research
Impulsive Control & Non-continuous Scheduling
Background In many systems, control is applied as instantaneous impulses rather than continuous forces. Impulsive control explores how to stabilize a …
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? |
Interaction
Interaction after Brain-Computer Interface (BCI): Will 'Zero-Latency' Transmission of Intent Change Human Self-Awareness?
The Ultimate Bandwidth: Transcending Language and Gestures From GUI to LUI, interaction has always been dedicated to reducing the signal-to-noise …
research
Logic Algebra & Formal Verification
Background In safety-critical systems, testing cannot prove the absence of errors. Formal verification uses mathematical proofs to guarantee that a …
Interaction
Multimodal Fusion: Why Concurrent Interaction is the Real 'Natural Interaction'?
Blind Men and an Elephant: Limitations of Single-Modality Interaction In traditional GUIs, interaction is extremely “narrow-band”—you …
research
Quantum Reconstruction of Signal Processing
Background Traditional Discrete Fourier Transform (DFT) faces complexity limits with massive data. Quantum Fourier Transform (QFT) leverages quantum …
Interaction
Reverse Interaction: When AI Becomes the Active Party, How to Define the Boundary Between 'Interruption' and 'Suggestion'?
The Inversion of Interaction Polarity Since the birth of computing, interaction has always followed the passive logic of "human issues command …
research
Stability Analysis of Switching Systems
Background Switching systems consist of a set of continuous-time subsystems and a logic rule governing the switching between them. Integrating …
research
Stochastic Dynamics & Risk Quantification
Background Real-world dynamical systems are constantly subject to noise—atmospheric turbulence, financial shocks, biological thermal noise. Stochastic …
Interaction
The Anthropomorphism Paradox: Why Does Human Defense Increase as Interaction Bebecomes More Human-like?
The Return of the Uncanny Valley In early HCI, anthropomorphism was seen as a silver bullet for lowering barriers to entry. We gave AI human names and …
research
Topological Robustness in Complex Networks
Background From the internet to power grids and shipping networks, our world relies on complex networks. Topological robustness theory quantifies a …