research
Wavelet Analysis & Feature Resolution
Background Fourier transform fails with non-stationary signals because it lacks time localization. Wavelet analysis solves this by using scalable, …
Mathematical Models
| No. | Category | Sub-topic | Core Question |
|---|---|---|---|
| 1-1 | Modeling Paradigm & Dynamics | Multi-Physics Field Coupling | How to collaboratively model energy exchange between microscopic particles and macroscopic fluids? |
| 1-2 | Modeling Paradigm & Dynamics | Stochastic Dynamics & Risk Quantification | With highly uncertain environmental parameters, how can stochastic mathematics predict the probability of system evolution? |
| 1-3 | Modeling Paradigm & Dynamics | Chaotic Evolution in Complex Systems | How do tiny deviations in initial conditions cause long-term prediction failure, and what is the underlying topological mathematical structure? |
| 2-1 | Discrete Structure & Logic | Topological Robustness in Complex Networks | How does discrete graph theory define the fragility and self-healing capacity of global distribution networks? |
| 2-2 | Discrete Structure & Logic | Combinatorial Optimization & NP-Hardness | When search spaces grow exponentially, how can mathematical structures help algorithms find approximate global optima? |
| 2-3 | Discrete Structure & Logic | Logic Algebra & Formal Verification | How does predicate logic transform into the safety verification cornerstone for autonomous driving or kernel design? |
| 3-1 | Dynamic Control & Hybrid Systems | Stability Analysis of Switching Systems | When a physical system switches between multiple operating modes, how do you ensure continuous trajectories do not diverge? |
| 3-2 | Dynamic Control & Hybrid Systems | Impulsive Control & Non-Continuous Scheduling | How can high-frequency non-continuous control commands achieve minimum-error coverage of precise continuous motion? |
| 3-3 | Dynamic Control & Hybrid Systems | Collaborative Modeling in Hybrid Automation | What is the mathematical coordination mechanism of AI discrete decisions and physical continuous execution in hybrid dynamic systems? |
| 4-1 | Signal Processing & Frequency Domain | Quantum Reconstruction of Signal Processing | How can quantum algorithms reduce the complexity of traditional digital signal processing from polynomial to logarithmic order? |
| 4-2 | Signal Processing & Frequency Domain | Wavelet Analysis & Feature Resolution | For non-stationary signals, how can variable-step translation achieve ultra-precise capture of local information? |
| 4-3 | Signal Processing & Frequency Domain | Compressive Sensing & Information Sparsity | How to break the Nyquist sampling theorem and reconstruct complete high-dimensional information from very few observations? |
Technology
AI Agent Discrimination: Hidden Ethical Bottom Lines in the Algorithmic World
Who is Intercepted Outside the Intent Chain? Under the AaaS (Agent-as-a-Service) model, AIOS is not just a scheduler but also a rule-maker. When a …
Technology
Birth of a Planetary Operating System: An AIOS Kernel Beyond Borders
A Unified Digital Base As AI Agents begin to take over global supply chains, traffic scheduling, and energy distribution, we no longer need hundreds …
Technology
Collapse of Consensus in the Post-Truth Era: When All Information is 'Generated for You'
The Disappearance of Objective Truth In the era of traditional media, although bias existed, humans shared a "base of objective facts." In …
Technology
Computing Power is Currency: The Settlement Logic of Hard Currency in the AIOS Era
The Weights and Measures of Intellectual Labor In the industrial age, energy (oil/electricity) was the underlying currency; in the mobile Internet …
Technology
Digital Totalitarianism and Code as Law: The Boundaries of Algorithmic Mandates
Compulsory “Soft Constraints” In the physical world, the execution of laws allows for middle grounds and elasticity. However, in the …
Technology
Energy-Based Global Governance: Computing Output as the New National Credit
From Gold Standard to Compute Standard In the 20th century, gold and the USD were the credit foundations of global governance. By the mid-21st …
Technology
Fusion of Biological and Silicon Intelligence: The Ultimate Form of AIOS
The Handshake of Carbon and Silicon Over the past decade, we have always treated AI as an external tool. But in the ultimate vision of AIOS, this …
Technology
Intellectual Equality: When Professional Knowledge is No Longer a Class Moat
The Regression of Knowledge Premiums For thousands of years in human civilization, the differentiation of classes depended heavily on the monopoly of …
Technology
Intellectual Property in the AI Era: Who Owns 'Synthetic Intelligence'?
The Vacuum Zone of Law The current legal system is built on the foundation of "humans as the sole creator." When AI Agents, under the …