> <strong>25 Academic Disciplines</strong> (e.g., Computer Science, Neuroscience).</li>
<li><span class="discipline-square" style="background: #9B59B6;"></span> <strong>235 Subdisciplines</strong> (e.g., AI, Cognitive Psychology).</li>
<li><span class="discipline-square" style="background: #F39C12;"></span> <strong>320K+ Interdisciplinary Connections</strong>.</li>
</ul>
<p style="margin-top: 20px;">
MLKN.lab is <strong>multifaceted</strong>, operating as:
</p>
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<div class="layer-card">
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<h3>Research Platform</h3>
<p>A <strong>living laboratory</strong> for testing hypotheses about the <strong>evolution of science</strong>.</p>
</div>
<div class="layer-card">
<div class="licon" style="color: #2ECC71;">⬢</div>
<h3>Scientific Instrument</h3>
<p>A <strong>high-precision tool</strong> for <strong>graph-theoretic analysis</strong> of knowledge networks.</p>
</div>
<div class="layer-card">
<div class="licon" style="color: #FF6347;">⬢</div>
<h3>Cognitive Interface</h3>
<p>A <strong>generative system</strong> to <strong>augment human reasoning</strong> through interactive knowledge maps.</p>
</div>
</div>
<br>
<p style="margin-top: 20px;">
Built for <strong>Research</strong>, <strong>Meta-Science</strong>, and <strong>Education</strong>.
</p>
<br>
<div class="chips" style="margin-top: 15px;">
<span class="chip" style="color:#9B59B6;border-color:#9B59B655">Knowledge Layers</span>
<span class="chip" style="color:#FF6347;border-color:#FF634755">Core Domains</span>
<span class="chip" style="color:#4A90E2;border-color:#4A90E255">Academic Disciplines</span>
<span class="chip" style="color:#50C878;border-color:#50C87855">Subdisciplines</span>
<span class="chip" style="color:#FFD700;border-color:#FFD70055">Connections</span>
</div>
<div class="chips" style="margin-top: 15px;">
<span class="chip" style="color:#9B59B6;border-color:#9B59B655">Data-Driven</span>
<span class="chip" style="color:#FF6347;border-color:#FF634755">Bibliometric</span>
<span class="chip" style="color:#4A90E2;border-color:#4A90E255">Polyhierarchical</span>
<span class="chip" style="color:#50C878;border-color:#50C87855">Multi-layered</span>
<span class="chip" style="color:#FFD700;border-color:#FFD70055">Multifaceted</span>
</div>
<div class="chips" style="margin-top: 15px;">
<span class="chip" style="color:#9B59B6;border-color:#9B59B655">Research Platform</span>
<span class="chip" style="color:#FF6347;border-color:#FF634755">Scientific Instrument</span>
<span class="chip" style="color:#4A90E2;border-color:#4A90E255">Cognitive Interface</span>
</div>
<div class="chips" style="margin-top: 15px;">
<span class="chip" style="color:#9B59B6;border-color:#9B59B655">Research</span>
<span class="chip" style="color:#FF6347;border-color:#FF634755">Metascience</span>
<span class="chip" style="color:#4A90E2;border-color:#4A90E255">Education</span>
</div>
<p style="margin-top: 20px; text-align: center;">
<a href="about/about.html" class="btn btn-s">
<i class="fas fa-info-circle"></i> Learn More About MLKN.lab
</a>
</p>
</section>
<section id="impact" class="section" aria-labelledby="impact-title">
<br>
<h2 class="sec-h" id="impact-title">Scientific Impact</h2>
<p class="sec-sub">Why MLKN.lab Matters for Research, Education, and Policy</p>
<p>
MLKN.lab is more than a tool—it’s a <strong>paradigm shift</strong> in how we understand and interact with knowledge.
Our framework enables <strong>groundbreaking applications</strong> across disciplines:
</p>
<div class="layers-grid" style="margin-top: 20px;">
<div class="layer-card">
<div class="licon" style="color: #1A6BAA;">⬢</div>
<h3>For Researchers</h3>
<p>Uncover <strong>hidden connections</strong> between disciplines, identify <strong>emerging fields</strong>, and test <strong>metascience hypotheses</strong>.</p>
<p style="margin-top: 10px; font-size: 0.9em;">
<strong>Example:</strong> How does interdisciplinarity impact citation networks?
</p>
</div>
<div class="layer-card">
<div class="licon" style="color: #2ECC71;">⬢</div>
<h3>For Educators</h3>
<p>Design <strong>interdisciplinary curricula</strong> and <strong>adaptive learning paths</strong> using MLKN.lab’s knowledge maps.</p>
<p style="margin-top: 10px; font-size: 0.9em;">
<strong>Example:</strong> Bridging Computer Science and Cognitive Psychology.
</p>
</div>
<div class="layer-card">
<div class="licon" style="color: #FF6347;">⬢</div>
<h3>For Policymakers</h3>
<p>Inform <strong>science policy</strong> by visualizing <strong>gaps, silos, and opportunities</strong> in research.</p>
<p style="margin-top: 10px; font-size: 0.9em;">
<strong>Example:</strong> Identifying underfunded interdisciplinary areas.
</p>
</div>
<div class="layer-card">
<div class="licon" style="color: #FFD700;">⬢</div>
<h3>For AI Developers</h3>
<p>Enhance <strong>AI reasoning</strong> with structured knowledge networks from MLKN.hypergraph.</p>
<p style="margin-top: 10px; font-size: 0.9em;">
<strong>Example:</strong> Grounding LLMs in scientific knowledge.
</p>
</div>
</div>
</section>
<section id="insights" class="section" aria-labelledby="insights-title">
<h2 class="sec-h" id="insights-title">Featured Insights</h2>
<p class="sec-sub">Discover the Hidden Patterns of Scientific Knowledge</p>
<!-- Conteneur "Featured" avec contenu centré -->
<div class="featured">
<div class="featured-content">
<p class="feat-eyebrow">★ Featured — Knowledge Diffusion</p>
<h3 class="feat-title">How Ideas Spread Across Disciplines</h3>
<p class="feat-desc">
Our analysis of <strong>320K+ connections</strong> reveals how concepts like <strong>"Transformers"</strong>
diffuse from AI to neuroscience, linguistics, and beyond.
</p>
</div>
<div class="feat-icon">
<svg viewBox="0 0 40 40" fill="none" stroke="currentColor" stroke-width="1.8" stroke-linecap="round">
<circle cx="20" cy="5" r="3"/><circle cx="5" cy="32" r="3"/><circle cx="35" cy="32" r="3"/>
<circle cx="20" cy="20" r="3"/><circle cx="20" cy="35" r="3"/>
<line x1="20" y1="8" x2="20" y2="17"/><line x1="8" y1="30" x2="17" y2="22"/>
<line x1="32" y1="30" x2="23" y2="22"/><line x1="7" y1="32" x2="33" y2="32"/>
<line x1="20" y1="5" x2="5" y2="32"/><line x1="20" y1="5" x2="35" y2="32"/>
<line x1="20" y1="35" x2="5" y2="32"/><line x1="20" y1="35" x2="35" y2="32"/>
</svg>
</div>
<a href="knowledge_network/MLKN-hypergraph.html" class="btn btn-p">
<i class="fas fa-project-diagram"></i> Explore the MLKN.hypergraph
</a>
</div>
<!-- Image avec légende -->
<div class="featured-image">
<img src="assets/images/mlkn-hypergraph-preview.png" alt="MLKN.lab Knowledge Network Preview: MLKN.hypergraph" width="100%">
<p class="featured-caption">
<em>Figure 1: Static preview of the Interactive visualization MLKN.hypergraph mapping knowledge topology across 25 disciplines and 5 ontological layers.</em><br>
</p>
</div>
</section>
<!-- Research Focus Section (First Section After Hero) -->
<section id="research" class="section" aria-labelledby="research-title">
<br>
<h2 class="sec-h" id="research-title">Research Focus</h2>
<p class="sec-sub">A Polyhierarchical Framework for Computational, Cognitive, and Interdisciplinary Research</p>
<!-- Navigation boxes for this section -->
<div class="nav-box">
<a href="#overview">Overview</a>
<a href="#research" class="active">Research</a>
<a href="#model">MLKN.model</a>
<a href="#mathematical-foundations">Mathematical Foundations</a>
<a href="#method">Method</a>
<a href="#polyhierarchy">Polyhierarchy</a>
<a href="#hypergraph">MLKN.hypergraph</a>
<a href="#data">Data</a>
<a href="#references">Scientific References</a>
<a href="#monographs">Open Access Monographs</a>
<a href="#applications">Applications</a>
<a href="#essays">Essays & Explorations</a>
<a href="#about">About</a>
<a href="#inspirations">Inspirations</a>
<a href="#normative">Normative Foundations</a>
</div>
<br>
<p>
Discover the research focus. These include the research foundations, research methods, research nexuses, and research applications.
</p>
<div class="chips">
<a href="research/research.html" class="chip" style="color:#1A6BAA;border-color:#1A6BAA55">Research Foundations</a>
<a href="research/research.html" class="chip" style="color:#4A90E2;border-color:#4A90E255">Research Methods</a>
<a href="research/research.html" class="chip" style="color:#50C878;border-color:#50C87855">Research Nexuses</a>
<a href="research/research.html" class="chip" style="color:#50C878;border-color:#50C87855">Research Applications</a>
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<br>
<div class="layers-grid" style="margin-top: 20px;">
<!-- Research Foundations -->
<div class="layer-card">
<div class="licon" style="color: #1A6BAA;">⬢</div>
<h3>Research Foundations</h3>
<p>The theoretical and philosophical underpinnings of MLKN-lab.</p>
<p style="margin-top: 10px; font-size: 0.9em;">
<div class="chips" style="margin-top: 10px;">
<span class="chip" style="color:#9B59B6;border-color:#9B59B655">Metascience</span>
<span class="chip" style="color:#1A6BAA;border-color:#1A6BAA55">Computational Epistemology</span>
<span class="chip" style="color:#E74C3C;border-color:#3498DB55">Network Science</span>
<span class="chip" style="color:#F39C12;border-color:#F39C1255">Systems Science</span>
<span class="chip" style="color:#2ECC71;border-color:#2ECC7155">Interdisciplinary Research</span>
<span class="chip" style="color:#E74C3C;border-color:#E74C3C55">Cognitive Science</span>
</div>
</p>
</div>
<!-- Research Methods -->
<div class="layer-card">
<div class="licon" style="color: #2ECC71;">⬢</div>
<h3>Research Methods</h3>
<p>The analytical and computational approaches driving MLKN-lab.</p>
<p style="margin-top: 10px; font-size: 0.9em;">
<div class="chips" style="margin-top: 10px;">
<span class="chip" style="color:#2ECC71;border-color:#2ECC7155">Interdisciplinary Research</span>
<span class="chip" style="color:#3498DB;border-color:#3498DB55">Network Science</span>
<span class="chip" style="color:#F39C12;border-color:#F39C1255">Systems Science</span>
<span class="chip" style="color:#FF6347;border-color:#FF634755">Graph Topology</span>
<span class="chip" style="color:#50C878;border-color:#50C87855">Semantic Research</span>
<span class="chip" style="color:#0A7E8C;border-color:#0A7E8C55">Data Science</span>
</div>
</p>
</div>
<!-- Research Nexuses -->
<div class="layer-card">
<div class="licon" style="color: #FF6347;">⬢</div>
<h3>Research Nexuses</h3>
<p>Convergent Hotspots of Innovation and Exploration.</p>
<p style="margin-top: 10px; font-size: 0.9em;">
<div class="chips" style="margin-top: 10px;">
<span class="chip" style="color:#3498DB;border-color:#3498DB55">Neuro-Cognitive-Computer Science Nexus</span>
<span class="chip" style="color:#50C878;border-color:#50C87855">Philosophy-Computer Science Nexus</span>
<span class="chip" style="color:#FF6347;border-color:#FF634755">AI Ethics Nexus</span>
<span class="chip" style="color:#9B59B6;border-color:#9B59B655">Eco-Neuro-Anthropology Nexus</span>
<span class="chip" style="color:#50C878;border-color:#50C87855">Techno-Ethical-Sustainability Nexus</span>
<span class="chip" style="color:#F39C12;border-color:#F39C1255">Adaptive Learning Nexus</span>
</div>
</p>
</div>
<!-- Research Applications -->
<div class="layer-card">
<div class="licon" style="color: #FFD700;">⬢</div>
<h3>Research Applications</h3>
<p>Practical implementations of MLKN-lab across domains.</p>
<p style="margin-top: 10px; font-size: 0.9em;">
<div class="chips" style="margin-top: 10px;">
<span class="chip" style="color:#FFD700;border-color:#FFD70055">Computational Research</span>
<span class="chip" style="color:#D35400;border-color:#D3540055">Systems Engineering</span>
<span class="chip" style="color:#8E44AD;border-color:#8E44AD55">Education</span>
<span class="chip" style="color:#1ABC9C;border-color:#1ABC9C55">Policy & Ethics</span>
</div>
</p>
</div>
</div>
<p style="margin-top: 20px; text-align: center;">
<a href="research/research.html" class="btn btn-s">
<i class="fas fa-microscope"></i> Explore Research Focus in Depth
</a>
</p>
</section>
<!-- MLKN.model Section -->
<section id="model" class="section" aria-labelledby="model-title">
<br>
<h2 class="sec-h" id="model-title">MLKN.model</h2>
<p class="sec-sub">The Computational Epistemology Engine</p>
<!-- Navigation boxes for this section -->
<div class="nav-box">
<a href="#overview">Overview</a>
<a href="#research">Research</a>
<a href="#model" class="active">MLKN.model</a>
<a href="#mathematical-foundations">Mathematical Foundations</a>
<a href="#method">Method</a>
<a href="#polyhierarchy">Polyhierarchy</a>
<a href="#hypergraph">MLKN.hypergraph</a>
<a href="#data">Data</a>
<a href="#references">Scientific References</a>
<a href="#monographs">Open Access Monographs</a>
<a href="#applications">Applications</a>
<a href="#essays">Essays & Explorations</a>
<a href="#about">About</a>
<a href="#inspirations">Inspirations</a>
<a href="#normative">Normative Foundations</a>
</div>
<br>
<p>
<strong>MLKN.model</strong> is the <strong>mathematical and computational heart</strong> of MLKN.lab.
It treats scientific knowledge as a <strong>dynamic, multi-layered hypergraph</strong> \( \mathcal{H} \),
enabling <strong>rigorous analysis, simulation, and prediction</strong> of how disciplines evolve, connect, and diffuse.
</p>
<p>
Just as physics engines simulate the behavior of physical systems,
<strong>MLKN.model simulates the behavior of knowledge systems</strong>—
revealing hidden patterns, testing hypotheses, and enabling breakthroughs in
<strong>metascience, AI, and interdisciplinary research</strong>.
</p>
<div class="layers-grid" style="margin-top: 20px;">
<div class="layer-card">
<div class="licon" style="color: #1A6BAA;">⬢</div>
<h3>Theoretical Foundations</h3>
<p>
Built on <strong>unified theories of cognition, network science, systems theory, and computational epistemology</strong>.
Models knowledge as a <strong>computational system</strong> where structure can be analyzed and optimized.
</p>
</div>
<div class="layer-card">
<div class="licon" style="color: #2ECC71;">⬢</div>
<h3>Mathematical Formalization</h3>
<p>
Formalizes knowledge as a <strong>multilayer hypergraph</strong> \( \mathcal{H} = (V, \mathcal{S}, \mathcal{P}, \mathcal{T}, \omega, \tau) \),
with <strong>5 ontological layers</strong> (Core Domains → Concepts) and <strong>hyperedges</strong> for cross-disciplinary connections.
</p>
</div>
<div class="layer-card">
<div class="licon" style="color: #FF6347;">⬢</div>
<h3>Architecture</h3>
<p>
Organized into <strong>3 core layers</strong>:
<strong>Knowledge Representation</strong> (polyhierarchy),
<strong>Network Analysis</strong> (graph theory, TDA),
<strong>Dynamic Simulation</strong> (random walks, GNNs).
</p>
</div>
</div>
<p style="margin-top: 20px; text-align: center;">
<a href="model/model.html" class="btn btn-s">
<i class="fas fa-cog"></i> Explore MLKN.model in Depth
</a>
</p>
</section>
<!-- MLKN.model Mathematical Foundations Section -->
<section id="mathematical-foundations" class="section" aria-labelledby="math-title">
<br>
<h2 class="sec-h" id="math-title">MLKN.model - Mathematical Foundations</h2>
<p class="sec-sub">The Rigor Behind MLKN.model</p>
<!-- Navigation boxes for this section -->
<div class="nav-box">
<a href="#overview">Overview</a>
<a href="#research">Research</a>
<a href="#model">MLKN.model</a>
<a href="#mathematical-foundations" class="active">Mathematical Foundations</a>
<a href="#method">Method</a>
<a href="#polyhierarchy">Polyhierarchy</a>
<a href="#hypergraph">MLKN.hypergraph</a>
<a href="#data">Data</a>
<a href="#references">Scientific References</a>
<a href="#monographs">Open Access Monographs</a>
<a href="#applications">Applications</a>
<a href="#essays">Essays & Explorations</a>
<a href="#about">About</a>
<a href="#inspirations">Inspirations</a>
<a href="#normative">Normative Foundations</a>
</div>
<br>
<p>
The <strong>mathematical backbone</strong> of MLKN.model is a <strong>multilayer hypergraph</strong>
\( \mathcal{H} = (V, \mathcal{S}, \mathcal{P}, \mathcal{T}, \omega, \tau) \),
where knowledge is formalized as a <strong>dynamic, multi-layered network</strong>.
This framework enables <strong>rigorous analysis, simulation, and prediction</strong> of scientific structures.
</p>
<div class="layers-grid" style="margin-top: 20px;">
<div class="layer-card">
<div class="licon" style="color: #1A6BAA;">⬢</div>
<h3>Formal Definition</h3>
<p>
A <strong>multilayer hypergraph</strong> where:
<ul class="discipline-list" style="margin-top: 10px;">
<li><span class="discipline-square" style="background: #1A6BAA;"></span> <strong>\( V \)</strong>: Nodes (Core Domains → Concepts).</li>
<li><span class="discipline-square" style="background: #1A6BAA;"></span> <strong>\( \mathcal{S} \)</strong>: Hyperedges (cross-disciplinary connections).</li>
<li><span class="discipline-square" style="background: #1A6BAA;"></span> <strong>\( \mathcal{P} \)</strong>: 5 ontological layers.</li>
<li><span class="discipline-square" style="background: #1A6BAA;"></span> <strong>\( \mathcal{T} \)</strong>: Hierarchical edges (adjacent layers).</li>
<li><span class="discipline-square" style="background: #1A6BAA;"></span> <strong>\( \omega \)</strong>: Weights (e.g., citations, semantic similarity).</li>
<li><span class="discipline-square" style="background: #1A6BAA;"></span> <strong>\( \tau \)</strong>: Temporal function (evolution over time).</li>
</ul>
</p>
</div>
<div class="layer-card">
<div class="licon" style="color: #2ECC71;">⬢</div>
<h3>Key Properties</h3>
<p>
The framework is:
<ul class="discipline-list" style="margin-top: 10px;">
<li><span class="discipline-square" style="background: #2ECC71;"></span> <strong>Multilayer</strong>: 5 ontological layers (Core Domains → Concepts).</li>
<li><span class="discipline-square" style="background: #2ECC71;"></span> <strong>Polyhierarchical</strong>: Nodes can have multiple parents.</li>
<li><span class="discipline-square" style="background: #2ECC71;"></span> <strong>Dynamic</strong>: Tracks evolution via \( \tau \) and \( \mathbf{T}_{\mathcal{H}} \).</li>
</ul>
</p>
</div>
<div class="layer-card">
<div class="licon" style="color: #FF6347;">⬢</div>
<h3>Mathematical Tools</h3>
<p>
Supports:
<ul class="discipline-list" style="margin-top: 10px;">
<li><span class="discipline-square" style="background: #FF6347;"></span> Graph theory (adjacency, Laplacian matrices).</li>
<li><span class="discipline-square" style="background: #FF6347;"></span> Topological Data Analysis (persistent homology).</li>
<li><span class="discipline-square" style="background: #FF6347;"></span> Optimal Transport (Wasserstein distance).</li>
</ul>
</p>
</div>
</div>
<p style="margin-top: 20px; text-align: center;">
<a href="model/model-mathematical-foundations.html" class="btn btn-s">
<i class="fas fa-square-root-alt"></i> Explore MLKN.model - Mathematical Foundations in Depth
</a>
</p>
</section>
<!-- Method Section -->
<section id="method" class="section" aria-labelledby="method-title">
<br>
<h2 class="sec-h" id="method-title">Method</h2>
<p class="sec-sub">How MLKN.lab was built: Data, Classification, and Validation</p>
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<a href="#overview">Overview</a>
<a href="#research">Research</a>
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<a href="#mathematical-foundations">Mathematical Foundations</a>
<a href="#method" class="active">Method</a>
<a href="#polyhierarchy">Polyhierarchy</a>
<a href="#hypergraph">MLKN.hypergraph</a>
<a href="#data">Data</a>
<a href="#references">Scientific References</a>
<a href="#monographs">Open Access Monographs</a>
<a href="#applications">Applications</a>
<a href="#essays">Essays & Explorations</a>
<a href="#about">About</a>
<a href="#inspirations">Inspirations</a>
<a href="#normative">Normative Foundations</a>
</div>
<br>
<p>
All the methods are available below. These include the data source, classification logic, network construction and validation.
</p>
<div class="chips">
<a href="method/method.html" class="chip" style="color:#1A6BAA;border-color:#1A6BAA55">Data Source</a>
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<a href="method/method.html" class="chip" style="color:#FFD700;border-color:#FFD70055">Validation</a>
</div>
<br>
<div class="layers-grid">
<div class="layer-card">
<div class="licon"><i class="fas fa-chart-bar" style="color: #2C3E50;"></i></div>
<h3>Data Sources</h3>
<p>We use <strong>OpenAlex</strong> as our primary data source, supplemented by <strong>Scopus, MeSH, and IEEE Thesaurus</strong> for thematic and conceptual mappings.</p>
</div>
<div class="layer-card">
<div class="licon"><i class="fas fa-tags" style="color: #2C3E50;"></i></div>
<h3>Classification Logic</h3>
<p>Disciplines and subdisciplines are classified using <strong>OECD Frascati Manual</strong> and <strong>UNESCO Fields of Science</strong>, ensuring alignment with global standards.</p>
</div>
<div class="layer-card">
<div class="licon"><i class="fas fa-network-wired" style="color: #2C3E50;"></i></div>
<h3>Network Construction</h3>
<p>We map <strong>connections between disciplines</strong> using <strong>co-occurrence analysis</strong> and <strong>citation networks</strong> to reveal interdisciplinary links.</p>
</div>
<div class="layer-card">
<div class="licon"><i class="fas fa-check-circle" style="color: #2C3E50;"></i></div>
<h3>Validation</h3>
<p>Our hierarchy is validated through <strong>network metrics</strong> (e.g., centrality, modularity) and <strong>expert review</strong> to ensure accuracy.</p>
</div>
</div>
<p style="margin-top: 20px; text-align: center;">
<a href="method/method.html" class="btn btn-s">
<i class="fas fa-square-root-alt"></i> Explore Method in Depth
</a>
</p>
</section>
<!-- Polyhierarchy Section -->
<section id="polyhierarchy" class="section" aria-labelledby="polyhierarchy-title">
<br>
<h2 class="sec-h" id="polyhierarchy-title">Polyhierarchy</h2>
<p class="sec-sub">A polyhierarchical framework of 6 Core Domains, 25 Disciplines, and 235 Subdisciplines</p>
<!-- Navigation boxes for this section -->
<div class="nav-box">
<a href="#overview">Overview</a>
<a href="#research">Research</a>
<a href="#model">MLKN.model</a>
<a href="#mathematical-foundations">Mathematical Foundations</a>
<a href="#method">Method</a>
<a href="#polyhierarchy" class="active">Polyhierarchy</a>
<a href="#hypergraph">MLKN.hypergraph</a>
<a href="#data">Data</a>
<a href="#references">Scientific References</a>
<a href="#monographs">Open Access Monographs</a>
<a href="#applications">Applications</a>
<a href="#essays">Essays & Explorations</a>
<a href="#about">About</a>
<a href="#inspirations">Inspirations</a>
<a href="#normative">Normative Foundations</a>
</div>
<br>
<p>
Explore the description of the hierarchy. These include the ontological layers, epistemological core domains, the academic disciplines, the subdisciplines, the topics, and the concepts.
</p>
<div class="chips">
<a href="hierarchy/hierarchy.html" class="chip" style="color:#1A6BAA;border-color:#1A6BAA55">Ontological Layers</a>
<a href="hierarchy/hierarchy.html" class="chip" style="color:#4A90E2;border-color:#4A90E255">Epistemological Core Domains</a>
<a href="hierarchy/hierarchy.html" class="chip" style="color:#50C878;border-color:#50C87855">Academic Disciplines</a>
<a href="hierarchy/hierarchy.html" class="chip" style="color:#FFD700;border-color:#FFD70055">Subdisciplines</a>
</div>
<!-- Ontological Layers -->
<h3 class="sec-h" style="margin-top: 30px;">Ontological Layers</h3>
<p class="sec-sub">5 Ontological Layers</p>
<div class="layers-grid">
<div class="layer-card">
<div class="licon">⬡</div>
<h3>Core Discipline Domains</h3>
<p><strong>Layer 1</strong> embraces 6 Core Domains: Engineering & Technology, Formal Sciences, Natural Sciences, Health & Medical Sciences, Social Sciences & Humanities.</p>
</div>
<div class="layer-card">
<div class="licon">⬢</div>
<h3>Academic Disciplines</h3>
<p><strong>Layer 2</strong> comprises 25 Academic Disciplines as distinct clusters, organized into their respective Core Domains.</p>
</div>
<div class="layer-card">
<div class="licon">◈</div>
<h3>Academic Subdisciplines</h3>
<p><strong>Layer 3</strong> represents 235 specialized subfields within each discipline (e.g., AI within Computer Science).</p>
</div>
<div class="layer-card">
<div class="licon">◎</div>
<h3>Core Thematic Domains</h3>
<p><strong>Layer 4</strong> contains thematic clusters within subdisciplines (e.g., Machine Learning within AI).</p>
</div>
<div class="layer-card">
<div class="licon">⚡</div>
<h3>Main Thematics</h3>
<p><strong>Layer 5</strong> includes fundamental thematics and concepts (e.g., Supervised Learning within Machine Learning).</p>
</div>
</div>
<p style="margin-top: 20px; text-align: center;">
<a href="polihierarchy/polyhierarchy.html" class="btn btn-s">
<i class="fas fa-square-root-alt"></i> Explore Polyhierarchy in Depth
</a>
</p>
</section>
<!-- MLKN.hypergraph Section -->
<section id="hypergraph" class="section" aria-labelledby="hypergraph-title">
<br>
<h2 class="sec-h" id="hypergraph-title">MLKN.hypergraph</h2>
<p class="sec-sub">Interdisciplinary Knowledge Networks</p>
<!-- Navigation boxes for this section -->
<div class="nav-box">
<a href="#overview">Overview</a>
<a href="#research">Research</a>
<a href="#model">MLKN.model</a>
<a href="#mathematical-foundations">Mathematical Foundations</a>
<a href="#method">Method</a>
<a href="#polyhierarchy">Polyhierarchy</a>
<a href="#hypergraph" class="active">MLKN.hypergraph</a>
<a href="#data">Data</a>
<a href="#references">Scientific References</a>
<a href="#monographs">Open Access Monographs</a>
<a href="#applications">Applications</a>