Category Archives: Graduate School

White Paper: Experimental Verification and Theoretical Modeling of the Logistics of Quantum Entanglement

Posted on September 22, 2025 by nathanalbright

Executive Summary Quantum entanglement remains one of the most profound and counterintuitive features of quantum mechanics, enabling correlations between particles that defy classical explanation. Its verification requires rigorous experimental frameworks, while its explanation requires theoretical models that balance mathematical precision, … Continue reading →

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White Paper: When Beloved Works Are Rejected: Authors, Audiences, and the Tension of Reception

Posted on September 21, 2025 by nathanalbright

Abstract Many artists face the paradox of finding their most personally meaningful works dismissed, misunderstood, or rejected by their audiences. This white paper examines this phenomenon through two case studies: Budd Schulberg’s What Makes Sammy Run?—which portrays the disillusionment of … Continue reading →

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White Paper: The Psychological Implications of Young Adult and Teen Protagonists as Saviors in YA Literature

Posted on September 21, 2025 by nathanalbright

Executive Summary Young Adult (YA) literature—particularly dystopian and fantasy works—frequently casts adolescent or teenage protagonists as society’s last hope. From Katniss Everdeen in The Hunger Games to Harry Potter in Harry Potter, this narrative choice has shaped generations of readers. … Continue reading →

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White Paper: How Ancient “Para-” Languages Illuminate Language Development and Relationships

Posted on September 18, 2025 by nathanalbright

Case studies: para-Munda (South Asia) and Para-Mongolic (Inner Asia) Abstract Scholars sometimes label ancient, poorly attested (or fully unattested) languages that are inferred from substratal effects or fragmentary records with the prefix “para-”: languages that are typologically or historically close … Continue reading →

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White Paper: AI-Centered Approaches to the Preservation, Study, and Instruction of Smaller and Vulnerable Languages in Developed Countries

Posted on September 18, 2025 by nathanalbright

Executive Summary Smaller and vulnerable languages in developed nations—including Indigenous tongues, minority immigrant languages, and regional dialects—are threatened by declining intergenerational transmission, urbanization, and the dominance of global lingua francas. Traditional preservation efforts, while valuable, are often underfunded, fragmented, and … Continue reading →

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White Paper: Maximizing Effectiveness and Minimizing Repetition in Homeschool Curricula

Posted on September 7, 2025 by nathanalbright

Executive Summary Homeschooling offers unparalleled flexibility, but its success hinges on curriculum design. An effective homeschool curriculum avoids unnecessary repetition while ensuring mastery, integrates subjects across disciplines, and balances individualized pacing with systematic coverage. This paper evaluates major approaches to … Continue reading →

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White Paper: Hostility Toward Critique and Its Implications for Scholarly Discourse

Posted on September 6, 2025 by nathanalbright

Executive Summary In recent years, public and academic culture has shown a heightened sensitivity to critique. Increasingly, individuals perceive criticism not as a form of engagement or improvement, but as an attempt to silence or delegitimize them. This shift undermines … Continue reading →

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Project Plan: “Endogenous vs. Exogenous Stimulation: How Uric Acid and Caffeine-Like Compounds Modulate Human Energy”

Posted on August 31, 2025 by nathanalbright

Specific Aims Quantify the acute and short-term effects of caffeine and caffeine-like compounds (paraxanthine, theacrine, theobromine) on objective and subjective energy. (Adenosine A1/A2A antagonism is the canonical mechanism for caffeine.  ) Test whether altering circulating uric acid (UA) levels changes … Continue reading →

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White Paper: Practical Applications of Algebra as a Basis for Instruction

Posted on August 30, 2025 by nathanalbright

Executive Summary Algebra is often perceived by students as abstract and detached from real-world concerns. Yet, algebra provides the foundational tools needed for problem-solving in science, engineering, economics, and daily decision-making. This white paper explores the practical applications of algebra … Continue reading →

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Theorem (square-gcd count, closed form)

Posted on August 26, 2025 by nathanalbright

For a positive integer n, let A_2(n):=\#\{\,1\le k\le n:\ \gcd(k,n)\ \text{is a perfect square}\,\}. Then A_2(n)\;=\;\sum_{d^2\mid n}\varphi\!\left(\frac{n}{d^2}\right) \;=\;\prod_{p^{\alpha}\parallel n}\frac{p^{\alpha+1}-(-1)^{\alpha+1}}{p+1}, where \varphi is Euler’s totient function and the product runs over the prime powers p^\alpha dividing n exactly. Explanation. We are … Continue reading →

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