arXiv subjects

Jiajun Yan

Publications and source records attributed to Jiajun Yan.

4 recordsLinked to original sources

arXiv2026

A Dynamical Framework for the McKay Correspondence via Gauge-Theoretic Morse Flow

The McKay correspondence establishes a bijection between the cohomology of a minimal resolution and the irreducible representations of a finite subgroup $\Gamma \subset \text{SU}(2)$. While traditional proofs rely on static algebraic isomorphisms, we propose a dynamical framework grounded in gauge theory and Morse-Bott theory. We analyze an $S^1$-invariant Morse-Bott function on the minimal resolution, interpreting its gradient flow lines as $1$-parameter families of holonomy representations of flat connections from $\Gamma$ to $GL(R)$. We conjecture that the flow emanating from a critical submanifold converges asymptotically at the boundary to a specific irreducible representation of $\Gamma$. This dynamical process explicitly constructs the identification between the cohomology basis and the irreducible representations of $\Gamma$ prescribed by the McKay correspondence. We prove this conjecture for cyclic cases.

math.DG↗

arXiv2025

BlinkBud: Detecting Hazards from Behind via Sampled Monocular 3D Detection on a Single Earbud

Failing to be aware of speeding vehicles approaching from behind poses a huge threat to the road safety of pedestrians and cyclists. In this paper, we propose BlinkBud, which utilizes a single earbud and a paired phone to online detect hazardous objects approaching from behind of a user. The core idea is to accurately track visually identified objects utilizing a small number of sampled camera images taken from the earbud. To minimize the power consumption of the earbud and the phone while guaranteeing the best tracking accuracy, a novel 3D object tracking algorithm is devised, integrating both a Kalman filter based trajectory estimation scheme and an optimal image sampling strategy based on reinforcement learning. Moreover, the impact of constant user head movements on the tracking accuracy is significantly eliminated by leveraging the estimated pitch and yaw angles to correct the object depth estimation and align the camera coordinate system to the user's body coordinate system, respectively. We implement a prototype BlinkBud system and conduct extensive real-world experiments. Results show that BlinkBud is lightweight with ultra-low mean power consumptions of 29.8 mW and 702.6 mW on the earbud and smartphone, respectively, and can accurately detect hazards with a low average false positive ratio (FPR) and false negative ratio (FNR) of 4.90% and 1.47%, respectively.

cs.CV↗

arXiv2025

A simulation-heuristics dual-process model for intuitive physics

The role of mental simulation in human physical reasoning is widely acknowledged, but whether it is employed across scenarios with varying simulation costs and where its boundary lies remains unclear. Using a pouring-marble task, our human study revealed two distinct error patterns when predicting pouring angles, differentiated by simulation time. While mental simulation accurately captured human judgments in simpler scenarios, a linear heuristic model better matched human predictions when simulation time exceeded a certain boundary. Motivated by these observations, we propose a dual-process framework, Simulation-Heuristics Model (SHM), where intuitive physics employs simulation for short-time simulation but switches to heuristics when simulation becomes costly. By integrating computational methods previously viewed as separate into a unified model, SHM quantitatively captures their switching mechanism. The SHM aligns more precisely with human behavior and demonstrates consistent predictive performance across diverse scenarios, advancing our understanding of the adaptive nature of intuitive physical reasoning.

physics.ed-ph↗

arXiv2023

A New Gauge-Theoretic Construction of 4-Dimensional Hyperk\"ahler ALE Spaces

Non-compact hyperk\"ahler spaces arise frequently in gauge theory. The 4-dimensional hyperk\"ahler ALE spaces are a special class of non-compact hyperk\"ahler spaces. They are in one-to-one correspondence with the finite subgroups of SU(2) and have interesting connections with representation theory and singularity theory, captured by the McKay Correspondence. The 4-dimensional hyperk\"ahler ALE spaces are first classified by Peter Kronheimer via a finite-dimensional hyperk\"ahler reduction. In this paper, we give a new gauge-theoretic construction of these spaces. More specifically, we realize each 4-dimensional hyperk\"ahler ALE space as a moduli space of solutions to a system of equations for a pair consisting of a connection and a section of a vector bundle over an orbifold Riemann surface, modulo a gauge group action. The construction given in this paper parallels Kronheimer's original construction and hence can also be thought of as a gauge-theoretic interpretation of Kronheimer's construction of these spaces.

math.DG↗