arXiv subjects

Wenhua Zhao

Publications and source records attributed to Wenhua Zhao.

At least 19 recordsLinked to original sources

arXiv2026

Time- and frequency-domain study for electron beams penetrating dielectric nanospheres: fingerprints of Cherenkov and transition radiation

We present a theoretical study of Cherenkov and transition radiation for swift electron beams penetrating dielectric nanospheres using material models of different sophistication. Specifically, we perform a combined time-domain (numerically, via the discontinuous Galerkin time-domain method) and frequency-domain (numerically and analytically, via Mie-based theory) study, including the induced-field distribution, cathodoluminescence (CL) multipole/directional decomposition, as well as the time-dependent angular power flow. For low velocities below the Cherenkov threshold, we show that transition radiation is dominant in the far-field CL, and the near-fields at the transition points are primarily responsible for the main features observed in the far-field. For higher velocities far beyond the Cherenkov threshold, we identify the fingerprints of the observable Cherenkov front. Specifically, a constant-permittivity model allows us to isolate the respective contributions of CR and TR to the far-field radiation, thereby facilitating the interpretation of the results for a more realistic material model that includes material resonances. Our combined time- and frequency-domain framework provides a direct view of radiative excitation channels for swift electron beams penetrating dielectric nanoparticles, thereby revealing their interplay beyond the conventional frequency-domain analyses.

physics.optics↗

arXiv2026

LLM-Metrics: Measuring Research Impact Through Large Language Model Memory

Citation counts remain the dominant metric for assessing research impact, yet they suffer from well-documented limitations: temporal lag, disciplinary bias, and Matthew effects. Here we propose LLM-Metrics, a research-impact assessment metric derived from the parametric memory of large language models (LLMs). The central hypothesis is that high-impact papers receive greater exposure in the academic community, that this exposure enters LLM training data in textual form, and that models consequently form stronger parametric memory of these papers. We designed four types of multiple-choice probes, covering title recognition, author recognition, method recognition, and venue recognition, and evaluated 549 computer science papers published in 2023-2024 across 17 LLMs spanning 0.5B to 72B parameters from six vendors. Of the 17 models, 15 produced positive predictions, 9 of which were significant at p less than 0.05, with an overall Spearman correlation of rho = 0.1495 and p = 0.0004 against citation counts. Three additional findings support the proposed mechanism. First, the predictive signal was stronger for 2024 papers, rho = 0.1880, whose citation counts were near zero at model-training time, reducing the plausibility of a simple reverse-causality explanation. Second, author-recognition probes showed the strongest discriminative power, consistent with an exposure-driven memory mechanism. Third, model scale and predictive power were non-monotonic: a 3B-parameter model, Llama-3.2-3B-Instruct, with rho = 0.1829, outperformed most larger models, supporting a selective-memory hypothesis in which the limited capacity of smaller models can serve as an effective information filter. LLM-Metrics offers a real-time, cross-disciplinary, citation-independent paradigm for research assessment.

cs.AI↗

arXiv2026

An affirmative answer to a question on connectivity of p-subgroup posets with irreducible characters

Let $p$ be a prime, $e$ a nonnegative integer, and G a finite p-group with $p^{e+1}$ dividing $|G|$. Let I be the intersection of all subgroups of order $p^{e+1}$ in $G$. It is proved that $|I\cap Z(G)|\le |π_0(Γ_{p,e}(G))|\le {\rm Irr}(I)$, where $Γ_{p,e}(G)$, whose connected components is denoted by $π_0(Γ_{p,e}(G))$, is the poset consisting of all pairs $(H, φ)$ with $H \le G$, $|H|\ge p^{e+1}$, and $φ\in {\rm Irr}(H)$. Hence, an affirmative answer to Question 2 raised by Meng and Yang is obtained.

math.GR↗

arXiv2025

Mitigating Think-Answer Mismatch in LLM Reasoning Through Noise-Aware Advantage Reweighting

Group-Relative Policy Optimization (GRPO) is a key technique for training large reasoning models, yet it suffers from a critical vulnerability: the \emph{Think-Answer Mismatch}, where noisy reward signals corrupt the learning process. This problem is most severe in unbalanced response groups, paradoxically degrading the signal precisely when it should be most informative. To address this challenge, we propose Stable Group-Relative Policy Optimization (S-GRPO), a principled enhancement that derives optimal, noise-aware advantage weights to stabilize training. Our comprehensive experiments on mathematical reasoning benchmarks demonstrate S-GRPO's effectiveness and robustness. On various models, S-GRPO significantly outperforms DR. GRPO, achieving performance gains of +2.5% on Qwen-Math-7B-Base, +2.2% on Llama-3.2-3B-Base, and +2.4% on Qwen-Math-1.5B-Instruct. Most critically, while standard GRPO fails to learn under 20% synthetic reward noise, S-GRPO maintains stable learning progress. These results highlight S-GRPO's potential for more robust and effective training of large-scale reasoning models. \footnote{Code and data are available at: https://github.com/shenpeijun0212/S-GRPO

cs.LG↗

arXiv2025

Feedback cooling of fermionic atoms in optical lattices

We discuss the preparation of topological insulator states with fermionic ultracold atoms in optical lattices by means of measurement-based Markovian feedback control. The designed measurement and feedback operators induce an effective dissipative channel that stabilizes the desired insulator state, either in an exact way or approximately in the case where additional experimental constraints are assumed. Successful state preparation is demonstrated in one-dimensional insulators as well as for Haldane's Chern insulator, by calculating the fidelity between the target ground state and the steady state of the feedback-modified master equation. The fidelity is obtained numerically through exact diagonalization or via time evolution of the system with moderate sizes. For larger 2D systems, we compare the mean occupation of the single-particle eigenstates for the ground and steady state computed through mean-field kinetic equations.

cond-mat.quant-gas↗

arXiv2025

ICH-Qwen: A Large Language Model Towards Chinese Intangible Cultural Heritage

The intangible cultural heritage (ICH) of China, a cultural asset transmitted across generations by various ethnic groups, serves as a significant testament to the evolution of human civilization and holds irreplaceable value for the preservation of historical lineage and the enhancement of cultural self-confidence. However, the rapid pace of modernization poses formidable challenges to ICH, including threats damage, disappearance and discontinuity of inheritance. China has the highest number of items on the UNESCO Intangible Cultural Heritage List, which is indicative of the nation's abundant cultural resources and emphasises the pressing need for ICH preservation. In recent years, the rapid advancements in large language modelling have provided a novel technological approach for the preservation and dissemination of ICH. This study utilises a substantial corpus of open-source Chinese ICH data to develop a large language model, ICH-Qwen, for the ICH domain. The model employs natural language understanding and knowledge reasoning capabilities of large language models, augmented with synthetic data and fine-tuning techniques. The experimental results demonstrate the efficacy of ICH-Qwen in executing tasks specific to the ICH domain. It is anticipated that the model will provide intelligent solutions for the protection, inheritance and dissemination of intangible cultural heritage, as well as new theoretical and practical references for the sustainable development of intangible cultural heritage. Furthermore, it is expected that the study will open up new paths for digital humanities research.

cs.CL↗

arXiv2025

Relativistic electron energy-loss spectroscopy in cylindrical waveguides and holes

Swift electrons passing near or through metallic structures have proven to be an excellent tool for studying plasmons and other types of confined optical modes involving collective charge oscillations in the materials hybridized with electromagnetic fields. In this work, we provide a general analytical framework for the simulation of electron energy-loss spectroscopy (EELS) in infinite systems with cylindrical symmetry, such as wires, holes, and optical fibers. While EELS theory is well developed for electrons moving parallel to the direction of translational symmetry, we introduce closed-form analytical solutions for perpendicular electron trajectories. These analytical results are corroborated by comparison to numerical simulations based on a frequency-domain boundary-element method and a discontinuous-Galerkin time-domain finite-element method. Numerical methods further allow us to study termination effects in finite-sized cylindrical objects such as nanorods. The present study of the interaction between free electrons and cylindrically symmetric photonics systems can find application in the analysis of EELS spectra and the design of free-electron--photonic hybrid systems.

physics.optics↗

arXiv2024

Real-time surface plasmon polariton propagation in silver nanowires

Electron microscopy techniques such as electron energy-loss spectroscopy (EELS) facilitate the spatio-spectral characterization of plasmonic nanostructures. In this work, a time-dependent perspective is presented, which significantly enhances the utility of EELS. Specifically, silver nanowires offer the material and geometric features for various high-quality plasmonic excitations. This provides an ideal illustrative system for combined experimental-theoretical analyses of the different plasmonic excitations and their real-time dynamics. It is demonstrated how the plasmonic excitations propagating inside the wire repeatedly interact with the swift electrons in an EELS configuration. In addition, the role of azimuthal modes, often overlooked for very thin wires, is observed and analyzed in both the energy-loss spectrum and the dynamical perspective. Such a complete understanding of the interaction of electrons and plasmonic excitation is key for the design of efficient plasmonic sensors, the study of hot electron dynamics in metals, and applications in the context of electron quantum optics, where full control of the spatial and temporal characteristics of the fields at the nanometer and femtosecond scales is highly desirable.

physics.optics↗

arXiv2024

Electron beams traversing spherical nanoparticles: analytic and numerical treatment

We present an analytic, Mie theory-based solution for the energy-loss and the photon-emission probabilities in the interaction of spherical nanoparticles with electrons passing nearby and through them, in both cathodoluminescence and electron energy-loss spectroscopies. In particular, we focus on the case of penetrating electron trajectories, for which the complete fully electrodynamic and relativistic formalism has not been reported as yet. We exhibit the efficiency of this method in describing collective excitations in matter through calculations for a dispersive and lossy system, namely a sphere described by a Drude permittivity. Subsequently, we use the analytic solution to corroborate the implementation of electron-beam sources in a state-of-the-art numerical method for problems in electrodynamics, the discontinuous Galerkin time-domain (DGTD) method. We show that the two approaches produce spectra in good mutual agreement, and demonstrate the versatility of DGTD via simulations of spherical nanoparticles characterized by surface roughness. The possibility of simultaneously employing both kinds of calculations (analytic and numerical) facilitates a better understanding of the rich optical response of nanophotonic architectures excited by fast electron beams.

cond-mat.mes-hall↗

arXiv2024

A local to global question for linear functionals

Let $F$ be an algebraically closed field and let $n\geq 3$. Consider $V=F^n$ with standard basis $\{\vec{e}_1,\ldots,\vec{e}_n\}$ and its dual space $V^*= {\mathrm{Hom}}_{F-{\mathrm{lin}}}(V,F)$ with dual basis $\{y_1,\ldots,y_n\}\subseteq V^*$ and let $\vec{y} = \sum_i y_i\otimes \vec{e}_i\in V^*\otimes V$. Let $d<n$ and consider the vectors $\vec{q}_1,\ldots,\vec{q}_d\in V^*\otimes V$. In this note we consider the question of whether $\vec{y}(\vec{v}) = \vec{v} \in Span_F(\vec{q}_1(\vec{v}),\ldots,\vec{q}_d(\vec{v}))$ for all $\vec{v}\in V$ implies that $\vec{y}\in Span_F(\vec{q}_1,\ldots,\vec{q}_d)$. We show this is true for $d=1$ or $d=2$, but that additional properties are needed for $d\geq 3$. We then interpret this result in terms of subspaces of $M_n(F)$ that do not contain any rank 1 idempotents.

math.AG↗

arXiv2022

Variability of wave power production of the M4 machine at two energetic open ocean locations: off Albany, Western Australia and at EMEC, Orkney, UK

Since intermittent and highly variable power supply is undesirable, quantifying power yield fluctuations of wave energy converters (WECs) aids with assessment of potential deployment sites. This paper presents analysis of 3-hourly, monthly, seasonal, and inter-annual variability of power output of the M4 WEC. We compare expected performance from deployment at two wave energy hotspots: off Albany on the south-western coast of Australia and off the European Marine Energy Centre (EMEC) at Orkney, UK. We use multi-decadal wave hindcast data to predict the power that would have been generated by M4 WEC machines. The M4 machine, as a floating articulated device which extracts energy from flexing motion about a hinge, is sized according to a characteristic wavelength of the local wave climate. Using probability distributions, production duration curves, and coefficients of variation we demonstrate larger variability of the 3-hourly power yield at Orkney compared to Albany. At longer timescales, seasonal trends are highlighted through average monthly power values. From a continuity of supply perspective, we investigate occurrences of low production at three different threshold levels and calculate duration and likelihood of such events. Orkney is found to suffer from more persistent lows, causing a more intermittent power output. We also consider the effect of machine size on its power performance. Smaller machines are found to more effectively smooth out the stochastic nature of the underlying wave resource.

physics.ao-ph↗

arXiv2022

Existence of Nonzero Trace-Zero Idempotents in the Group Algebras of Finite Groups

Let $G$ be a finite group and $K$ a splitting field of $G$ of characteristic $p>0$. Denote by $KG$ the group algebra of $G$ over $K$ and $Z(KG)$ the center of $KG$. Let $V_G$ be the $K$-subspace of trace-zero elements of $KG$. We give some numerical sufficient and necessary conditions for $V_G$ and $V_G\cap Z(KG)$, respectively, to be Mathieu subspaces of $KG$ in terms of the degrees of irreducible representations of $G$ over $K$. The same numerical conditions also characterize the finite groups $G$ that $KG$ has no nonzero trace-zero idempotents and the finite groups $G$ that $KG$ has no nonzero central trace-zero idempotents, respectively.

math.RA↗

arXiv2022

Some Open Problems on Locally Finite or Locally Nilpotent Derivations and ${\mathcal E}$-Derivations

Let $R$ be a commutative ring and $\mathcal A$ an $R$-algebra. An $R$-$\mathcal E$-derivation of $\mathcal A$ is an $R$-linear map of the form $\operatorname{I}-ϕ$ for some $R$-algebra endomorphism $ϕ$ of $\mathcal A$, where $\operatorname{I}$ denotes the identity map of $\mathcal A$. In this paper we discuss some open problems on whether or not the image of a locally finite $R$-derivation or $R$-$\mathcal E$-derivation of $\mathcal A$ is a Mathieu subspace [Z2, Z3] of $\mathcal A$, and whether or not a locally nilpotent $R$-derivation or $R$-$\mathcal E$-derivation of $\mathcal A$ maps every ideal of $\mathcal A$ to a Mathieu subspace of $\mathcal A$. We propose and discuss two conjectures which state that both questions above have positive answers if the base ring $R$ is a field of characteristic zero. We give some examples to show the necessity of the conditions of the two conjectures, and discuss some positive cases known in the literature. We also show some cases of the two conjectures. In particular, both the conjectures are proved for locally finite or locally nilpotent algebraic derivations and $\mathcal E$-derivations of integral domains of characteristic zero.

math.RA↗

arXiv2022

The Radical of the Kernel of a Certain Differential Operator and Applications to Locally Algebraic Derivations

Let $R$ be a commutative ring, $\mathcal A$ an $R$-algebra (not necessarily commutative) and $V$ an $R$-subspace or $R$-submodule of $\mathcal A$. By the radical of $V$ we mean the set of all elements $a\in \mathcal A$ such that $a^m\in V$ for all $m\gg 0$. We derive (and show) some necessary conditions satisfied by the elements in the radicals of the kernel of some (partial) differential operators, such as all differential operators of commutative algebras; the differential operators $P(D)$ of (noncommutative) $\mathcal A$ with certain conditions, where $P(\cdot)$ is a polynomial in $n$ commutative free variables and $D=(D_1, D_2, \dots, D_n)$ are either commuting locally finite $R$-derivations or commuting $R$-derivations of $\mathcal A$ such that for each $1\le i\le n$, $\mathcal A$ can be decomposed as a direct sum of the generalized eigen-subspaces of $D_i$; etc. In particular, we show that the kernel of certain differential operators of $\mathcal A$ is a Mathieu subspace (see \cite{GIC, MS}) of $\mathcal A$. We then apply some results above to study $R$-derivations of $\mathcal A$, which are locally algebraic or locally integral over $R$. In particular, we show that if $R$ is an integral domain of characteristic zero and $\mathcal A$ is reduced and torsion-free as an $R$-module, then $\mathcal A$ has no nonzero locally algebraic $R$-derivations. We also show a formula for the determinant of a differential vandemonde matrix over a commutative algebra $\mathcal A$. This formula not only provides some information for the elements in the radical of the kernel of all ordinary differential operators of $\mathcal A$, but also is interesting on its own right.

math.RA↗

arXiv2022

On the Image Conjecture for Locally Finite Derivations and $\mathcal E$-Derivations

Some cases of the LFED Conjecture, proposed by the second author [Z3], for certain integral domains are proved. In particular, the LFED Conjecture is completely established for the field of fractions $k(x)$ of the polynomial algebra $k[x]$, the formal power series algebra $k[[x]]$ and the Laurent formal power series algebra $k[[x]][x^{-1}]$, where $x=(x_1, x_2, \dots, x_n)$ denotes $n$ commutative free variables and $k$ a field of characteristic zero. Furthermore, the relation between the LFED Conjecture and the Duistermaat-van der Kallen Theorem [DK] is also discussed and emphasized.

math.AC↗

arXiv2022

A Family of Maximal Mathieu Subspaces of Matrix Algebras

Let $F$ be a field. In this note we give a construction for a family of maximal Mathieu subspaces (or Mathieu-Zhao subspaces) of the matrix algebras $M_n(F)$ $(n\ge 2)$. As an application we also give a classification of Mathieu subspaces of $M_2(F)$ under the condition that $F$ is algebraically closed.

math.RA↗

arXiv2017

Images of Ideals under Derivations and $\mathcal E$-Derivations of Univariate Polynomial Algebras over a Field of Characteristic Zero

Let $K$ be a field of characteristic zero and $x$ a free variable. A $K$-$\mathcal E$-derivation of $K[x]$ is a $K$-linear map of the form $\operatorname{I}-ϕ$ for some $K$-algebra endomorphism $ϕ$ of $K[x]$, where $\operatorname{I}$ denotes the identity map of $K[x]$. In this paper we study the image of an ideal of $K[x]$ under some $K$-derivations and $K$-$\mathcal E$-derivations of $K[x]$. We show that the LFED conjecture proposed in [Z4] holds for all $K$-$\mathcal E$-derivations and all locally finite $K$-derivations of $K[x]$. We also show that the LNED conjecture proposed in [Z4] holds for all locally nilpotent $K$-derivations of $K[x]$, and also for all locally nilpotent $K$-$\mathcal E$-derivations of $K[x]$ and the ideals $uK[x]$ such that either $u=0$, or $\operatorname{deg}\, u\le 1$, or $u$ has at least one repeated root in the algebraic closure of $K$. As a bi-product, the homogeneous Mathieu subspaces (Mathieu-Zhao spaces) of the univariate polynomial algebra over an arbitrary field have also been classified.

math.AC↗

arXiv2017

The LNED and LFED Conjectures for Algebraic Algebras

Let $K$ be a field of characteristic zero and $\mathcal A$ a $K$-algebra such that all the $K$-subalgebras generated by finitely many elements of $\mathcal A$ are finite dimensional over $K$. A $K$-$\mathcal E$-derivation of $\mathcal A$ is a $K$-linear map of the form $\operatorname{I}-ϕ$ for some $K$-algebra endomorphism $ϕ$ of $\mathcal A$, where $\operatorname{I}$ denotes the identity map of $\mathcal A$. In this paper we first show that for all locally finite $K$-derivations $D$ and locally finite $K$-algebra automorphisms $ϕ$ of $\mathcal A$, the images of $D$ and $\operatorname{I}-ϕ$ do not contain any nonzero idempotent of $\mathcal A$. We then use this result to show some cases of the LFED and LNED conjectures proposed in [Z4]. More precisely, We show the LNED conjecture for $\mathcal A$, and the LFED conjecture for all locally finite $K$-derivations of $\mathcal A$ and all locally finite $K$-$\mathcal E$-derivations of the form $δ=\operatorname{I}-ϕ$ with $ϕ$ being surjective. In particular, both conjectures are proved for all finite dimensional $K$-algebras. Furthermore, some finite extensions of derivations and automorphism to inner derivations and inner automorphisms, respectively, have also been established. This result is not only crucial in the proofs of the results above, but also interesting on its own right.

math.RA↗