arXiv subjects

Xin-Jian Xu

Publications and source records attributed to Xin-Jian Xu.

At least 19 recordsLinked to original sources

arXiv2026

The inverse eigenvalue problems for perturbed Bessel operator with mixed data

We consider inverse eigenvalue problems for the perturbed Bessel operator in $L^{2}(0,1)$. (1) For the case where the angular-momentum quantum number $\ell\in\mathbb{N}\cup\{0\}$, we establish a uniqueness result for the inverse spectral problem by utilizing the closedness condition of a certain function system constructed based on the eigenvalues and the norming constants. (2) For the broader case where $\ell \geq -1/2$, we provide a uniqueness result for the inverse problem by using the density condition satisfied by the eigenvalues and the norming constants, where an additional smoothness condition may be imposed on the potential. (3) In the last section of this article, we present some corollaries based on (2). The results in these corollaries have already been established for the case $\ell=0$ by Gesztesy, Simon, Wei, Xu, Hatinoǧlu, et al., and we extend these results to the general case $\ell \geq -1/2$.

math.SP↗

arXiv2025

Overlap-aware meta-learning attention to enhance hypergraph neural networks for node classification

Although hypergraph neural networks (HGNNs) have emerged as a powerful framework for analyzing complex datasets, their practical performance often remains limited. On one hand, existing networks typically employ a single type of attention mechanism, focusing on either structural or feature similarities during message passing. On the other hand, assuming that all nodes in current hypergraph models have the same level of overlap may lead to suboptimal generalization. To overcome these limitations, we propose a novel framework, overlap-aware meta-learning attention for hypergraph neural networks (OMA-HGNN). First, we introduce a hypergraph attention mechanism that integrates both structural and feature similarities. Specifically, we linearly combine their respective losses with weighted factors for the HGNN model. Second, we partition nodes into different tasks based on their diverse overlap levels and develop a multi-task Meta-Weight-Net (MWN) to determine the corresponding weighted factors. Third, we jointly train the internal MWN model with the losses from the external HGNN model and train the external model with the weighted factors from the internal model. To evaluate the effectiveness of OMA-HGNN, we conducted experiments on six real-world datasets and benchmarked its perfor-mance against nine state-of-the-art methods for node classification. The results demonstrate that OMA-HGNN excels in learning superior node representations and outperforms these baselines.

cs.LG↗

arXiv2025

Recent Advances in Hypergraph Neural Networks

The growing interest in hypergraph neural networks (HGNNs) is driven by their capacity to capture the complex relationships and patterns within hypergraph structured data across various domains, including computer vision, complex networks, and natural language processing. This paper comprehensively reviews recent advances in HGNNs and presents a taxonomy of mainstream models based on their architectures: hypergraph convolutional networks (HGCNs), hypergraph attention networks (HGATs), hypergraph autoencoders (HGAEs), hypergraph recurrent networks (HGRNs), and deep hypergraph generative models (DHGGMs). For each category, we delve into its practical applications, mathematical mechanisms, literature contributions, and open problems. Finally, we discuss some common challenges and promising research directions.This paper aspires to be a helpful resource that provides guidance for future research and applications of HGNNs.

cs.LG↗

arXiv2025

Improved estimation of the effective reproduction number with heterogeneous transmission rates and reporting delays

In the face of an infectious disease, a key epidemiological measure is the basic reproduction number, which quantifies the average secondary infections caused by a single case in a susceptible population. In practice, the effective reproduction number, denoted as $R_t$, is widely used to assess the transmissibility of the disease at a given time $t$. Real-time estimating this metric is vital for understanding and managing disease outbreaks. Traditional statistical inference often relies on two assumptions. One is that samples are assumed to be drawn from a homogeneous population distribution, neglecting significant variations in individual transmission rates. The other is the ideal case reporting assumption, disregarding time delays between infection and reporting. In this paper, we thoroughly investigate these critical factors and assess their impact on estimating $R_t$. We first introduce negative binomial and Weibull distributions to characterize transmission rates and reporting delays, respectively, based on which observation and state equations are formulated. Then, we employ a Bayesian filtering for estimating $R_t$. Finally, validation using synthetic and empirical data demonstrates a significant improvement in estimation accuracy compared to conventional methods that ignore these factors.

physics.soc-ph↗

arXiv2025

Multi-view Spectral Clustering on the Grassmannian Manifold With Hypergraph Representation

Graph-based multi-view spectral clustering methods have achieved notable progress recently, yet they often fall short in either oversimplifying pairwise relationships or struggling with inefficient spectral decompositions in high-dimensional Euclidean spaces. In this paper, we introduce a novel approach that begins to generate hypergraphs by leveraging sparse representation learning from data points. Based on the generated hypergraph, we propose an optimization function with orthogonality constraints for multi-view hypergraph spectral clustering, which incorporates spectral clustering for each view and ensures consistency across different views. In Euclidean space, solving the orthogonality-constrained optimization problem may yield local maxima and approximation errors. Innovately, we transform this problem into an unconstrained form on the Grassmannian manifold. Finally, we devise an alternating iterative Riemannian optimization algorithm to solve the problem. To validate the effectiveness of the proposed algorithm, we test it on four real-world multi-view datasets and compare its performance with seven state-of-the-art multi-view clustering algorithms. The experimental results demonstrate that our method outperforms the baselines in terms of clustering performance due to its superior low-dimensional and resilient feature representation.

cs.LG↗

arXiv2023

Strong Consistency of Spectral Clustering for the Sparse Degree-Corrected Hypergraph Stochastic Block Model

We prove strong consistency of spectral clustering under the degree-corrected hypergraph stochastic block model in the sparse regime where the maximum expected hyperdegree is as small as $Ω(\log n)$ with $n$ denoting the number of nodes. We show that the basic spectral clustering without preprocessing or postprocessing is strongly consistent in an even wider range of the model parameters, in contrast to previous studies that either trim high-degree nodes or perform local refinement. At the heart of our analysis is the entry-wise eigenvector perturbation bound derived by the leave-one-out technique. To the best of our knowledge, this is the first entry-wise error bound for degree-corrected hypergraph models, resulting in the strong consistency for clustering non-uniform hypergraphs with heterogeneous hyperdegrees.

cs.SI↗

arXiv2023

Hyperlink prediction via local random walks and Jensen-Shannon divergence

Many real-world systems involving higher-order interactions can be modeled by hypergraphs, where vertices represent the systemic units and hyperedges describe the interactions among them. In this paper, we focus on the problem of hyperlink prediction which aims at inferring missing hyperlinks based on observed hyperlinks. We propose three similarity indices for hyperlink prediction based on local random walks and Jensen-Shannon divergence. Numerical experiments show that the proposed indices outperform the state-of-the-art methods on a broad range of datasets.

cs.SI↗

arXiv2022

Dynamics of the threshold model on hypergraphs

The threshold model has been widely adopted as a prototype for studying contagion processes on social networks. In this paper, we consider individual interactions in groups of three or more vertices and study the threshold model on hypergraphs. To understand how high-order interactions affect the breakdown of the system, we develop a theoretical framework based on generating function technology to derive the cascade condition and the giant component of vulnerable vertices, which depend on both hyperedges and hyperdegrees. First, we find a dual role of the hyperedge in propagation: when the average hyperdegree is small, increasing the size of the hyperedges may make the system fragile, while the average hyperdegree is relatively large, the increase of the hyperedges causes the system to be robust. Then, we identify the effects of threshold, hyperdegree, and hyperedge heterogeneities. The heterogeneity of individual thresholds causes the system to be more fragile, while the heterogeneity of individual hyperdegrees or hyperedges increases the robustness of the system. Finally, we show that the higher hyperdegree a vertex has, the larger possibility and faster speed it will get activated. We verify these results by simulating meme spreading on both random hypergraph models and hypergraphs constructed from empirical data.

physics.soc-ph↗

arXiv2021

Efficient hypothesis testing for community detection in heterogeneous networks

Identifying communities in networks is a fundamental and challenging problem of practical importance in many fields of science. Current methods either ignore the heterogeneous distribution of nodal degrees or assume prior knowledge of the number of communities. Here we propose an efficient hypothesis test for community detection based on quantifying dissimilarities between graphs. Given a random graph, the null hypothesis is that it is of degree-corrected Erdös-Rényi type. We compare the dissimilarity between them by a measure incorporating the vertex distance distribution, the clustering coefficient distribution, and the alpha-centrality distribution, which is used for our hypothesis test. We design a two-stage bipartitioning algorithm to uncover the number of communities and the corresponding structure simultaneously. Experiments on synthetic and real networks show that our method outperforms state-of-the-art ones.

cs.SI↗

arXiv2021

Dynamic analysis of influential stocks based on conserved networks

Characterizing temporal evolution of stock markets is a fundamental and challenging problem. The literature on analyzing the dynamics of the markets has focused so far on macro measures with less predictive power. This paper addresses this issue from a micro point of view. Given an investigating period, a series of stock networks are constructed first by the moving-window method and the significance test of stock correlations. Then, several conserved networks are generated to extract different backbones of the market under different states. Finally, influential stocks and corresponding sectors are identified from each conserved network, based on which the longitudinal analysis is performed to describe the evolution of the market. The application of the above procedure to stocks belonging to Standard \& Pool's 500 Index from January 2006 to April 2010 recovers the 2008 financial crisis from the evolutionary perspective.

cond-mat.dis-nn↗

arXiv2018

Efficient construction of threshold networks of stock markets

Although the threshold network is one of the most used tools to characterize the underlying structure of a stock market, the identification of the optimal threshold to construct a reliable stock network remains challenging. In this paper, the concept of dynamic consistence between the threshold network and the stock market is proposed. The optimal threshold is estimated by maximizing the consistence function. The application of this procedure to stocks belonging to Standard \& Pool's 500 Index from January 2006 to December 2011 yields the threshold value 0.28. In analyzing topological characteristics of the generated network, three globally financial crises can be distinguished well from the evolutionary perspective.

q-fin.ST↗

arXiv2016

Contagion on complex networks with persuasion

The threshold model has been widely adopted as a classic model for studying contagion processes on social networks. We consider asymmetric individual interactions in social networks and introduce a persuasion mechanism into the threshold model. Specifically, we study a combination of adoption and persuasion in cascading processes on complex networks. It is found that with the introduction of the persuasion mechanism, the system may become more vulnerable to global cascades, and the effects of persuasion tend to be more significant in heterogeneous networks than those in homogeneous networks: a comparison between heterogeneous and homogeneous networks shows that under weak persuasion, heterogeneous networks tend to be more robust against random shocks than homogeneous networks; whereas under strong persuasion, homogeneous networks are more stable. Finally, we study the effects of adoption and persuasion threshold heterogeneity on systemic stability. Though both heterogeneities give rise to global cascades, the adoption heterogeneity has an overwhelmingly stronger impact than the persuasion heterogeneity when the network connectivity is sufficiently dense.

physics.soc-ph↗

arXiv2016

Prevention of infectious diseases by public vaccination and individual protection

In the face of serious infectious diseases, governments endeavour to implement containment measures such as public vaccination at a macroscopic level. Meanwhile, individuals tend to protect themselves by avoiding contacts with infections at a microscopic level. However, a comprehensive understanding of how such combined strategy influences epidemic dynamics is still lacking. We study a susceptible-infected-susceptible epidemic model with imperfect vaccination on dynamic contact networks, where the macroscopic intervention is represented by random vaccination of the population and the microscopic protection is characterised by susceptible individuals rewiring contacts from infective neighbours. In particular, the model is formulated both in populations without and then with demographic effects. Using the pairwise approximation and the probability generating function approach, we investigate both dynamics of the epidemic and the underlying network. For populations without demography, the emerging degree correlations, bistable states, and oscillations demonstrate the combined effects of the public vaccination program and individual protective behavior. Compared to either strategy in isolation, the combination of public vaccination and individual protection is more effective in preventing and controlling the spread of infectious diseases by increasing both the invasion threshold and the persistence threshold. For populations with additional demographic factors, the integration between vaccination intervention and individual rewiring may promote epidemic spreading due to the birth effect. Moreover, the degree distributions of both networks in the steady state is closely related to the degree distribution of newborns, which leads to uncorrelated connectivity. All the results demonstrate the importance of both local protection and global intervention, as well as the demographic effects.

physics.soc-ph↗

arXiv2014

Modeling nonuniversal citation distributions: the role of scientific journals

Whether a scientific paper is cited is related not only to the influence of its author(s) but also to the journal publishing it. Scientists, either proficient or tender, usually submit their most important work to prestigious journals which receives higher citations than the ordinary. How to model the role of scientific journals in citation dynamics is of great importance. In this paper we address this issue through two folds. One is the intrinsic heterogeneity of a paper determined by the impact factor of the journal publishing it. The other is the mechanism of a paper being cited which depends on its citations and prestige. We develop a model for citation networks via an intrinsic nodal weight function and an intuitive ageing mechanism. The node's weight is drawn from the distribution of impact factors of journals and the ageing transition is a function of the citation and the prestige. The node-degree distribution of resulting networks shows nonuniversal scaling: the distribution decays exponentially for small degree and has a power-law tail for large degree, hence the dual behaviour. The higher the impact factor of the journal, the larger the tipping point and the smaller the power exponent that are obtained. With the increase of the journal rank, this phenomenon will fade and evolve to pure power laws.

physics.soc-ph↗

arXiv2013

Temporal prediction of epidemic patterns in community networks

Most previous studies of epidemic dynamics on complex networks suppose that the disease will eventually stabilize at either a disease-free state or an endemic one. In reality, however, some epidemics always exhibit sporadic and recurrent behaviour in one region because of the invasion from an endemic population elsewhere. In this paper we address this issue and study a susceptible-infected-susceptible epidemiological model on a network consisting of two communities, where the disease is endemic in one community but alternates between outbreaks and extinctions in the other. We provide a detailed characterization of the temporal dynamics of epidemic patterns in the latter community. In particular, we investigate the time duration of both outbreak and extinction, and the time interval between two consecutive inter-community infections, as well as their frequency distributions. Based on the mean-field theory, we theoretically analyze these three timescales and their dependence on the average node degree of each community, the transmission parameters, and the number of intercommunity links, which are in good agreement with simulations, except when the probability of overlaps between successive outbreaks is too large. These findings aid us in better understanding the bursty nature of disease spreading in a local community, and thereby suggesting effective time-dependent control strategies.

physics.soc-ph↗

arXiv2013

Modeling citation networks based on vigorousness and dormancy

In citation networks, the activity of papers usually decreases with age and dormant papers may be discovered and become fashionable again. To model this phenomenon, a competition mechanism is suggested which incorporates two factors: vigorousness and dormancy. Based on this idea, a citation network model is proposed, in which a node has two discrete stage: vigorous and dormant. Vigorous nodes can be deactivated and dormant nodes may be activated and become vigorous. The evolution of the network couples addition of new nodes and state transitions of old ones. Both analytical calculation and numerical simulation show that the degree distribution of nodes in generated networks displays a good right-skewed behavior. Particularly, scale-free networks are obtained as the deactivated vertex is target selected and exponential networks are realized for the random-selected case. Moreover, the measurement of four real-world citation networks achieves a good agreement with the stochastic model.

physics.soc-ph↗

arXiv2013

Vaccination intervention on epidemic dynamics in networks

Vaccination is an important measure available for preventing or reducing the spread of infectious diseases. In this paper, an epidemic model including susceptible, infected, and imperfectly vaccinated compartments is studied on Watts-Strogatz small-world, Barabási-Albert scale-free, and random scale-free networks. The epidemic threshold and prevalence are analyzed. For small-world networks, the effective vaccination intervention is suggested and its influence on the threshold and prevalence is analyzed. For scale-free networks, the threshold is found to be strongly dependent both on the effective vaccination rate and on the connectivity distribution. Moreover, so long as vaccination is effective, it can linearly decrease the epidemic prevalence in small-world networks, whereas for scale-free networks it acts exponentially. These results can help in adopting pragmatic treatment upon diseases in structured populations.

physics.soc-ph↗

arXiv2010

Fitness-driven deactivation in network evolution

Individual nodes in evolving real-world networks typically experience growth and decay --- that is, the popularity and influence of individuals peaks and then fades. In this paper, we study this phenomenon via an intrinsic nodal fitness function and an intuitive aging mechanism. Each node of the network is endowed with a fitness which represents its activity. All the nodes have two discrete stages: active and inactive. The evolution of the network combines the addition of new active nodes randomly connected to existing active ones and the deactivation of old active nodes with possibility inversely proportional to their fitnesses. We obtain a structured exponential network when the fitness distribution of the individuals is homogeneous and a structured scale-free network with heterogeneous fitness distributions. Furthermore, we recover two universal scaling laws of the clustering coefficient for both cases, $C(k) \sim k^{-1}$ and $C \sim n^{-1}$, where $k$ and $n$ refer to the node degree and the number of active individuals, respectively. These results offer a new simple description of the growth and aging of networks where intrinsic features of individual nodes drive their popularity, and hence degree.

physics.soc-ph↗