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The Cost of Protection with Slowed Circulation: Long-Term Vitality Traded for Short-Term Stability

A common pattern is emerging across multiple institutional sectors, including universities and research institutions. Policymakers and administrators are increasingly debating how to retain the valuable skills of senior talent approaching retirement. In the short term, such protective measures are effective: they enhance stability, preserve accumulated experience, and delay the loss of expertise. Over time, however, less visible costs accumulate. Talent turnover declines, entry pathways for younger scholars narrow, innovation slows, and institutions gradually trade long-term vitality for short-term stability. The current debate surrounding the role of distinguished professors over the age of 65 exemplifies this broader structural problem. It is often framed as an ethical dispute or an issue of age discrimination. In reality, it is neither. At its core, this is a question of system design—how a national research ecosystem balances protection with circulation. One point must be stated cl...
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Comparison of Contemporary Large Language Models

This blog presents a concise structural comparison of five prominent large language models: GPT, Claude, Gemini, LLaMA, and xAI. Although all are built on  Transformer -based foundations, they differ markedly in mathematical design, alignment strategy, training dynamics, and multimodal architecture. GPT (OpenAI) follows a scaling-law paradigm using a Transformer backbone enhanced by  s parse Mixture-of-Experts  layers. Claude (Anthropic) preserves the same basic architecture but introduces  Constitutional  AI, an alignment method that incorporates explicit behavioral constraints. Gemini (Google) adopts a unified  multimodal  Transformer that represents text, images, audio, and video within a single token sequence.   LLaMA ( Meta AI ) emphasizes dense (non-MoE) Transformer scaling and data efficiency, prioritizing compute-optimal training and architectural simplicity. xAI's Grok retains the Transformer form but is trained on a non-stationary, con...
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Effective PDE Coefficients for Electrical Tissue Property Imaging

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In this blog, I discuss how the effective (or homgenized) coefficient of the elliptic partial differential equation \(\sum_{i=1}^3 \partial_i \big( a_{ij}\,\partial_j u \big) = 0\) in a body arises in the context of electrical tissue property imaging, where \(u\) denotes the electrical potential. In brief, bioimpedance is directly linked to this coefficient, and several companies , such as  InBody  and  Sciospec , are actively developing bioimpedance-based devices. This blog is based on the book *Electromagnetic Tissue Properties MRI* (Imperial College Press) written by Jin Keun Seo, Eung Je Woo, Ulrich Katscher, and Yi Wang.  The mathematical model for electrical tissue property imaging is derived from an appropriate reduction of Maxwell’s equations. In the time-harmonic regime, the electric field \( \mathbf{E} \), current density \( \mathbf{J} \), magnetic field \( \mathbf{H} \), and magnetic flux density \( \mathbf{B} \) satisfy the following relations: ...
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Practical Vector Calculus for the AI Era

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This blog presents undergraduate-level vector calculus with examples and perspectives drawn from artificial intelligence. It was created in response to the limitations of many existing calculus textbooks in addressing the conceptual demands of this rapidly evolving field. Before we begin, it is important to clarify how the variable \(\mathbf{x}\) will be used throughout the text. In classical calculus, the variable \(\mathbf{x}\)  typically denotes a physical coordinate, such as position in space. In deep learning, however, \(\mathbf{x}\) often represents a token or a feature vector that encodes complex structures, including language, images, or speech. This shift reflects a transition from modeling physical space to modeling abstract, high-dimensional data spaces. 1. Vectors Vectors  are mathematical entities characterized by both magnitude and direction. They are essential for describing physical quantities such as blood flow velocity, forces acting on joints, an...
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