arXiv subjects

Xia Zhao

Publications and source records attributed to Xia Zhao.

At least 19 recordsLinked to original sources

arXiv2026

A Comparative Study of Feature Selection Methods for EHR Diagnosis Codes in Opioid Use Disorder Prediction

Feature selection is a critical step in electronic health record (EHR)-based predictive modeling, where input variables are often high-dimensional, sparse, noisy, and redundant. Large feature sets not only increase computational burden and overfitting risk, but also make model interpretation difficult, leading to limited usefulness in clinical settings. In this study, we focus on diagnosis-related features and compare five feature selection paradigms for opioid use disorder (OUD) prediction: recurrence enrichment, NTK-motivated early gradient sensitivity, LightGBM-SHAP, Elastic Net, and large language model (LLM)-guided semantic selection. We use a unified preprocessing and evaluation framework and assess each method by downstream predictive performance, resampling stability, and representation of infrequent diagnosis codes. Our results demonstrate that performance improves with larger feature budgets with diminishing returns beyond a moderate size. NTK sensitivity provides the best overall balance of accuracy and stability, and LLM-guided selection contributes complementary clinically meaningful signals despite lower standalone performance.

cs.LG↗

arXiv2026

The Minkowski problem for the $k$-torsional rigidity

P. Salani [Adv. Math., 229 (2012)] introduced the $k$-torsional rigidity associated with a $k$-Hessian equation and obtained the Brunn-Minkowski inequalities $w.r.t.$ the torsional rigidity in $\mathbb{R}^3$. Following this work, we first construct, in the present paper, a Hadamard variational formula for the $k$-torsional rigidity with $1\leq k\leq n-1$, then we can deduce a $k$-torsional measure from the Hadamard variational formula. Based on the $k$-torsional measure, we propose the Minkowski problem for the $k$-torsional rigidity and confirm the existence of its smooth non-even solutions by the method of a curvature flow. Specially, a new proof method for the uniform lower bound estimation in the $C^0$ estimation for the solution to the curvature flow is presented with the help of invariant functional $Φ(Ω_t)$.

math.DG↗

arXiv2026

The distinction of time-reversal-like degeneracy by electronic transport in a new compound

We report the discovery of a new compound, Ce$_3$MgBi$_5$, and reveal the hidden time-reversal-like degenerate states within it. Ce$_3$MgBi$_5$ is an antiferromagnet with the distorted kagome lattice of Ce atoms, in which several fractional magnetization plateaus emerge with the increase of magnetic field. At the 1/2 magnetization plateau, obvious hysteresis has been observed in the magnetoresistance and Hall resistivity during the rise and fall of the magnetic field. However, hysteresis vanishes in the corresponding measurements of magnetization, indicating the existence of degenerate states with the same net magnetization but different electronic transport properties. The degenerate states can be connected by the time-reversal-like operation. In addition, by comparing with HoAgGe, it is suggested that the special crystal structure in Ce$_3$MgBi$_5$ may have a shielding effect on the time-reversal-like operation, thereby affecting the distinction of degenerate states. Our work establishes Ce$_3$MgBi$_5$ as an example of utilizing electronic transport properties to identify and distinguish hidden symmetries in frustrated magnetic systems.

cond-mat.str-el↗

arXiv2026

FSD-CAP: Fractional Subgraph Diffusion with Class-Aware Propagation for Graph Feature Imputation

Imputing missing node features in graphs is challenging, particularly under high missing rates. Existing methods based on latent representations or global diffusion often fail to produce reliable estimates, and may propagate errors across the graph. We propose FSD-CAP, a two-stage framework designed to improve imputation quality under extreme sparsity. In the first stage, a graph-distance-guided subgraph expansion localizes the diffusion process. A fractional diffusion operator adjusts propagation sharpness based on local structure. In the second stage, imputed features are refined using class-aware propagation, which incorporates pseudo-labels and neighborhood entropy to promote consistency. We evaluated FSD-CAP on multiple datasets. With $99.5\%$ of features missing across five benchmark datasets, FSD-CAP achieves average accuracies of $80.06\%$ (structural) and $81.01\%$ (uniform) in node classification, close to the $81.31\%$ achieved by a standard GCN with full features. For link prediction under the same setting, it reaches AUC scores of $91.65\%$ (structural) and $92.41\%$ (uniform), compared to $95.06\%$ for the fully observed case. Furthermore, FSD-CAP demonstrates superior performance on both large-scale and heterophily datasets when compared to other models.

cs.LG↗

arXiv2025

The $p$-th dual Minkowski problem for the $k$-torsional rigidity corresponding to a $k$-Hessian equation

The study of the dual curvature measures [Y. Huang, E. Lutwak, D. Yang \& G. Y. Zhang, Acta. Math. 216 (2016): 325-388], which connects the cone-volume measure and Aleksandrov's integral curvature, and has created a precedent for the theoretical research of the dual Brunn-Minkowski theory. Motivated by the foregoing groundbreaking works, the present paper introduces the $p$-th dual $k$-torsional rigidity associated with a $k$-Hessian equation and establishes its Hadamard variational formula with $1\leq k\leq n-1$, which induces the $p$-th dual $k$-torsional measure. Further, based on the $p$-th dual $k$-torsional measure, this article, for the first time, proposes the $p$-th dual Minkowski problem of the $k$-torsional rigidity which can be equivalently converted to a nonlinear partial differential equation in smooth case: \begin{align}\label{eq01} f(x)=τ(|\nabla h|^2+h^2)^{\frac{p-n}{2}}h_Ω(x)|Du(ν^{-1}_Ω(x))|^{k+1}σ_{n-k}(h_{ij}(x)+h_Ω(x)δ_{ij}), \end{align} where $τ>0$ is a constant, $f$ is a positive smooth function defined on $S^{n-1}$ and $σ_{n-k}$ is the $(n-k)$-th elementary symmetric function of the principal curvature radii. We confirm the existence of smooth non-even solution to the $p$-th dual Minkowski problem of the $k$-torsional rigidity for $p<n-2$ by the method of a curvature flow which converges smoothly to the solution of equation (\ref{eq01}). Specially, a novel approach for the uniform lower bound estimation in the $C^0$ estimation for the solution to the curvature flow is presented with the help of invariant functional $Φ(Ω_t)$.

math.DG↗

arXiv2025

Structural, optical, and dielectric properties of Cr-doped ZnO films via DC magnetron sputtering

Cr-doped ZnO films were fabricated by a new but feasible method, that is, annealing Cr-Zn layers deposited via DC magnetron sputtering in air. Microstructures of the films were investigated using X-ray diffraction, scanning electron microscopy, and atomic force microscopy, intrinsic point defects were identified via photoluminescence spectroscopy, and optical and dielectric properties were analyzed using a UV-vis spectrophotometer and dielectric spectrometer, respectively. It was found that the average grain sizes decrease (56.34 - 39.50 nm), the band gap increases (from 3.18 to 3.23 eV), and the transmittance (at 600 nm) decreases (from 91% to 83%) with increasing Cr. Two activation energies of conduction increase after doping Cr, indicating enhanced temperature stability. At optimal Cr levels, ZnO films exhibit high transmittance and conductivity, exhibiting potential for transparent electrode development. This method can be extended to other doped ZnO films, such as Al-doped ZnO transparent electrodes, to achieve simultaneous improvements in transmittance, conductivity, and stability for flexible and wearable applications.

cond-mat.mtrl-sci↗

arXiv2025

Flow by Gauss Curvature to the Orlicz Minkowski Problem for q-torsional rigidity

The celebrated Minkowski problem for the torsional rigidity ($2$-torsional rigidity) was firstly studied by Colesanti and Fimiani \cite{CA} using variational method. Moreover, Hu, Liu and Ma \cite{HJ} also studied the Minkowski problem {\it w.r.t.} $2$-torsional rigidity by method of curvature flows and obtain the existence of smooth even solutions. Up to now, as far as we know, the study of the Minkowski problem for the $q$-torsional rigidity is still blank. In the present paper, we propose and investigate the Orlicz Minkowski problem for the $q$-torsional rigidity corresponding to the $q$-Laplace equation inspired by the foregoing works, and then confirm the existence of smooth non-even solutions to the Orlicz Minkowski problem for the $q$-torsional rigidity with $q>1$ by the method of a Gauss curvature flow.

math.DG↗

arXiv2024

The dual Minkowski problem for $q$-torsional rigidity

The Minkowski problem for torsional rigidity ($2$-torsional rigidity) was firstly studied by Colesanti and Fimiani \cite{CA} using variational method. Moreover, Hu \cite{HJ00} also studied this problem by the method of curvature flows and obtained the existence of smooth even solutions. In addition, the smooth non-even solutions to the Orlicz Minkowski problem $w. r. t$ $q$-torsional rigidity were given by Zhao et al. \cite{ZX} through a Gauss curvature flow. The dual curvature measure and the dual Minkowski problem were first posed and considered by Huang, Lutwak, Yang and Zhang in \cite{HY}. The dual Minkowski problem is a very important problem, which has greatly contributed to the development of the dual Brunn-Minkowski theory and extended the other types dual Minkowski problem. To the best of our knowledge, the dual Minkowski problem $w. r. t$ ($q$) torsional rigidity is still open because the dual ($q$) torsional measure is blank. Thus, it is a natural problem to consider the dual Minkowski problem for ($q$) torsional rigidity. In this paper, we introduce the $p$-th dual $q$-torsional measure and propose the $p$-th dual Minkowski problem for $q$-torsional rigidity with $q>1$. Then we confirm the existence of smooth even solutions for $p<n$ ($p\neq 0$) to the $p$-th dual Minkowski problem for $q$-torsional rigidity by method of a Gauss curvature flow. Specially, we also obtain the smooth non-even solutions with $p<0$ to this problem.

math.DG↗

arXiv2024

Gauss curvature flow to the $L_p$-Gaussian chord Minkowski problem

Recently, Huang and Qin \cite{HY01} introduced the Gaussian chord measure and $L_p$-Gaussian chord measure by variational methods. Meanwhile, they posed Gaussian chord Minkowski problem for $p=1$ and used variational methods to obtain an origin-symmetric normalized measure solution for the Gaussian chord Minkowski problem. The smooth solution, up to now, to the $L_p$-Gaussian chord Minkowski problem is still open. Motivated by the forgoing works by Huang and Qin in \cite{HY01}, we propose in the present paper the $L_p(p>0)$-Gaussian chord Minkowski problem and log-Gaussian chord Minkowski problem, and obtain the smooth even solutions to these two types of problems by the method of a Gauss curvature flow.

math.DG↗

arXiv2024

Flow by Gauss curvature to the Minkowski problem of p-harmonic measure

The Minkowski problem of harmonic measures was first studied by Jerison [19]. Recently, Akman and Mukherjee [1] studied the Minkowski problem corresponding to $p$-harmonic measures on convex domains and generalized Jerison's results. In this paper, we prove the existence of the smooth solution to the Minkowski problem for the $p$-harmonic measure by method of the Gauss curvature flow.

math.AP↗

arXiv2024

Flow by Gauss Curvature to the orlicz Chord Minkowski Problem

The $L_p$ chord Minkowski problem based on Chord measures and $L_p$ chord measures introduced firstly by Lutwak, Xi, Yang and Zhang [38] is a very important and meaningful geometric measure problem in the $L_p$ Brunn-Minkowski theory. Xi, Yang, Zhang and Zhao [45] using variational methods gave a measure solution when $p > 1$ and $0<p<1$ in the symmetric case. Recently, Guo, Xi and Zhao [18] also obtained a measure solution for $0\leq p<1$ by similar methods without the symmetric assumption. In the present paper, we investigate and confirm the orlicz chord Minkowski problem, which generalizes the $L_p$ chord Minkowski problem by replacing $p$ with a fixed continuous function $φ:(0,\infty)\rightarrow(0,\infty)$, and achieve the existence of smooth solutions to the orlicz chord Minkowski problem by using methods of Gauss curvature flows.

math.DG↗

arXiv2023

The Minkowski problem in Heisenberg groups

As we all know, the Minkowski type problem is the cornerstone of the Brunn-Minkowski theory in Euclidean space. The Heisenberg group as a sub-Riemannian space is the simplest non-Abelian degenerate Riemannian space that is completely different from a Euclidean space. By analogy with the Minkowski type problem in Euclidean space, the Minkowski type problem in Heisenberg groups is still open. In the present paper, we develop for the first time a sub-Riemannian version of Minkowski type problem in the horizontal distributions of Heisenberg groups, and further give a positive answer to this sub-Riemannian Minkowski type problem via the variational method.

math.DG↗

arXiv2023

Anisotropic in-plane heat transport of Kitaev magnet Na$_2$Co$_2$TeO$_6$

We report a study on low-temperature heat transport of Kitaev magnet Na$_2$Co$_2$TeO$_6$, with the heat current and magnetic fields along the honeycomb spin layer (the $ab$ plane). The zero-field thermal conductivity of $κ^a_{xx}$ and $κ^{a*}_{xx}$ display similar temperature dependence and small difference in their magnitudes; whereas, their magnetic field (parallel to the heat current) dependence are quite different and are related to the field-induced magnetic transitions. The $κ^a_{xx}(B)$ data for $B \parallel a$ at very low temperatures have an anomaly at 10.25--10.5 T, which reveals an unexplored magnetic transition. The planar thermal Hall conductivity $κ^a_{xy}$ and $κ^{a*}_{xy}$ show very weak signals at low fields and rather large values with sign change at high fields. This may point to a possible magnetic structure transition or the change of the magnon band topology that induces a radical change of magnon Berry curvature distribution before entering the spin polarized state. These results put clear constraints on the high-field phase and the theoretical models for Na$_2$Co$_2$TeO$_6$.

cond-mat.str-el↗

arXiv2023

An inverse Gauss curvature flow and its application to p-capacitary Orlicz-Minkowski problem

In [Calc. Var., 57:5 (2018)], Hong-Ye-Zhang proposed the $p$-capacitary Orlicz-Minkowski problem and proved the existence of convex solutions to this problem by variational method for $p\in(1,n)$. However, the smoothness and uniqueness of solutions are still open. Notice that the $p$-capacitary Orlicz-Minkowski problem can be converted equivalently to a Monge-Ampère type equation in smooth case: \begin{align}\label{0.1} fϕ(h_K)|\nablaΨ|^p=τG \end{align} for $p\in(1,n)$ and some constant $τ>0$, where $f$ is a positive function defined on the unit sphere $\mathcal{S}^{n-1}$, $ϕ$ is a continuous positive function defined in $(0,+\infty)$, and $G$ is the Gauss curvature. In this paper, we confirm the existence of smooth solutions to $p$-capacitary Orlicz-Minkowski problem with $p\in(1,n)$ for the first time by a class of inverse Gauss curvature flows, which converges smoothly to the solution of Equation (\ref{0.1}). Furthermore, we prove the uniqueness result for Equation (\ref{0.1}) in a special case.

math.AP↗

arXiv2022

Scene Graph Generation: A Comprehensive Survey

Deep learning techniques have led to remarkable breakthroughs in the field of generic object detection and have spawned a lot of scene-understanding tasks in recent years. Scene graph has been the focus of research because of its powerful semantic representation and applications to scene understanding. Scene Graph Generation (SGG) refers to the task of automatically mapping an image into a semantic structural scene graph, which requires the correct labeling of detected objects and their relationships. Although this is a challenging task, the community has proposed a lot of SGG approaches and achieved good results. In this paper, we provide a comprehensive survey of recent achievements in this field brought about by deep learning techniques. We review 138 representative works that cover different input modalities, and systematically summarize existing methods of image-based SGG from the perspective of feature extraction and fusion. We attempt to connect and systematize the existing visual relationship detection methods, to summarize, and interpret the mechanisms and the strategies of SGG in a comprehensive way. Finally, we finish this survey with deep discussions about current existing problems and future research directions. This survey will help readers to develop a better understanding of the current research status and ideas.

cs.CV↗

arXiv2022

The Lp Minkowski problem for q-torsional rigidity

In this paper, we introduce the so-called $L_p$ $q$-torsional measure for $p\in\mathbb{R}$ and $q>1$ by establishing the $L_p$ variational formula for the $q$-torsional rigidity of convex bodies without smoothness conditions. Moreover, we achieve the existence of solutions to the $L_p$ Minkowski problem $w.r.t.$ the $q$-torsional rigidity for discrete measure and general measure when $0 1$.

math.DG↗

arXiv2019

Cross-lingual Data Transformation and Combination for Text Classification

Text classification is a fundamental task for text data mining. In order to train a generalizable model, a large volume of text must be collected. To address data insufficiency, cross-lingual data may occasionally be necessary. Cross-lingual data sources may however suffer from data incompatibility, as text written in different languages can hold distinct word sequences and semantic patterns. Machine translation and word embedding alignment provide an effective way to transform and combine data for cross-lingual data training. To the best of our knowledge, there has been little work done on evaluating how the methodology used to conduct semantic space transformation and data combination affects the performance of classification models trained from cross-lingual resources. In this paper, we systematically evaluated the performance of two commonly used CNN (Convolutional Neural Network) and RNN (Recurrent Neural Network) text classifiers with differing data transformation and combination strategies. Monolingual models were trained from English and French alongside their translated and aligned embeddings. Our results suggested that semantic space transformation may conditionally promote the performance of monolingual models. Bilingual models were trained from a combination of both English and French. Our results indicate that a cross-lingual classification model can significantly benefit from cross-lingual data by learning from translated or aligned embedding spaces.

cs.IR↗

arXiv2019

Some Permanence for Large Subalgebra

In this paper, we give two properties of C*-algebra that could be deduced from the properties of its large subalgebra. Let A be an infinite dimensional simple unital C*-algebra and let B be a centrally large subalgebra of A, we prove that A has real rank zero if B has real rank zero. If A is stablely fnite in addition, B is a large subalgebra of A, we prove that B has local weak comparison if A has local weak comparison, and A has local weak comparison if M2(B) has local weak comparison. As a consequence, we show that A has weak comparison if and only if B has weak comparison. These results could be used to study some properties of C*-algebra from its large subalgebra or centrally large subalgebra.

math.OA↗