#harmonic analysis
25 related articles
·3 min
Graduate Student Proves Quantum Uncertainty Principle on Fractals: A Breakthrough Bridging Fourier Analysis and Geometry
A graduate student proved the quantum uncertainty principle on fractals, establishing quantitative constraints between function concentration on fractal sets and Fourier transforms, opening new research directions.
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The Mathematical Physics of Rainbows a…
·4 min
The Mathematical Physics of Rainbows and Glories: From Geometric Optics to Complex Angular Momentum Theory
An in-depth analysis of the mathematical physics behind rainbows and glories, from Descartes' geometric optics and Airy function wave theory to complex angular momentum scattering theory.
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·5 min
The AI Agent Security Crisis: Why Generators Cannot Also Be Validators
Based on real data from Snyk's 4,800 enterprise customers, a deep analysis of three AI agent security pain points: automated attacks, untrusted outputs, and governance blind spots.
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·4 min
How to Write the Research Design for a Machine Learning Paper? A Detailed Guide Using Player Churn Prediction as an Example
How to define research design in ML papers? Using mobile game player churn prediction as an example, this guide details mixed-methods comparative empirical study positioning, covering CRISP-DM, quantitative evaluation, and SHAP interpretability analysis.
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·2 min
A Game With No Assets: Generating All Graphics and Sound Effects in Real-Time Using Sine Waves
Indie developer Zanzlanz built a game with zero asset files—all textures and sounds are generated in real-time using sine wave math functions. Exploring the tech behind procedural generation.
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·3 min
Walk on Decomposed Subdomains: A Mesh-Free Approach to Accelerating Monte Carlo PDE Solvers
Deep dive into Walk on Decomposed Subdomains, exploring how subdomain decomposition accelerates Monte Carlo PDE solving and improves WoS convergence in complex geometries.
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·2 min
Mathematics Under AI's Impact: A Mathematician's Late-Night Self-Reflection
When AI starts proving theorems, how do mathematicians view their own value? Exploring the existential anxiety AI brings to mathematics and the future of human-AI collaboration.
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·3 min
Maxwell Conjecture Disproven: GPT Produces Counterexample That Shakes the Math World
GPT 5.6 allegedly constructed a counterexample disproving the long-standing Maxwell Conjecture. We analyze the conjecture, what the AI counterexample means, and the math community's cautious response.
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·3 min
AI Synthetic Choreography Experiment: Full Workflow for Music Video Creation with Midjourney + Uisato Studio
Deep dive into the Humannequins AI synthetic choreography project, exploring the Midjourney v8.1 and Uisato Studio Music Video Pro workflow for independent creators producing professional music videos.
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·3 min
U.S. Ban on Chinese Humanoid Robots: A New Front in the AI Race
Analysis of the U.S. ban on Chinese humanoid robots: data security concerns, industrial protection motives, and how the AI race extends into Physical AI and robotics hardware.
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·3 min
U.S. Ban Targets Chinese Humanoid Robots: A New Front in the AI Race
Analysis of the U.S. ban on Chinese humanoid robots: data security concerns, industrial protection motives, and how the AI race extends into Physical AI and robotics hardware.
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·3 min
The Enigma of Harmony: Can Music Be Fully Explained by Scientific Theory?
Exploring the scientific foundations of musical harmony: from overtone physics and mathematical frequency ratios to auditory perception, examining why certain note combinations please the ear and the ambitions and limits of scientific music theory.
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Terence Tao on AI and Mathematics: For…
·4 min
Terence Tao on AI and Mathematics: Formal Proofs, Human-AI Collaboration, and the Road Ahead
Fields Medalist Terence Tao analyzes AI's impact on math research, discussing LLM-assisted proofs, Lean formal verification, large-scale collaboration, and the future of math education in the AI era.
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·3 min
AI Is Conquering World-Class Math Conjectures — Will Mathematicians Become "Curators"?
AI is cracking world-class math conjectures at scale — from IMO gold medals to the Langlands Program. Terence Tao says math has entered a "proof abundance" era, but AI can't judge research significance. The mathematician's edge is shifting from proving to curating.
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·3 min
Terence Tao: AI Will Take Over Much of Mathematicians' Work Within a Decade — But That's Not the Core of Mathematics
Fields Medalist Terence Tao on AI and mathematics: within a decade, AI will handle much of mathematicians' routine work — but that work was never the core of the discipline.
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·2 min
The Tritone Paradox: How the Same Sound Can Be Heard in Completely Opposite Ways
Diana Deutsch's Tritone Paradox proves that identical sounds can be heard in opposite ways. Explore the acoustics of Shepard Tones, why perception varies by culture, and what this means for AI.
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Frieve Vinyl: How Microscopic Physical…
·3 min
Frieve Vinyl: How Microscopic Physical Simulation Recreates the Mechanics of a Vinyl Stylus
Frieve Vinyl digitally recreates vinyl playback through microscopic stylus/groove physics simulation. Explore stylus geometry, contact mechanics, and tracking distortion.
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Terrence Tao on AI Coding Agents: How …
·2 min
Terrence Tao on AI Coding Agents: How a Mathematician Sees the Transformation of App Development
Fields Medalist Terry Tao shares his experience with AI coding agents—rebuilding legacy apps and rapidly building new tools. A mathematician's view on their capabilities and impact.
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·4 min
DIY Robot Lamp Full-Body Motion Test: A Firsthand Account from Components to Coordinated Movement
A maker builds a DIY robot lamp with Robstride actuators, completing its first full-body joint motion test. This article breaks down hardware selection, trajectory planning, PID tuning, and more.
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·7 min
1X Unveils NEO Robotic Hand: 25 DoF Tendon-Driven Design Ushers Dexterous Hands into the Mass-Production Era
1X unveils a new robotic hand for its NEO humanoid: 25 DoF, tendon-driven quasi-direct-drive architecture, full-joint force control, tactile skin, IP68 waterproofing, and compliant safety design, with capacity for 10,000 units a year.
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