arXiv subjects

Dan Li

Publications and source records attributed to Dan Li.

At least 91 records · Page 5Linked to original sources

arXiv2025

Spectral Turán problem for $\mathcal{K}_{3,3}^{-}$-free signed graphs

The classical spectral Turán problem is to determine the maximum spectral radius of an $\mathcal{F}$-free graph of order $n$. Zhai and Wang [Linear Algebra Appl, 437 (2012) 1641-1647] determined the maximum spectral radius of ${C}_{4}$-free graphs of given order. Additionally, Nikiforov obtained spectral strengthenings of the Kővari-Sós-Turán theorem [Linear Algebra Appl, 432 (2010) 1405-1411] when the forbidden graphs are complete bipartite. The spectral Turán problem concerning forbidden complete bipartite graphs in signed graphs has also attracted considerable attention. Let $\mathcal{K}_{s,t}^-$ be the set of all unbalanced signed graphs with underlying graphs $K_{s,t}$. Since the cases where $s=1$ or $t=1$ do not conform to the definition of $\mathcal{K}_{s,t}^-$, it follows that $s,t\geq 2$. Wang and Lin [Discrete Appl. Math, 372 (2025) 164-172] have solved the case of $s=t=2$ since $\mathcal{K}_{2,2}^-$ is $\mathcal{C}_{4}^{-}$ in this situation. This paper gives an answer for $s=t=3$ and completely characterizes the corresponding extremal signed graphs.

math.CO↗

arXiv2025

A Bayesian Ensemble Projection of Climate Change and Technological Impacts on Future Crop Yields

This paper introduces a Bayesian hierarchical modeling framework within a fully probabilistic setting for crop yield estimation, model selection, and uncertainty forecasting under multiple future greenhouse gas emission scenarios. By informing on regional agricultural impacts, this approach addresses broader risks to global food security. Extending an established multivariate econometric crop-yield model to incorporate country-specific error variances, the framework systematically relaxes restrictive homogeneity assumptions and enables transparent decomposition of predictive uncertainty into contributions from climate models, emission scenarios, and crop model parameters. In both in-sample and out-of-sample analyses focused on global wheat production, the results demonstrate significant improvements in calibration and probabilistic accuracy of yield projections. These advances provide policymakers and stakeholders with detailed, risk-sensitive information to support the development of more resilient and adaptive agricultural and climate strategies in response to escalating climate-related risks.

stat.AP↗

arXiv2025

Influence of the external electromagnetic field on the properties of the Novikov-Thorne accretion disk in Kerr spacetime

The Novikov-Thorne accretion disk model is widely employed in astrophysics, yet computing its blackbody spectrum theoretically requires analytical expressions for the orbital parameters -- specific energy, angular momentum, and angular velocity -- of the constituent timelike particles, a task extremely challenging in non-integrable curved spacetimes. In this work, we numerically obtain these orbital parameters for quasi-Keplerian motion in Kerr spacetime with an asymptotically uniform magnetic field using iterative, finite-difference, and interpolation methods, enabling simulations of the disk's energy flux density, temperature, and blackbody spectra across diverse spin parameters, observational inclinations, and magnetic field strengths. We demonstrate that when the magnetic field aligns with the black hole's angular momentum, the disk's radiation positively correlates with field strength, while spectral analysis for our specific black hole mass and accretion rate reveals a conservative detectable threshold of $1.0638 \times 10^{-9}$ T for ambient magnetic fields. This study not only extends the Novikov-Thorne model to non-integrable axisymmetric spacetimes but also establishes the first direct relationship between external magnetic fields and disk properties, providing critical theoretical support for future magnetic environment studies through disk radiation observations.

gr-qc↗

arXiv2025

Global attractor of chemotaxis system with weak degradation and density-dependent motion

This paper investigates the following chemotaxis system featuring weak degradation and nonlinear motility functions \begin{equation}\label{Model1} \begin{cases} u_{t} = (γ(v)u)_{xx} + r - μu, & x \in [0,L],\ t > 0, v_{t} = v_{xx} - v + u, & x \in [0,L],\ t > 0, \end{cases} \end{equation} defined on the bounded interval $[0,L]$ with homogeneous Neumann boundary conditions. The motility function $γ(v)$ satisfies the regularity conditions $γ\in C^{2}[0,\infty)$ with $γ(v) > 0$ for all $v \geq 0$, and has bounded logarithmic derivative in the sense that $\sup_{v\geq 0} \frac{|γ'(v)|^{2}}{γ(v)} < \infty$. Our main results establish three fundamental properties of the system. Firstly, using energy estimate methods, we prove the existence of globally bounded solutions for all positive parameters $r, μ> 0$ and non-negative, non-trivial initial data $u_{0} \in W^{1,\infty}([0,L])$. Secondly, through the construction of an appropriate Lyapunov function, we demonstrate that all solutions $(u,v)$ converge exponentially to the unique constant equilibrium $(r/μ, r/μ)$ in the parameter regime $μ> \frac{H_{0}}{16}$, where $H_{0} := \sup_{v \geq 0} \frac{|γ'(v)|^{2}}{γ(v)}$ quantifies the maximal relative variation of the motility function. Finally, we present numerical results that not only validate the theoretical findings but also investigate the long-term behavior of solutions under diverse parameter configurations and initial conditions in two- and three-dimensional domains, providing valuable benchmarks for future research.

math.AP↗

arXiv2025

Activation Approximations Can Incur Safety Vulnerabilities Even in Aligned LLMs: Comprehensive Analysis and Defense

Large Language Models (LLMs) have showcased remarkable capabilities across various domains. Accompanying the evolving capabilities and expanding deployment scenarios of LLMs, their deployment challenges escalate due to their sheer scale and the advanced yet complex activation designs prevalent in notable model series, such as Llama, Gemma, Mistral. These challenges have become particularly pronounced in resource-constrained deployment scenarios, where mitigating inference bottlenecks is imperative. Among various recent efforts, activation approximation has emerged as a promising avenue for pursuing inference efficiency, sometimes considered indispensable in applications such as private inference. Despite achieving substantial speedups with minimal impact on utility, even appearing sound and practical for real-world deployment, the safety implications of activation approximations remain unclear. In this work, we fill this critical gap in LLM safety by conducting the first systematic safety evaluation of activation approximations. Our safety vetting spans seven state-of-the-art techniques across three popular categories (activation polynomialization, activation sparsification, and activation quantization), revealing consistent safety degradation across ten safety-aligned LLMs. To overcome the hurdle of devising a unified defense accounting for diverse activation approximation methods, we perform an in-depth analysis of their shared error patterns and uncover three key findings. We propose QuadA, a novel safety enhancement method tailored to mitigate the safety compromises introduced by activation approximations. Extensive experiments and ablation studies corroborate QuadA's effectiveness in enhancing the safety capabilities of LLMs after activation approximations.

cs.CR↗

arXiv2025

Enhancing LLM Reasoning for Time Series Classification by Tailored Thinking and Fused Decision

The reasoning capabilities of large language models (LLMs) have significantly advanced their performance by enabling in-depth understanding of diverse tasks. With growing interest in applying LLMs to the time series domain, this has proven nontrivial, as evidenced by the limited efficacy of straightforwardly adapting text-domain reasoning techniques. Although recent work has shown promise in several time series tasks, further leveraging advancements in LLM reasoning remains under-explored for time series classification (TSC) tasks, despite their prevalence and significance in many real-world applications. In this paper, we propose ReasonTSC, a novel framework designed to effectively leverage LLM reasoning for time series classification through both a multi-turn reasoning and a fused decision-making strategy tailored to TSC. Rather than straightforwardly applying existing reasoning techniques or relying solely on LLMs' built-in reasoning capabilities, ReasonTSC first steers the model to think over the essential characteristics of time series data. Next, it integrates predictions and confidence scores from plug-in classifiers, e.g., domain-specific time series models, as in-context examples. Finally, ReasonTSC guides the LLM through a structured reasoning process: it evaluates the initial assessment, backtracks to consider alternative hypotheses, and compares their merits before arriving at a final classification. Extensive experiments and systematic ablation studies demonstrate that ReasonTSC consistently outperforms both existing time series reasoning baselines and plug-in models, and is even capable of identifying and correcting plug-in models' false predictions.

cs.AI↗

arXiv2025

Novel inner shadows of the Kerr black hole with a tilted thin accretion disk

The inner shadow of a black hole, as a projection of the event horizon, is regarded as a potential tool for testing gravitational theories and constraining system parameters. Whether this holds in the case of a tilted accretion disk warrants further investigation. In this paper, we employ a ray-tracing algorithm to simulate images of the Kerr black hole illuminated by a tilted thin accretion disk, with particular attention to the relationship between the inner shadow and system parameters. Our findings reveal that in the case of an equatorial accretion disk, the Kerr black hole exhibits a minimum inner shadow size of $S_{\textrm{min}} = 13.075$ M$^{2}$, where M denotes the black hole mass. This minimum is achieved when the viewing angle is $0^{\circ}$ and the spin parameter approaches $1$. However, with a non-zero disk tilt, the inner shadow exhibits novel configurations -- taking on petal, crescent, or eyebrow shapes -- significantly smaller than $S_{\textrm{min}}$ across various parameter spaces. This indicates that the inner shadow is highly sensitive to the accretion environment, suggesting that caution is needed when using it as a diagnostic tool for black holes. Notably, an observed inner shadow smaller than $S_{\textrm{min}}$ would either indicate the presence of a tilted accretion disk or support the viability of modified gravity. Moreover, in certain parameter spaces, we identify the emergence of a dual-shadow structure, which could also serve as a probe for the tilted accretion disk.

gr-qc↗

arXiv2025

Beyond Dielectrics: Interfacial Water Polarization Governs Graphene-Based Electrochemical Interfaces

Water molecules are traditionally regarded as passive dielectric media in electrochemical systems. In this work, we challenge this conventional perspective using molecular dynamics simulations and theoretical analysis. We show that interfacial water is polarized differently from bulk water and effectively screens the electrostatic potential between ions and the surface. This goes beyond the classic electric double layer (EDL) model, which treated water as merely a passive dielectric. The observed overscreening occurs because a significant portion of water polarization directly responds to the graphene surface, in addition to screening the electrostatic interactions between ions and charged surfaces. Furthermore, we reveal that this surface-induced polarization of interfacial water governs the electric potential distribution and EDL capacitance, and can even invert the electrode surface potential polarity, overriding the contribution of ions. These molecular-level insights lead to a revised EDL model that more accurately describes the electric and chemical potential distributions in the interfacial EDL regions.

physics.chem-ph↗

arXiv2025

The index of unbalanced signed complete graphs whose negative-edge-induced subgraph is ${K}_{2,2}$-minor free

Let $Γ=(K_n,H^-)$ be a signed complete graph with the negative edges induced subgraph $H$. According to the properties of the negative-edge-induced subgraph, characterizing the extremum problem of the index of the signed complete graph is a concern in signed graphs. A graph $G$ is called $H$-minor free if $G$ has no minor which is isomorphic to $H$. In this paper, we characterize the extremal signed complete graphs that achieve the maximum and the second maximum index when $H$ is a $K_{2,2}$-minor free spanning subgraph of $K_n$.

math.CO↗

arXiv2025

MPd5 kagome superconductors studied by density functional calculations

Kagome materials, which are composed of hexagons tiled with a shared triangle, have inspired enormous interest due to their unique structures and rich physical properties; exploring superconducting material systems with new kagome structures is still an important research direction. Here, we predict a type of kagome superconductor, MPd5 (M is a group-IIA metal element), and identify that it exhibits coexistence of superconductivity and nontrivial topological properties. We uncover its phonon-mediated superconductivity by the density functional theory for superconductors, predicting the superconducting transition temperatures (Tc) of 2.64, 2.03, and 1.50 K for CaPd5, SrPd5, and BaPd5, respectively. These Tc can be effectively tuned through the application of external pressure and electron doping. The present results also demonstrate that MPd5 have topological properties; e.g., CaPd5 shows topological nontrivial intersection near the Fermi level (EF). Our results indicate that MPd5 materials can be an emerging material platform with rich exotic physics in their kagome structures, and render themselves excellent candidates for superconducting and advanced functional materials that could be utilized in topological quantum computing and information technology.

cond-mat.supr-con↗

arXiv2025

The Immediate, Exemplary, and Fleeting echelle spectroscopy of SN 2023ixf: Monitoring acceleration of slow progenitor circumstellar material, driven by shock interaction

We present high resolution WIYN/NEID echelle spectroscopy (R $\approx70$,000) of the supernova (SN) 2023ixf in M101, obtained 1.51 to 18.51 days after explosion over nine epochs. Daily monitoring for the first four days after explosion shows narrow emission features ($\leq200$ km s$^{-1}$), exhibiting predominantly blueshifted velocities, that rapidly weaken, broaden, and vanish in a manner consistent with radiative acceleration and the SN shock eventually overrunning or enveloping the full extent of dense circumstellar medium (CSM). The most rapid evolution is in the He I emission, which is visible on day 1.51 but disappears by day 2.62. We measure the maximum pre-SN speed of He I to be 25 $^{+0}_{-5} \pm2$ km s$^{-1}$, where the error is attributable to the uncertainty in how much the He I had already been radiatively accelerated, and to measurement of the emission line profile. The radiative acceleration of material is likely driven by the shock-CSM interaction, and the CSM is accelerated to $\geq200$ km s$^{-1}$ before being completely swept up by the SN shock to $\sim 2000$ km s$^{-1}$. We compare the observed spectra with spherically-symmetric r16wb HERACLES/CMFGEN model spectra and find the line evolution to generally be consistent with radiative acceleration and optical depth effects. The progenitor of SN2023ixf underwent an enhanced mass loss phase $\gtrsim 4$ year prior to core-collapse, creating a dense, asymmetric CSM region extending out to approximately $r_{CSM} = 3.7 \times 10^{14}$ ($v_\textrm{shock}$/9500 km s$^{-1}$) cm.

astro-ph.HE↗

arXiv2025

The 2D Materials Roadmap

Over the past two decades, 2D materials have rapidly evolved into a diverse and expanding family of material platforms. Many members of this materials class have demonstrated their potential to deliver transformative impact on fundamental research and technological applications across different fields. In this roadmap, we provide an overview of the key aspects of 2D material research and development, spanning synthesis, properties and commercial applications. We specifically present roadmaps for high impact 2D materials, including graphene and its derivatives, transition metal dichalcogenides, MXenes as well as their heterostructures and moiré systems. The discussions are organized into thematic sections covering emerging research areas (e.g., twisted electronics, moiré nano-optoelectronics, polaritronics, quantum photonics, and neuromorphic computing), breakthrough applications in key technologies (e.g., 2D transistors, energy storage, electrocatalysis, filtration and separation, thermal management, flexible electronics, sensing, electromagnetic interference shielding, and composites) and other important topics (computational discovery of novel materials, commercialization and standardization). This roadmap focuses on the current research landscape, future challenges and scientific and technological advances required to address, with the intent to provide useful references for promoting the development of 2D materials.

cond-mat.mtrl-sci↗

arXiv2025

The Digital Cybersecurity Expert: How Far Have We Come?

The increasing deployment of large language models (LLMs) in the cybersecurity domain underscores the need for effective model selection and evaluation. However, traditional evaluation methods often overlook specific cybersecurity knowledge gaps that contribute to performance limitations. To address this, we develop CSEBenchmark, a fine-grained cybersecurity evaluation framework based on 345 knowledge points expected of cybersecurity experts. Drawing from cognitive science, these points are categorized into factual, conceptual, and procedural types, enabling the design of 11,050 tailored multiple-choice questions. We evaluate 12 popular LLMs on CSEBenchmark and find that even the best-performing model achieves only 85.42% overall accuracy, with particular knowledge gaps in the use of specialized tools and uncommon commands. Different LLMs have unique knowledge gaps. Even large models from the same family may perform poorly on knowledge points where smaller models excel. By identifying and addressing specific knowledge gaps in each LLM, we achieve up to an 84% improvement in correcting previously incorrect predictions across three existing benchmarks for two cybersecurity tasks. Furthermore, our assessment of each LLM's knowledge alignment with specific cybersecurity roles reveals that different models align better with different roles, such as GPT-4o for the Google Senior Intelligence Analyst and Deepseek-V3 for the Amazon Privacy Engineer. These findings underscore the importance of aligning LLM selection with the specific knowledge requirements of different cybersecurity roles for optimal performance.

cs.CR↗

arXiv2025

AnomalyGen: An Automated Semantic Log Sequence Generation Framework with LLM for Anomaly Detection

The scarcity of high-quality public log datasets has become a critical bottleneck in advancing log-based anomaly detection techniques. Current datasets exhibit three fundamental limitations: (1) incomplete event coverage, (2) artificial patterns introduced by static analysis-based generation frameworks, and (3) insufficient semantic awareness. To address these challenges, we present AnomalyGen, the first automated log synthesis framework specifically designed for anomaly detection. Our framework introduces a novel four-phase architecture that integrates enhanced program analysis with Chain-of-Thought reasoning (CoT reasoning), enabling iterative log generation and anomaly annotation without requiring physical system execution. Evaluations on Hadoop and HDFS distributed systems demonstrate that AnomalyGen achieves substantially broader log event coverage (38-95 times improvement over existing datasets) while producing more operationally realistic log sequences compared to static analysis-based approaches. When augmenting benchmark datasets with synthesized logs, we observe maximum F1-score improvements of 3.7% (average 1.8% improvement across three state-of-the-art anomaly detection models). This work not only establishes a high-quality benchmarking resource for automated log analysis but also pioneers a new paradigm for applying large language models (LLMs) in software engineering workflows.

cs.SE↗

arXiv2025

Planar and Outerplanar Spectral Extremal Problems based on Paths

Let SPEX$_\mathcal{P}(n,F)$ and SPEX$_\mathcal{OP}(n,F)$ denote the sets of graphs with the maximum spectral radius over all $n$-vertex $F$-free planar and outerplanar graphs, respectively. Define $tP_l$ as a linear forest of $t$ vertex-disjoint $l$-paths and $P_{t\cdot l}$ as a starlike tree with $t$ branches of length $l-1$. Building on the structural framework by Tait and Tobin [J. Combin. Theory Ser. B, 2017] and the works of Fang, Lin and Shi [J. Graph Theory, 2024] on the planar spectral extremal graphs without vertex-disjoint cycles, this paper determines the extremal graphs in $\text{SPEX}_\mathcal{P}(n,tP_l)$ and $\text{SPEX}_\mathcal{OP}(n,tP_l)$ for sufficiently large $n$. When $t=1$, since $tP_l$ is a path of a specific length, our results adapt Nikiforov's findings [Linear Algebra Appl. 2010] under the (outer)planarity condition. When $l=2$, note that $tP_l$ consists of $t$ independent $K_2$, then as a corollary, we generalize the results of Wang, Huang and Lin [arXiv: 2402.16419] and Yin and Li [arXiv:2409.18598v2]. Moreover, motivated by results of Zhai and Liu [Adv. in Appl. Math, 2024], we consider the extremal problems for edge-disjoint paths and determine the extremal graphs in $\text{SPEX}_\mathcal{P}(n,P_{t\cdot l})$ and $\text{SPEX}_\mathcal{OP}(n,P_{t\cdot l})$ for sufficiently large $n$.

math.CO↗

arXiv2025

Spectral extremal problems on outerplanar and planar graphs

Let $\emph{spex}_{\mathcal{OP}}(n,F)$ and $\emph{spex}_{\mathcal{P}}(n,F)$ be the maximum spectral radius over all $n$-vertex $F$-free outerplanar graphs and planar graphs, respectively. Define $tC_l$ as $t$ vertex-disjoint $l$-cycles, $B_{tl}$ as the graph obtained by sharing a common vertex among $t$ edge-disjoint $l$-cycles %$B_{tl}$ as the graph obtained by connecting all cycles in $tC_l$ at a single vertex, and $(t+1)K_{2}$ as the disjoint union of $t+1$ copies of $K_2$. In the 1990s, Cvetković and Rowlinson conjectured $K_1 \vee P_{n-1}$ maximizes spectral radius in outerplanar graphs on $n$ vertices, while Boots and Royle (independently, Cao and Vince) conjectured $K_2 \vee P_{n-2} $ does so in planar graphs. Tait and Tobin [J. Combin. Theory Ser. B, 2017] determined the fundamental structure as the key to confirming these two conjectures for sufficiently large $n.$ Recently, Fang et al. [J. Graph Theory, 2024] characterized the extremal graph with $\emph{spex}_{\mathcal{P}}(n,tC_l)$ in planar graphs by using this key. In this paper, we first focus on outerplanar graphs and adopt a similar approach to describe the key structure of the connected extremal graph with $\emph{spex}_{\mathcal{OP}}(n,F)$, where $F$ is contained in $K_1 \vee P_{n-1}$ but not in $K_{1} \vee ((t-1)K_2\cup(n-2t+1)K_1)$. Based on this structure, we determine $\emph{spex}_{\mathcal{OP}}(n,B_{tl})$ and $\emph{spex}_{\mathcal{OP}}(n,(t+1)K_{2})$ along with their unique extremal graphs for all $t\geq1$, $l\geq3$ and large $n$. Moreover, we further extend the results to planar graphs, characterizing the unique extremal graph with $\emph{spex}_{\mathcal{P}}(n,B_{tl})$ for all $t\geq3$, $l\geq3$ and large $n$.

math.CO↗

arXiv2025

Personalized Continual EEG Decoding: Retaining and Transferring Knowledge

The significant inter-subject variability in electroen-cephalogram (EEG) signals often results in substantial changes to neural network weights as data distributions shift. This variability frequently causes catastrophic forgetting in continual EEG decoding tasks, where previously acquired knowledge is overwritten as new subjects are introduced. While retraining the entire dataset for each new subject can mitigate forgetting, this approach imposes significant computational costs, rendering it impractical for real-world applications. Therefore, an ideal brain-computer interface (BCI) model should incrementally learn new information without requiring complete retraining, thereby reducing computational overhead. Existing EEG decoding meth-ods typically rely on large, centralized source-domain datasets for pre-training to improve model generalization. However, in practical scenarios, data availability is often constrained by privacy concerns. Furthermore, these methods are susceptible to catastrophic forgetting in continual EEG decoding tasks, significantly limiting their utility in long-term learning scenarios. To address these issues, we propose the Personalized Continual EEG Decoding (PCED) framework for continual EEG decoding. The framework uses Euclidean Alignment for fast domain adap-tation, reducing inter-subject variability. To retain knowledge and prevent forgetting, it includes an exemplar replay mechanism that preserves key information from past tasks. A reservoir sampling-based memory management strategy optimizes exemplar storage to handle memory constraints in long-term learning. Experiments on the OpenBMI dataset with 54 subjects show that PCED balances knowledge retention and classification performance, providing an efficient solution for real-world BCI applications.

eess.SP↗

arXiv2025

Using Powerful Prior Knowledge of Diffusion Model in Deep Unfolding Networks for Image Compressive Sensing

Recently, Deep Unfolding Networks (DUNs) have achieved impressive reconstruction quality in the field of image Compressive Sensing (CS) by unfolding iterative optimization algorithms into neural networks. The reconstruction quality of DUNs depends on the learned prior knowledge, so introducing stronger prior knowledge can further improve reconstruction quality. On the other hand, pre-trained diffusion models contain powerful prior knowledge and have a solid theoretical foundation and strong scalability, but it requires a large number of iterative steps to achieve reconstruction. In this paper, we propose to use the powerful prior knowledge of pre-trained diffusion model in DUNs to achieve high-quality reconstruction with less steps for image CS. Specifically, we first design an iterative optimization algorithm named Diffusion Message Passing (DMP), which embeds a pre-trained diffusion model into each iteration process of DMP. Then, we deeply unfold the DMP algorithm into a neural network named DMP-DUN. The proposed DMP-DUN can use lightweight neural networks to achieve mapping from measurement data to the intermediate steps of the reverse diffusion process and directly approximate the divergence of the diffusion model, thereby further improving reconstruction efficiency. Extensive experiments show that our proposed DMP-DUN achieves state-of-the-art performance and requires at least only 2 steps to reconstruct the image. Codes are available at https://github.com/FengodChen/DMP-DUN-CVPR2025.

cs.CV↗