arXiv subjects

Dan Han

Publications and source records attributed to Dan Han.

17 recordsLinked to original sources

arXiv2026

Empirical-Bayes Elastic-Net Computation for Exponential Random Graph Models

Exponential random graph models (ERGMs) describe dependence among network ties, but inference becomes difficult when the likelihood is intractable and candidate network statistics are strongly correlated. We introduce BERGM Elastic Net, an adaptive empirical-Bayes approach that combines lasso shrinkage with ridge stabilization in a Bayesian ERGM. A latent-variable formulation supports approximate exchange sampling, while empirical-Bayes updates adapt the amount of regularization to the observed network. We connect the proposed prior to elastic-net penalized likelihood and clarify the interpretation of thresholded reporting and coefficient grouping. The method is developed for over-specified network models containing many related structural and covariate effects.

stat.ME↗

arXiv2026

Scattering Criteria for the Three-Dimensional Focusing Energy-Critical Generalized Hartree Equation

Two nonradial scattering criteria are established for the three-dimensional focusing energy-critical generalized Hartree equation below the ground-state threshold, under a bounded-scale concentration--compactness reduction. The first criterion is formulated in terms of fixed-center occupation windows and quantitative bounds on the motion of the concentration center. The second is based on uniform low-frequency $L^2$-decay, which yields finite mass, precompactness in the inhomogeneous energy space, a zero-momentum normalization, and sublinear center drift. The proofs combine a localized Hartree virial identity with a critical Hardy--Littlewood--Sobolev estimate controlling the nonlocal tail.

math.AP↗

arXiv2026

Finite-mass soliton-type rigidity and four-channel reduction for the three-dimensional nonradial focusing energy-critical nonlinear Schr\"odinger equation

The concentration--compactness channels below the ground-state threshold are investigated for the three-dimensional nonradial focusing energy-critical nonlinear Schr\"odinger equation. After one-sided normalization, a minimal critical element falls into four classes: the finite-time, rapid-cascade, bounded-scale finite-mass, and residual quasi-soliton channels. The first three classes are rigorously excluded. The main result shows, without radial symmetry, zero momentum, or a slow spatial center, that every finite-mass bounded-scale almost-periodic solution is identically zero. Consequently, any minimal counterexample to below-threshold scattering must lie in the residual quasi-soliton channel; if its scale is bounded, then it has infinite mass at every time.

math.AP↗

arXiv2026

SAGE-Net: Semantics-Augmented Geometric Encoder for Material Property Prediction

Reliable structure-property modeling is crucial for accelerating materials discovery, where crystal graphs and structure-derived crystallographic descriptions provide complementary geometric and semantic information. Existing multimodal materials models primarily incorporate textual information through post-encoding fusion, latent-space alignment, or attention-based representation interaction mechanisms. However, in most cases, crystallographic semantics are introduced after structural encoding and therefore cannot directly guide the formation of atom-level crystal-graph representations. Here, we present Semantics-Augmented Geometric Encoder Network (SAGE-Net), a flexible multimodal framework that injects description-derived chemical and crystallographic semantics into geometric message passing. SAGE-Net introduces Semantic-Guided Message Passing (SGMP), which gates atom-level updates and enables crystallographic semantics to directly modulate local geometric interactions across multiple graph neural network (GNN) backbones. Across benchmarks covering bandgap, mechanical, transport-related properties, and synthesizability assessment, the SAGE-Net instantiated with different GNN backbones achieves the lowest MAE on eight out of ten JARVIS-DFT regression targets and delivers strong or highly competitive performance against both structure-based and multimodal baselines. For synthesizability assessment, the SAGE-Net demonstrate outstanding classification performance and high recall rates. Interpretability analysis unravels that SAGE-Net effectively captures physically interpretable crystallographic features, viz. space group, dimensionality, polyhedral environments, among others. Together, these results demonstrate SGMP-based SAGE-Net as a general and transferable framework for deeply integrated multimodal materials learning.

cond-mat.mtrl-sci↗

arXiv2026

Conditional scattering criteria for cylindrical threshold dynamics of the three-dimensional focusing energy-critical Schr\"odinger equation

Below-threshold scattering is studied for the three-dimensional focusing energy-critical Schr\"odinger equation in the cylindrically symmetric class. For soliton-like compact critical elements, two linked rigidity entrances are isolated: a best fixed-axis window condition for the axial center and a low-frequency tail smallness condition. A shifted localized virial estimate and a finite-mass virial argument after axial zero-momentum normalization exclude these entrances, yielding a conditional cylindrical threshold scattering criterion via compactness reduction.

math.AP↗

arXiv2026

Scattering and Low-Speed Critical Elements for the 3D Focusing Energy-Critical NLS

The below-threshold scattering problem is considered for the three-dimensional focusing energy-critical nonlinear Schr\"odinger equation. A main non-radial obstruction is the possible drift of the concentration center of a soliton-like critical element, which prevents a fixed-center localized virial estimate from closing directly. It is shown that such a compact critical solution must vanish if it has an $L_t^\infty L_x^q$ bound and its center drifts sufficiently slowly. The result covers the pure-energy, endpoint $L^4$, and finite-mass regimes and gives a corresponding conditional scattering criterion.

math.AP↗

arXiv2025

Estimating dynamic transmission rates with a Black-Karasinski process in stochastic SIHR models using particle MCMC

Compartmental models are effective in modeling the spread of infectious pathogens, but have remaining weaknesses in fitting to real datasets exhibiting stochastic effects. We propose a stochastic SIHR model with a dynamic transmission rate, where the rate is modeled by the Black-Karasinski (BK) process - a mean-reverting stochastic process with a stable equilibrium distribution, making it well-suited for modeling long-term epidemic dynamics. To generate sample paths of the BK process and estimate static parameters of the system, we employ particle Markov Chain Monte Carlo (pMCMC) methods due to their effectiveness in handling complex state-space models and jointly estimating parameters. We designed experiments on synthetic data to assess estimation accuracy and its impact on inferred transmission rates; all BK-process parameters were estimated accurately except the mean-reverting rate. We also assess the sensitivity of pMCMC to misspecification of the mean-reversion rate. Our results show that estimation accuracy remains stable across different mean-reversion rates, though smaller values increase error variance and complicate inference results. Finally, we apply our model to Arizona flu hospitalization data, finding that parameter estimates are consistent with published survey data.

stat.ME↗

arXiv2025

Formulation a new SIR model with non-local mobility

In this manuscript, we develop a mobility-based Susceptible-Infectious-Recovered (SIR) model to elucidate the dynamics of pandemic propagation. While traditional SIR models within the field of epidemiology aptly characterize transitions among susceptible, infected, and recovered states, they typically neglect the inherent spatial mobility of particles. To address this limitation, we introduce a novel dynamical SIR model that incorporates nonlocal spatial motion for three distinct particle types, thereby bridging the gap between epidemiological theory and real-world mobility patterns. This paper primarily focuses on analyzing the long-term behavior of this dynamic system, with specific emphasis on the computation of first and second moments. We propose a new reproduction number $R_0^m$ and compare it with the classical reproduction number $R_0$ in the traditional SIR model. Furthermore, we rigorously examine the phenomenon of intermittency within the context of this enhanced SIR model. The results contribute to a more comprehensive understanding of pandemic spread dynamics, considering both the interplay between disease transmission and population mobility and the impact of spatial motion on the system's behavior over time.

math.DS↗

arXiv2024

A Survey of Third-Party Library Security Research in Application Software

In the current software development environment, third-party libraries play a crucial role. They provide developers with rich functionality and convenient solutions, speeding up the pace and efficiency of software development. However, with the widespread use of third-party libraries, associated security risks and potential vulnerabilities are increasingly apparent. Malicious attackers can exploit these vulnerabilities to infiltrate systems, execute unauthorized operations, or steal sensitive information, posing a severe threat to software security. Research on third-party libraries in software becomes paramount to address this growing security challenge. Numerous research findings exist regarding third-party libraries' usage, ecosystem, detection, and fortification defenses. Understanding the usage and ecosystem of third-party libraries helps developers comprehend the potential risks they bring and select trustworthy libraries. Third-party library detection tools aid developers in automatically discovering third-party libraries in software, facilitating their management. In addition to detection, fortification defenses are also indispensable. This article profoundly investigates and analyzes this literature, summarizing current research achievements and future development directions. It aims to provide practical and valuable insights for developers and researchers, jointly promoting the healthy development of software ecosystems and better-protecting software from security threats.

cs.SE↗

arXiv2024

Spectral Analysis of Lattice Schr\"{o}dinger-Type Operators Associated with the Nonstationary Anderson Model and Intermittency

The research explores a high irregularity, commonly referred to as intermittency, of the solution to the non-stationary parabolic Anderson problem: \begin{equation*} \frac{\partial u}{\partial t} = \varkappa \mathcal{L}u(t,x) + \xi_{t}(x)u(t,x) \end{equation*} with the initial condition $u(0,x) \equiv 1$, where $(t,x) \in [0,\infty)\times \mathbb{Z}^d$. Here, $\varkappa \mathcal{L}$ denotes a non-local Laplacian, and $\xi_{t}(x)$ is a correlated white noise potential. The observed irregularity is intricately linked to the upper part of the spectrum of the multiparticle Schr\"{o}dinger equations for the moment functions $m_p(t,x_1,x_2,\cdots,x_p) = \langle u(t,x_1)u(t,x_2)\cdots u(t,x_p)\rangle$. In the first half of the paper, a weak form of intermittency is expressed through moment functions of order $p\geq 3$ and established for a wide class of operators $\varkappa \mathcal{L}$ with a positive-definite correlator $B=B(x))$ of the white noise. In the second half of the paper, the strong intermittency is studied. It relates to the existence of a positive eigenvalue for the lattice Schr\"odinger type operator with the potential $B$. This operator is associated with the second moment $m_2$. Now $B$ is not necessarily positive-definite, but $\sum B(x)\geq 0$.

math-ph↗

arXiv2023

Non-stationary Lattice Anderson Model with Non-local Laplacian and Correlated White Noise

We study the non-stationary Anderson parabolic problem on the lattice $Z^d$, i.e., the equation \begin{equation}\label{andersonmodel} \begin{aligned} \frac{\partial u}{\partial t} &=\varkappa \mathcal{A}u(t,x)+\xi_{t}(x)u(t,x) u(0,x) &\equiv 1, \, (t,x) \in [0,\infty)\times Z^d. \end{aligned} \end{equation} Here $\mathcal{A}$ is non-local Laplacian, $\xi_t (x), \ t \geq 0, \ x \in Z^d$ is the family of the correlated white noises and $\varkappa >0$ is the diffusion coefficient. The changes of $\varkappa$ (large versus small) are responsible for the qualitative phase transition in the model. At the first step the analysis of the model is reduced to the solution of the stochastic differential equation(SDE) (in the standard It\^{o}'s form) on the weighted Hilbert space $l^2(Z^d,\mu)$ with appropriate measure $\mu$. The equations of first two moments of the solution $u(t,x)$ are derived and studied using the spectral analysis of the corresponding Schr\"{o}dinger operators with special class of the positive definite potentials. The analysis reveals several bifurcations depending on the properties of the kernel of $\mathcal{A}$ and the correlation function in the potential.

math.PR↗

arXiv2021

Cation disorder in stoichiometric MgSnN2 and ambipolar self-doping behavior in off-stoichiometric MgSnN2

Investigations on II-Sn-N2 (II = Mg, Ca) have been started very recently compared to the intense research of the Zn-IV-N2 (IV = Si, Ge, Sn). In this work, we perform a comprehensive study of cation disorder in stoichiometric MgSnN2 and crystal structure characteristic, doping behavior of off-stoichiometric Mg1+xSn1-xN2 (x = -0.8, -0.6, -0.5, -0.4, -0.2, 0.2, 0.4, 0.5, 0.6, 0.8) by using the cluster expansion method and first principles calculations. It is found that cation disorder in stoichiometric MgSnN2 induces a band gap reduction because of a violation of the octet rule. Moreover, the local disorder, namely forming (4,0) or (0,4) tetrahedra, would lead to an appreciable band gap reduction and hinder the enhancement of the optical absorption. An off-stoichiometric Mg/Sn ratio can strongly affect the morphology of Mg1+xSn1-xN2 samples due to the higher ionicity of the Mg-N bonds in comparison with Zn-N bonds. Furthermore, Mg1+xSn1-xN2 compounds show an ambipolar self-doping behavior, i.e., Mg-rich Mg1+xSn1-xN2 show p-type doping while Sn-rich ones exhibit n-type doping owing to the formation of acceptor-type antisite defect MgSn or donor-type antisite defect SnMg, respectively.

cond-mat.mtrl-sci↗

arXiv2021

MFR 2021: Masked Face Recognition Competition

This paper presents a summary of the Masked Face Recognition Competitions (MFR) held within the 2021 International Joint Conference on Biometrics (IJCB 2021). The competition attracted a total of 10 participating teams with valid submissions. The affiliations of these teams are diverse and associated with academia and industry in nine different countries. These teams successfully submitted 18 valid solutions. The competition is designed to motivate solutions aiming at enhancing the face recognition accuracy of masked faces. Moreover, the competition considered the deployability of the proposed solutions by taking the compactness of the face recognition models into account. A private dataset representing a collaborative, multi-session, real masked, capture scenario is used to evaluate the submitted solutions. In comparison to one of the top-performing academic face recognition solutions, 10 out of the 18 submitted solutions did score higher masked face verification accuracy.

cs.CV↗

arXiv2021

Structure-Composition-Property Relationships in Antiperovskite Nitrides: Guiding a Rational Alloy Design

The alloy strategy through A- or X-site is a common method for experimental preparation of high-performance and stable lead-based perovskite solar cells. As one of the important candidates for lead-free and stable photovoltaic absorber, the inorganic antiperovskite family has recently been reported to exhibit excellent optoelectronic properties. However, the current reports on the design of antiperovskite alloys are rare. In this work, we investigated the previously overlooked electronic property (e.g., conduction band convergence), static dielectric constant, and exciton binding energy in inorganic antiperovskite nitrides by first-principles calculations. Then, we reveal a linear relationship between tolerance factor and various physical quantities. Guided by the established structure-composition-property relationship in six antiperovskite nitrides X3NA (X2+ = Mg2+, Ca2+, Sr2+; A3- = P3-, As3-, Sb3-, Bi3-), for the first time, we design a promising antiperovskite alloy Mg3NAs0.5Bi0.5 with the quasi-direct band gap of 1.402 eV. Finally, we make a comprehensive comparison between antiperovskite nitrides and conventional halide perovskites for pointing out the future direction for device applications.

cond-mat.mtrl-sci↗

arXiv2020

One Explicitly Solvable Model For The Galton-Watson Processes In the Random Environment

In this paper, we study the Galton-Watson process in the random environment for the particular case when the number of the offsprings in each generation has the fractional linear generation function with random parameters. In this case, the distribution of $N_t$, the number of particles at the moment time $t=0,1,2,\cdots$ can be calculated explicitly. We present the classification of such processes and limit theorems of two types: quenched type which is for the fixed realization of the random environment and annealed type which includes the averaging over the environment.

math.PR↗

arXiv2019

Impact of Metal ns2 Lone Pair on Luminescence Efficiency in Low-Dimensional Halide Perovskites

Based on first-principles calculations, we show that chemically active metal ns2 lone pairs play an important role in exciton relaxation and dissociation in low-dimensional halide perovskites. We studied excited-state properties of several recently discovered luminescent all-inorganic and hybrid organic-inorganic zero-dimensional (0D) Sn and Pb halides. The results show that, despite the similarity in ground-state electronic structure between Sn and Pb halide perovskites, the chemically more active Sn2+ lone pair leads to stronger excited-state structural distortion and larger Stokes shift in Sn halides. The enhanced Stokes shift hinders excitation energy transport, which reduces energy loss to defects and increases the photoluminescence quantum efficiency (PLQE). The presence of the ns2 metal cations in the 0D halide perovskites also promotes the exciton dissociation into electron and hole polarons especially in all-inorganic compounds, in which the coupling between metal-halide clusters is significant.

cond-mat.mtrl-sci↗

arXiv2018

Population Processes with Immigration

The paper contains the complete analysis of the Galton-Watson models with immigration, including the processes in the random environment, stationary or non-stationary ones. We also study the branching random walk on $Z^d$ with immigration and prove the existence of the limits for the first two correlation functions.

math.PR↗