arXiv subjects

Hongjin Wu

Publications and source records attributed to Hongjin Wu.

5 recordsLinked to original sources

arXiv2025

Benign nonconvexity of synchronization landscape induced by graph skeletons

We study the homogeneous Kuramoto model on a graph and the associated nonconvex optimization problem $\min_{\boldsymbol{\theta}\in\mathbb{R}^n}-\frac12\sum_{1\leq i,j\leq n}A_{ij}\cos(\theta_i-\theta_j)$. The objective defines an energy over configurations of points on the unit circle and serves as a Lyapunov potential for the dynamics. We prove that every connected quasi-threshold graph is second-order globally synchronizing: every second-order stationary point is a global minimizer corresponding to full synchronization. Consequently, the dynamics converge to full synchronization from almost every initial condition. These graphs are precisely the comparability graphs of partially ordered sets induced by rooted trees. Viewing these trees as graph skeletons, we establish an upward propagation mechanism: synchronization within each child subtree forces the parent and all its descendants to synchronize. The argument proceeds from the leaves to the root and relies on phasor geometry and second-order optimality conditions. Our result provides a structural route to global synchronization that complements existing results based on minimum-degree or spectral proximity to complete graphs.

math.CO↗

arXiv2025

Global synchronization beyond dense graphs: the case of threshold graphs

Given a graph $G$ with adjacency matrix $A$, consider the homogeneous Kuramoto energy $E_G(\boldsymbol{\theta}):=\frac{1}{2}\sum_{1\leq i,j\leq n}A_{ij}\bigl(1-\cos(\theta_i-\theta_j)\bigr)$. We call $G$ \emph{second-order globally synchronizing} if every second-order stationary point of $E_G$ is fully synchronized. This property implies \emph{global synchronization}, namely that, up to a measure-zero set of initial conditions, trajectories of the Kuramoto model converge to a fully synchronized state. A fundamental graph-theoretic question is to identify which graph structures have this property. Existing guarantees for global synchronization typically require large minimum degree which forces the graph to be very dense, or good expansion properties. In this paper, we show that synchronization can also arise from a different, purely structural mechanism. More precisely, we prove that threshold graphs, a classical recursively defined graph class, are second-order globally synchronizing, and hence globally synchronizing. Thus, globally synchronizing graphs need not be very dense, have large minimum degree, or satisfy strong expansion-type conditions. The proof exploits the recursive construction of threshold graphs: local phasor constraints imposed by second-order stationarity are propagated along the construction sequence until full synchronization is forced.

math.DS↗

arXiv2024

Traditional Chinese Medicine Case Analysis System for High-Level Semantic Abstraction: Optimized with Prompt and RAG

This paper details a technical plan for building a clinical case database for Traditional Chinese Medicine (TCM) using web scraping. Leveraging multiple platforms, including 360doc, we gathered over 5,000 TCM clinical cases, performed data cleaning, and structured the dataset with crucial fields such as patient details, pathogenesis, syndromes, and annotations. Using the $Baidu\_ERNIE\_Speed\_128K$ API, we removed redundant information and generated the final answers through the $DeepSeekv2$ API, outputting results in standard JSON format. We optimized data recall with RAG and rerank techniques during retrieval and developed a hybrid matching scheme. By combining two-stage retrieval method with keyword matching via Jieba, we significantly enhanced the accuracy of model outputs.

cs.CL↗

arXiv2019

Global boundedness of the curl for a p-curl system in convex domains

In this paper, we study a semilinear system involving the curl operator in a bounded and convex domain in $R^3$, which comes from the steady-state approximation for Bean critical-state model for type-II superconductors. We show the existence and the $L^{\infty}$ estimate for weak solutions to this system.

math.AP↗

arXiv2019

Task-Oriented Optimal Sequencing of Visualization Charts

A chart sequence is used to describe a series of visualization charts generated in the exploratory analysis by data analysts. It provides information details in each chart as well as a logical relationship among charts. While existing research targets on generating chart sequences that match human's perceptions, little attention has been paid to formulate task-oriented connections between charts in a chart design space. We present a novel chart sequencing method based on reinforcement learning to capture the connections between charts in the context of three major analysis tasks, including correlation analysis, anomaly detection, and cluster analysis. The proposed method formulates a chart sequencing procedure as an optimization problem, which seeks an optimal policy to sequencing charts for the specific analysis task. In our method, a novel reward function is introduced, which takes both the analysis task and the factor of human cognition into consideration. We conducted one case study and two user studies to evaluate the effectiveness of our method under the application scenarios of visualization demonstration, sequencing charts for reasoning analysis results, and making a chart design choice. The study results showed the power of our method.

cs.HC↗