Selected work

Representative Papers

Formalization of Amicable Numbers Theory

Jan 12, 2026

This work presents the first complete formalization of amicable number theory in Lean 4, addressing a longstanding gap in formal proof systems. It introduces rigorous definitions of proper divisors, the sum-of-divisors function, and amicable pairs, and formally verifies Thābit’s formula, Euler’s generalization, and—novelly—the Borho–Hoffmann multiplication method, the latter constituting its first machine-checked proof. The development extends to sociable and betrothed numbers, culminating in a modular 2,076-line codebase comprising 139 theorems. Leveraging tactics such as zify and ring, the framework supports reasoning about divisor sums, multiplicativity, and coprimality, enabling the verification of Poulet’s fifth-order sociable cycle, classical amicable pairs, and a lower bound (>10⁶⁵) for coprime amicable pairs. The library is structured for seamless integration into Mathlib.

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Zebrafish Counting Using Event Stream Data

Apr 18, 2025

To address the challenges of manual counting of zebrafish—owing to their small size—and the low accuracy and poor robustness of existing methods in dense, small-object scenarios, this paper pioneers the integration of event cameras into automated zebrafish counting. Our approach comprises camera calibration, multi-frame event image fusion, motion trajectory reconstruction, and sliding-time-window statistics, augmented by trajectory modeling and ceiling-based decision making to enable real-time, low-complexity counting at high temporal resolution. We conduct 100 independent trials in a 4-L tank containing 20 zebrafish; the method achieves a mean counting accuracy of 97.95%, significantly outperforming conventional frame-based imaging approaches. This work establishes a novel paradigm for dynamic counting of microscopic biological organisms, offering high precision, strong robustness against occlusion and motion blur, and practical deployability in laboratory settings.

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PNE-SGAN: Probabilistic NDT-Enhanced Semantic Graph Attention Network for LiDAR Loop Closure Detection

Apr 11, 2025

LiDAR-based loop closure detection (LCD) in SLAM suffers from insufficient robustness and accuracy under dynamic objects, sensor noise, and viewpoint variations. To address this, we propose a spatiotemporal graph neural network framework that jointly exploits geometric and semantic cues. Specifically, we introduce the NDT covariance matrix as a discriminative geometric node feature—a novel design enabling robust geometric representation. We further construct a semantic graph and model its structural dependencies using a Graph Attention Network (GAT). Additionally, we develop a probabilistic temporal similarity model grounded in Hidden Markov Models (HMMs) and Bayesian filtering, enhanced with forward–backward smoothing to mitigate loop ambiguity. Evaluated on KITTI sequences 00 and 08, our method achieves mean average precision of 96.2% and 95.1%, respectively—outperforming state-of-the-art approaches, particularly in challenging bidirectional loop scenarios.

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Recent publications

Latest Papers

Formalization of Amicable Numbers Theory

Jan 12, 2026

This work presents the first complete formalization of amicable number theory in Lean 4, addressing a longstanding gap in formal proof systems. It introduces rigorous definitions of proper divisors, the sum-of-divisors function, and amicable pairs, and formally verifies Thābit’s formula, Euler’s generalization, and—novelly—the Borho–Hoffmann multiplication method, the latter constituting its first machine-checked proof. The development extends to sociable and betrothed numbers, culminating in a modular 2,076-line codebase comprising 139 theorems. Leveraging tactics such as zify and ring, the framework supports reasoning about divisor sums, multiplicativity, and coprimality, enabling the verification of Poulet’s fifth-order sociable cycle, classical amicable pairs, and a lower bound (>10⁶⁵) for coprime amicable pairs. The library is structured for seamless integration into Mathlib.

0 citationsRead paper

Zebrafish Counting Using Event Stream Data

Apr 18, 2025

To address the challenges of manual counting of zebrafish—owing to their small size—and the low accuracy and poor robustness of existing methods in dense, small-object scenarios, this paper pioneers the integration of event cameras into automated zebrafish counting. Our approach comprises camera calibration, multi-frame event image fusion, motion trajectory reconstruction, and sliding-time-window statistics, augmented by trajectory modeling and ceiling-based decision making to enable real-time, low-complexity counting at high temporal resolution. We conduct 100 independent trials in a 4-L tank containing 20 zebrafish; the method achieves a mean counting accuracy of 97.95%, significantly outperforming conventional frame-based imaging approaches. This work establishes a novel paradigm for dynamic counting of microscopic biological organisms, offering high precision, strong robustness against occlusion and motion blur, and practical deployability in laboratory settings.

0 citationsRead paper

PNE-SGAN: Probabilistic NDT-Enhanced Semantic Graph Attention Network for LiDAR Loop Closure Detection

Apr 11, 2025

LiDAR-based loop closure detection (LCD) in SLAM suffers from insufficient robustness and accuracy under dynamic objects, sensor noise, and viewpoint variations. To address this, we propose a spatiotemporal graph neural network framework that jointly exploits geometric and semantic cues. Specifically, we introduce the NDT covariance matrix as a discriminative geometric node feature—a novel design enabling robust geometric representation. We further construct a semantic graph and model its structural dependencies using a Graph Attention Network (GAT). Additionally, we develop a probabilistic temporal similarity model grounded in Hidden Markov Models (HMMs) and Bayesian filtering, enhanced with forward–backward smoothing to mitigate loop ambiguity. Evaluated on KITTI sequences 00 and 08, our method achieves mean average precision of 96.2% and 95.1%, respectively—outperforming state-of-the-art approaches, particularly in challenging bidirectional loop scenarios.

0 citationsRead paper