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Xuefeng Xu

Publications and source records attributed to Xuefeng Xu.

At least 19 recordsLinked to original sources

FedPS: Federated Preprocessing for structured data via aggregated Statistics

Federated Learning (FL) enables multiple parties to collaboratively train machine learning models without sharing raw data. However, before training, data must be preprocessed to address missing values, inconsistent formats, and heterogeneous feature scales. This preprocessing stage is critical for model performance but is largely overlooked in FL research. In practical FL systems, privacy constraints prohibit centralizing raw data, while communication efficiency introduces further challenges for distributed preprocessing. We introduce FedPS, a framework for federated data preprocessing based on aggregated statistics. FedPS leverages data-sketching techniques to efficiently summarize local datasets while preserving essential statistical information. Building on these summaries, we design federated algorithms for feature scaling, encoding, discretization, and missing-value imputation, and extend preprocessing-related models such as Bayesian Linear Regression to both horizontal and vertical FL settings. FedPS provides flexible, communication-efficient, and consistent preprocessing pipelines for practical FL deployments.

cs.LG

Federated Computation of ROC and PR Curves

Receiver Operating Characteristic (ROC) and Precision-Recall (PR) curves are fundamental tools for evaluating machine learning classifiers, offering detailed insights into the trade-offs between true positive rate vs. false positive rate (ROC) or precision vs. recall (PR). However, in Federated Learning (FL) scenarios, where data is distributed across multiple clients, computing these curves is challenging due to privacy and communication constraints. Specifically, the server cannot access raw prediction scores and class labels, which are used to compute the ROC and PR curves in a centralized setting. In this paper, we propose a novel method for approximating ROC and PR curves in a federated setting by estimating quantiles of the prediction score distribution under distributed differential privacy. We provide theoretical bounds on the Area Error (AE) between the true and estimated curves, demonstrating the trade-offs between approximation accuracy, privacy, and communication cost. Empirical results on real-world datasets demonstrate that our method achieves high approximation accuracy with minimal communication and strong privacy guarantees, making it practical for privacy-preserving model evaluation in federated systems.

cs.LG

Power Transform Revisited: Numerically Stable, and Federated

Power transforms are popular parametric methods for making data more Gaussian-like, and are widely used as preprocessing steps in statistical analysis and machine learning. However, we find that direct implementations of power transforms suffer from severe numerical instabilities, which can lead to incorrect results or even crashes. In this paper, we provide a comprehensive analysis of the sources of these instabilities and propose effective remedies. We further extend power transforms to the federated learning setting, addressing both numerical and distributional challenges that arise in this context. Experiments on real-world datasets demonstrate that our methods are both effective and robust, substantially improving stability compared to existing approaches.

cs.LG

Variations of saturation vapor pressure and evaporation rate of liquids with their vaporization enthalpy

The phase transition enthalpy of condensed materials can be altered by factors such as electric fields, and such variations in turn affect physical and chemical behaviors including phase equilibrium. However, due to the neglect of non-expansion work, the Clapeyron equation does not account for the effect of changes in phase transition enthalpy on equilibrium. In this paper, by analyzing the electric-field-induced changes in phase transition enthalpy and incorporating the non-expansion work performed on the system, we extended both the Clapeyron and Clausius-Clapeyron equations to explicitly include variations in phase transition enthalpy. Building upon these extensions, analytical expressions for the vapor pressure of liquids and for the total evaporation rate of sessile liquid droplets as functions of the change in vaporization enthalpy have been derived, showing that an approximately 1% decrease in vaporization enthalpy of a liquid can cause an increase of about 20% in its vapor pressure and an almost twofold increase in its evaporation rate. The theoretical predictions by the present equations were compared and found to be in good agreement with the experimental observations.

cond-mat.soft

Convergence analysis of two-grid methods for symmetric positive semidefinite systems

Two-grid theory plays a fundamental role in the design and analysis of multigrid methods. This paper is devoted to a new convergence analysis of two-grid methods for singular and symmetric positive semidefinite systems. Specifically, we derive a concise identity for characterizing the convergence factor of two-grid methods, with the Moore--Penrose inverse of coarse-grid matrix being used as a coarse solver. Furthermore, we present a convergence estimate for two-grid methods with approximate coarse solvers. Our new theory does not require any additional assumptions on the coefficient matrix, especially on its null space.

math.NA

Effect of UV light irradiation on charge neutralization in XPS measurements

When XPS analyses are performed on insulator surfaces, shift and deformation of spectra peaks typically take place due to the surface charging. To achieve reliable XPS measurements, neutralization techniques have been widely adopted but their effectiveness are still limited, and thus, new neutralization technologies are urgently needed. Here, stable XPS spectra in which all the peaks undergo a reduced and nearly constant shift without significant deformation and broadening were obtained by introducing the UV light irradiation, implying that the introduction of the UV light can not only greatly attenuate the strength but also significantly improve both the temporal stability and the spatial uniformity of the surface charging during XPS measurements. This phenomenon, referred to as UV-assisted neutralization in this article, was found as effective as the most commonly used dual beam charge neutralization. Further observations show that the suppression of the charging issue comes from the adsorption of the UV-excited photoelectrons onto the X-ray irradiation region. This neutralization method, combined with the binding energy referencing, can be expected to become a promising alternative technique for solving the charging issues in XPS measurements.

physics.ins-det

Multiphoton fusion of light nuclei in intense laser fields

We investigate the fusion cross sections of light nuclei in the presence of linearly polarized intense laser fields. By combining the Coulomb-Volkov solutions with the complex spherical square-well nuclear potential, we derive an explicit formulation of the multiphoton cross section in a self-consistent manner. Our analysis is specifically focused on deuteron-triton (DT) and proton-boron (p$^{11}{\rm B}$) fusion reactions, both of which have garnered widespread attention. The theoretical results reveal that, under conditions of longer laser wavelengths and lower incident particle kinetic energies, a few thousands of photons can participate in the fusion reactions, resulting in a substantial enhancement of fusion cross sections by almost ten orders of magnitude. We elucidate the multiphoton mechanism underlying these findings and discuss their implications.

nucl-th

Convergence analysis of two-grid methods for nonsymmetric positive definite systems

The convergence theory of multigrid methods for symmetric positive definite systems is well established. For nonsymmetric systems, however, the corresponding theory remains far from mature. Two-grid analysis is fundamental to the design and analysis of multigrid methods. This paper presents a convergence analysis of two-grid methods for nonsymmetric positive definite systems. When the coarse-grid system is solved exactly, we derive a succinct identity for the two-grid convergence factor measured in a smoother-induced norm. More generally, under mild assumptions, we develop a convergence theory for inexact two-grid methods, where convergence is measured in a generic norm.

math.NA

Convergence analysis of two-level methods with general coarse solvers

Multilevel methods are among the most efficient numerical methods for solving large-scale linear systems that arise from discretized partial differential equations. The fundamental module of such methods is a two-level procedure, which consists of compatible relaxation and coarse-level correction. Regarding two-level convergence theory, most previous works focus on the case of exact (Galerkin) coarse solver. In practice, however, it is often too costly to solve the Galerkin coarse-level system exactly when its size is relatively large. Compared with the exact case, the convergence theory of inexact two-level methods is of more practical significance, while it is still less developed in the literature, especially when nonlinear coarse solvers are used. In this paper, we establish a general framework for analyzing the convergence of inexact two-level methods, in which the coarse-level system is solved approximately by an inner iterative procedure. The framework allows us to use various (linear, nonlinear, deterministic, randomized, or hybrid) solvers in the inner iterations, as long as the corresponding accuracy estimates are available.

math.NA

A new characterization of the convergence factor of two-level methods

Multilevel methods are among the most efficient numerical methods for solving large-scale systems of equations that arise from discretized partial differential equations. Two-level convergence theory plays a fundamental role in the analysis and design of multilevel methods. In this paper, we present a concise and easy-to-use identity for characterizing the convergence factor of two-level methods, whose hierarchical spaces can be either overlapping or non-overlapping. In order to illustrate its usability and convenience, we give several applications, which offer new insights into the design of multilevel methods.

math.NA

Convergence analysis of inexact two-grid methods: A theoretical framework

Multigrid is one of the most efficient methods for solving large-scale linear systems that arise from discretized partial differential equations. As a foundation for multigrid analysis, two-grid theory plays an important role in motivating and analyzing multigrid algorithms. For symmetric positive definite problems, the convergence theory of two-grid methods with exact solution of the Galerkin coarse-grid system is mature, and the convergence factor of exact two-grid methods can be characterized by an identity. Compared with the exact case, the convergence theory of inexact two-grid methods (i.e., the coarse-grid system is solved approximately) is of more practical significance, while it is still less developed in the literature (one reason is that the error propagation matrix of inexact coarse-grid correction is not a projection). In this paper, we develop a theoretical framework for the convergence analysis of inexact two-grid methods. More specifically, we present two-sided bounds for the energy norm of the error propagation matrix of inexact two-grid methods, from which one can readily obtain the identity for exact two-grid convergence. As an application, we establish a unified convergence theory for multigrid methods, which allows the coarsest-grid system to be solved approximately.

math.NA

A new analytical framework for the convergence of inexact two-grid methods

Two-grid methods with exact solution of the Galerkin coarse-grid system have been well studied by the multigrid community: an elegant identity has been established to characterize the convergence factor of exact two-grid methods. In practice, however, it is often too costly to solve the Galerkin coarse-grid system exactly, especially when its size is large. Instead, without essential loss of convergence speed, one may solve the coarse-grid system approximately. In this paper, we develop a new framework for analyzing the convergence of inexact two-grid methods: two-sided bounds for the energy norm of the error propagation matrix of inexact two-grid methods are presented. In the framework, a restricted smoother involved in the identity for exact two-grid convergence is used to measure how far the actual coarse-grid matrix deviates from the Galerkin one. As an application, we establish a unified convergence theory for multigrid methods.

math.NA

The electron transfer dynamics in the contact electrification and its effects on the intensity of triboluminescence

With the growing threat of energy crisis and the increasing need to power microelectronic devices, people are seeking potential alternative energies that can replace the conventional sources such as fossil fuels. Due to its simple structure, low cost, and high performance, the triboelectric nanogenerator (TENG) which is based on the contact electrification has become one of the most promising candidates. Although plays a crucial role in determining the amount of charge transfer of TENG, the fundamental mechanism that underlies the charge transfer in the contact electrification of insulator-insulator contacts has still not been completely understood. In this paper, the dynamics of charge transfer in the contact electrification is investigated by observing the triboluminescence of the sliding contacts and a theoretical model is proposed for the electrification of insulator-insulator contacts. In the present "Capacitor model", the electron tunneling is assumed to be the dominating mechanism in the electrification and the driving force for the electron transfer is the contact potential difference, and thus, the electrification is considered as a charging process of the capacitor formed by the contact surfaces. The consistency between the predictions by the present model and the experiments may confirm again that the electron transfer is the dominant process in the contact electrification of insulator-insulator contacts.

physics.app-ph

On the perturbation of an $L^2$-orthogonal projection

The $L^2$-orthogonal projection onto a subspace is an important mathematical tool, which has been widely applied in many fields such as linear least squares problems, eigenvalue problems, ill-posed problems, and randomized algorithms. In some numerical applications, the entries of a matrix will seldom be known exactly, so it is necessary to develop some bounds to characterize the effects of the uncertainties caused by matrix perturbation. In this paper, we establish new perturbation bounds for the $L^2$-orthogonal projection onto the column space of a matrix, which involve upper (lower) bounds and combined upper (lower) bounds. The new bounds contain some sharper counterparts of the existing ones. Numerical examples are also given to illustrate our theoretical results.

math.NA

On the perturbation of the Moore-Penrose inverse of a matrix

The Moore-Penrose inverse of a matrix has been extensively investigated and widely applied in many fields over the past decades. One reason for the interest is that the Moore-Penrose inverse can succinctly express some important geometric constructions in finite-dimensional spaces, such as the orthogonal projection onto a subspace and the linear least squares problem. In this paper, we establish new perturbation bounds for the Moore-Penrose inverse under the Frobenius norm, some of which are sharper than the existing ones.

math.NA

On the Ideal Interpolation Operator in Algebraic Multigrid Methods

Various algebraic multigrid algorithms have been developed for solving problems in scientific and engineering computation over the past decades. They have been shown to be well-suited for solving discretized partial differential equations on unstructured girds in practice. One key ingredient of algebraic multigrid algorithms is a strategy for constructing an effective prolongation operator. Among many questions on constructing a prolongation, an important question is how to evaluate its quality. In this paper, we establish new characterizations (including sufficient condition, necessary condition, and equivalent condition) of the so-called ideal interpolation operator. Our result suggests that, compared with common wisdom, one has more room to construct an ideal interpolation, which can provide new insights for designing algebraic multigrid algorithms. Moreover, we derive a new expression for a class of ideal interpolation operators.

math.NA

Effects of the Position Reversal of Friction Pairs on the Strength of Tribocharging and Tribodischarging

The friction-induced charging (i.e., tribocharging) and the following discharging (referred here as tribodischarging) are always believed to have negative effects on the daily life and on the industrial production. Thus, how to inhibit the tribocharging and the tribodischarging has caused wide public concern. Because the discharge caused by the electrical breakdown of the ambient gas is generally accompanied with the generation of light, we investigated here the tribocharging and the tribodischarging by observing the light emitted during friction. We found that the position reversal of the friction pair has a dramatic impact on the intensity of the tribo-induced light. Experimental results show that an intense light is produced when a stationary Al2O3 disk is sliding on a rotating SiO2 disk, but only a weak light is observed for the case of a stationary SiO2 disk and a rotating Al2O3 disk. This means that the process of the tribocharging and the tribodischarging can be significantly influenced owing to the change in the relative position of the friction couple. The experimentally measured polarities of the tribo-induced charge on the friction surfaces further indicated that the strong discharging occurs when the rotating surface is negatively charged. The reason for the difference in the intensity of the tribocharging and tribodischarging can be attributed to the combined effects of the contact potential difference and the temperature gradient between the contacting surfaces on the charge transfer when friction. Finally, a simple, low cost, yet effective approach, i.e., just keep the friction partner whose surface is tribo-induced negatively charged as the stationary one, can be utilized to suppress the intensity of the tribocharging and the tribodischarging. This work may provide potential applications in numerous areas of science and engineering and also in the everyday life.

cond-mat.mtrl-sci