arXiv subjects

Xu Xu

Publications and source records attributed to Xu Xu.

At least 19 recordsLinked to original sources

arXiv2026

Combinatorial Yamabe flow on infinitely triangulated hyperbolic surfaces

We study the combinatorial Yamabe flow on infinitely triangulated surfaces with piecewise hyperbolic metrics. Under the assumptions of uniformly bounded vertex degree and $\epsilon$-uniformly nondegenerate initial metric, we first establish the short-time existence of smooth solutions to the combinatorial Yamabe flow. Under the additional $\epsilon$-uniformly Delaunay condition on the initial metric, we further obtain the short-time uniqueness of solutions to the flow. To address the potential degeneration of triangles along the evolution, we introduce an extended flow with generalized curvature, and establish the global existence of solutions to the extended flow. Furthermore, under uniformly bounded vertex degrees and some integrability condition, we establish the uniqueness of solutions to this extended flow, which follows from the stability property of the solutions. These results provide a well-posedness theory for both the hyperbolic combinatorial Yamabe flow (locally in time) and its extended flow (globally in time) on infinitely triangulated surfaces.

math.DG↗

arXiv2026

Spherical orthogonal ring patterns on surfaces and modified combinatorial total geodesic curvatures

Orthogonal ring patterns are natural generalizations of circle patterns. Bobenko-Hoffmann-R\"orig and Bobenko established the variational principles of the classical combinatorial curvature for the Euclidean, hyperbolic and spherical orthogonal ring patterns. Bobenko-Hoffmann-R\"orig's work and Bobenko's work imply the rigidity of Euclidean and hyperbolic orthogonal ring patterns on closed surfaces, while the rigidity of spherical orthogonal ring patterns on closed surfaces is not known. In this paper, we study the spherical orthogonal ring patterns on closed surfaces with cellular decompositions satisfying certain necessary conditions. Using a modification of the combinatorial total geodesic curvature introduced by Nie in \cite{Nie}, we prove the rigidity of spherical orthogonal ring patterns on closed surfaces by variational principles.

math.GT↗

arXiv2026

SwarmSense-DNN: A Trustworthy and Decentralized Neural Framework for Proactive Anomaly Defense in Consumer IoT

The rapid growth of consumer IoT devices has introduced unprecedented challenges in trustworthy anomaly detection against AI-enabled cyber threats, requiring real-time, privacy-preserving, and scalable defense mechanisms. Traditional centralized strategies face critical limitations, including communication bottlenecks, single points of failure, and privacy vulnerabilities when processing distributed consumer data. We propose SwarmSense-DNN, a novel decentralized neural framework employing swarm intelligence for secure, cooperative anomaly detection across distributed IoT environments. The framework integrates autonomous agents with deep neural networks to form a self-organizing defense system that detects evolving anomalies without centralized coordination. It utilizes hierarchical federated learning with graph neural networks and attention mechanisms to capture local and global anomaly behaviors while ensuring data privacy. Extensive experiments demonstrate SwarmSense-DNN's superior performance: it achieves 95.44% average detection accuracy across five benchmark datasets while reducing communication overhead by 67%. The framework maintains robust resilience against adversarial threats through differential privacy safeguards and demonstrates strong fault tolerance under node failures and AI-enabled attacks.

cs.CR↗

arXiv2026

ChronoMedicalWorld: A Medical World Model for Learning Patient Trajectories from Longitudinal Care Data

Long-horizon clinical simulation -- predicting how a patient's physiology evolves over years under specified interventions -- is central to chronic-disease care, yet existing electronic health record (EHR) models are predominantly discriminative, and general-purpose large language models drift under repeated interventions. We propose the \textbf{ChronoMedicalWorld Model (CMWM)}, an action-conditioned latent world-model framework for learning patient trajectories from longitudinal care data. CMWM couples a joint-embedding state encoder with a wide action encoder that admits both structured intervention indicators and free-text communication embeddings, and trains a recurrent latent transition module under a six-term objective: next-observation supervision, next-latent prediction, SIGReg latent regularisation, and three physiology-aware shape priors (slope, continuity, large-jump penalty). A closed-loop rollout-prefix protocol matches training to deployment, so the model is optimised against the same multi-step error it exhibits at inference. As a concrete case study, we instantiate CMWM for annual estimated glomerular filtration rate (eGFR) trajectory forecasting in chronic kidney disease (CKD). On a 2{,}232-patient nephrology cohort, the CKD instantiation achieves a dynamic-50\% history rollout test mean absolute error (MAE) of 7.384 and root-mean-square error (RMSE) of 10.256, against 7.964 and 11.069 for a tuned GPT-5.5 structured-prompting baseline ($-7.28\%$ MAE, $-7.35\%$ RMSE), with the gain dominated by the dialogue portion of patient--health-coach communication. The framework is not CKD-specific: its architecture, loss design, and training protocol apply to any chronic condition that can be cast as periodic clinical state interleaved with structured and conversational interventions.

cs.LG↗

arXiv2026

HexAGenT: Efficient Agentic LLM Serving via Workflow- and Heterogeneity-Aware Scheduling

Agentic LLM applications increasingly execute user requests as multi-step workflows involving planning, tool use, branching, refinement, and synthesis. In such settings, users experience the end-to-end latency of an entire workflow, not the latency of any single LLM call. In this paper, we study how to schedule online agentic workflows across heterogeneous prefill-decode disaggregated LLM serving clusters to efficiently meet workflow-level latency objectives. The problem is challenging because workflow dependencies are revealed incrementally at runtime, calls have heterogeneous prompts, outputs, and KV-cache requirements, and the prefill and decode stages impose different compute, memory, and transfer constraints across heterogeneous GPUs. To solve this problem, we present HexAGenT, a workflow-aware scheduler for a heterogeneous prefill-decode inference service. HexAGenT models each request as an online-revealed DAG, maintains a running estimate of the workflow's standalone completion horizon, prioritizes ready calls by projected risk of missing that horizon, and jointly selects prefill placement, decode placement, and local queue priority while accounting for KV-cache capacity and cross-stage transfer latency. Across representative agentic workloads and heterogeneous A100/H100/H200 clusters, HexAGenT reduces the SLO scale required for timely workflow completion by an average of 20.1% at 95% attainment and 33.0% at 99% attainment, with maximum reductions of 45.0% and 80.5%, respectively.

cs.DC↗

arXiv2026

Experimental realization and self-testing of semisymmetric informationally complete measurements via a one-dimensional photonic quantum walk

Generalized quantum measurements play a crucial role in quantum mechanics, and symmetric informationally complete positive operator-valued measurements (SIC POVMs) provide a powerful and flexible framework for extracting information from quantum systems. However, the existence of SIC-POVMs in every finite dimension remains an open question, which has stimulated extensive research into alternative classes of POVMs. Recently, Geng $et$ $al$. [Phys. Rev. Lett. 126, 100401 (2021)] proposed a broader class of SIC POVM, called semisymmetric informationally complete POVM (semi-SIC POVM), which extends beyond SIC POVM. In this work, we focus on the four-outcome POVMs and experimentally realize the semi-SIC POVMs using a one-dimensional discrete-time quantum walk. Additionally, employing single photons and linear optics, we perform an experimental self-testing of semi-SIC POVMs in the semi-device-independent manner. Our results pave the way for exploring quantum certification with generalized quantum measurements.

quant-ph↗

arXiv2025

Breaking Rank -- A Novel Unscented Kalman Filter for Parameter Estimations of a Lumped-Parameter Cardiovascular Model

We make modifications to the unscented Kalman filter (UKF) which bestow almost complete practical identifiability upon a lumped-parameter cardiovascular model with 10 parameters and 4 output observables - a highly non-linear, stiff problem of clinical significance. The modifications overcome the challenging problems of rank deficiency when applying the UKF to parameter estimation. Rank deficiency usually means only a small subset of parameters can be estimated. Traditionally, pragmatic compromises are made, such as selecting an optimal subset of parameters for estimation and fixing non-influential parameters. Kalman filters are typically used for dynamical state tracking, to facilitate the control u at every time step. However, for the purpose of parameter estimation, this constraint no longer applies. Our modification has transformed the utility of UKF for the parameter estimation purpose, including minimally influential parameters, with excellent robustness (i.e., under severe noise corruption, challenging patho-physiology, and no prior knowledge of parameter distributions). The modified UKF algorithm is robust in recovering almost all parameters to over 98% accuracy, over 90% of the time, with a challenging target data set of 50, 10-parameter samples. We compare this to the original implementation of the UKF algorithm for parameter estimation and demonstrate a significant improvement.

cs.IT↗

arXiv2025

Infinite rigidity of inversive distance circle packings in the Poincar\'{e} disk

The maximum principle for hyperbolic inversive distance circle packings on polyhedral surfaces is established,which unifies and generalizes existing maximum principles for various types of circle packings in the literature.As an application of this principle, a discrete Schwarz-Ahlfors lemma is established.Furthermore, an infinite rigidity theorem for weighted Delaunay triangulations of the Poincar\'{e} disk is proved,which generalizes He's hyperbolic rigidity result \cite{He2}.

math.DG↗

arXiv2025

VeriEquivBench: An Equivalence Score for Ground-Truth-Free Evaluation of Formally Verifiable Code

Formal verification is the next frontier for ensuring the correctness of code generated by Large Language Models (LLMs). While methods that co-generate code and formal specifications in formal languages, like Dafny, can, in principle, prove alignment with user intent, progress is bottlenecked by specification quality evaluation. Current benchmarks rely on matching against ground-truth specifications, a manual and expertise-intensive process that has limited existing datasets to a few hundred simple problems and also suffers from a reliability issue. To address this, we introduce VeriEquivBench, a new benchmark with $2,389$ complex algorithmic problems that probe the limitations of current models in both code generation and formal reasoning. Our evaluation framework replaces ground-truth matching with a formally grounded metric, the equivalence score, and rigorously verifies the quality of generated specifications and code. Our results show that generating formally verifiable code remains a profound challenge for state-of-the-art LLMs. This underscores both the difficulty of the task and the need for benchmarks like VeriEquivBench to drive progress toward scalable and reliable coding agents.

cs.PL↗

arXiv2025

Local Success Does Not Compose: Benchmarking Large Language Models for Compositional Formal Verification

We introduce DafnyCOMP, a benchmark for evaluating large language models (LLMs) on compositional specification generation in Dafny. Unlike prior benchmarks that focus on single-function tasks, DafnyCOMP targets programs composed of multiple interacting functions with data dependencies, requiring reasoning across component boundaries. The benchmark consists of 300 automatically synthesized multi-function programs. We evaluate several state-of-the-art LLM families and find that, while they perform well on single-function verification, their performance drops sharply on compositional tasks. Analysis reveals systematic failures in cross-functional reasoning, including fragile specifications, misalignment between implementations and proofs, and unstable reasoning. DafnyCOMP thus provides a diagnostic tool for measuring progress toward reliable, verifiable, and compositional code generation with LLMs.

cs.PL↗

arXiv2025

Exploring and Reshaping the Weight Distribution in LLM

The performance of Large Language Models is influenced by their characteristics such as architecture, model sizes, decoding methods and so on. Due to differences in structure or function, the weights in different layers of large models have varying distributions. This paper explores the correlations between different types of layers in terms of weights distribution and studies the potential impact of these correlations on LoRA training effectiveness. Firstly, the study reveals that in the model the cosine distances between weights of different layers manifest power-law distribution. We extract Query-projection, down-projection and other weight matrices from the self-attention layers and MLP layers, calculate the singular values of the matrices using singular value decomposition, and organize a certain number of singular values into matrices according to projection's type. By analyzing the probability distribution of the cosine distances between these matrices, it is found that the cosine distances values between them have distinct power-law distribution characteristics. Secondly, based on the results of distance calculations and analysis across different layers of model, a qualitative method is proposed to describe the distribution characteristics of different models. Next, to construct weights that align with the distribution characteristics, a data generator is designed using a combination of Gaussian process and Pareto distribution functions. The generator is used to simulate the generation of data that aligns with specific distribution characteristics. Finally, based on the aforementioned distribution characteristics and data generation method, the weights in LoRA initialization are reshaped for training. Experimental results indicate that, without altering the model structure or training process, this method achieves a certain improvement in the performance of LoRA training.

cs.LG↗

arXiv2025

Discrete conformal structures on surfaces with boundary (III) -- Deformation

The present work constitutes the third installment in a series of investigations devoted to discrete conformal structures on surfaces with boundary. In our preceding works \cite{X-Z DCS1, X-Z DCS2}, we established, respectively, a classification of these discrete conformal structures and results on their rigidity and existence. Building on this foundation, the present work focuses on the deformation theory of discrete conformal structures on surfaces with boundary. Specifically, we introduce the combinatorial Ricci flow and the combinatorial Calabi flow, and establish the longtime existence and global convergence of solutions to these combinatorial curvature flows. These results yield effective algorithms for finding discrete hyperbolic metrics on surfaces with totally geodesic boundaries of prescribed lengths.

math.DG↗

arXiv2025

Re:Form -- Reducing Human Annotations in Scalable Formal Software Verification with RL in LLMs: A Preliminary Study on Dafny

Existing informal language-based (e.g., human language) Large Language Models (LLMs) trained with Reinforcement Learning (RL) face a significant challenge: their verification processes, which provide crucial training signals, are neither reliable nor scalable. In fact, the prevalent large proprietary models could hardly generate verifiable programs. A promising yet largely uncharted alternative is formal language-based reasoning. Grounding LLMs in rigorous formal systems where generative models operate in formal language spaces (e.g., Dafny) enables the automatic and mathematically provable verification of their reasoning processes and outcomes. This capability is pivotal for achieving large-scale, reliable formal software verification. It is a common practice to employ human-annotated chain-of-thought and answers to induce the reasoning and coding capabilities of LLMs. Unfortunately, it becomes unacceptably all-consuming to provide such priors for supervising complex programming tasks. In this work, we systematically explore ways to reduce human annotations with the formal language, Dafny, as the main environment for our pilot study. Our pipeline mainly relies on introducing an automatic and scalable data curation pipeline, and careful RL designs integrated with feedback from the formal language verifier. We introduce DafnyComp, a benchmark of compositional formal programs with auto-formalized specifications for specification reasoning. Our supervised fine-tuning (SFT) stage enables even small models (e.g., 0.5B) to generate syntactically valid and verifiable Dafny code, surpassing proprietary models. RL with regularization further improves performance, achieving stronger generalization to out-of-domain tasks and outperforming all strong baselines on the challenging DafnyComp benchmark.

cs.CL↗

arXiv2025

DatasetAgent: A Novel Multi-Agent System for Auto-Constructing Datasets from Real-World Images

Common knowledge indicates that the process of constructing image datasets usually depends on the time-intensive and inefficient method of manual collection and annotation. Large models offer a solution via data generation. Nonetheless, real-world data are obviously more valuable comparing to artificially intelligence generated data, particularly in constructing image datasets. For this reason, we propose a novel method for auto-constructing datasets from real-world images by a multiagent collaborative system, named as DatasetAgent. By coordinating four different agents equipped with Multi-modal Large Language Models (MLLMs), as well as a tool package for image optimization, DatasetAgent is able to construct high-quality image datasets according to user-specified requirements. In particular, two types of experiments are conducted, including expanding existing datasets and creating new ones from scratch, on a variety of open-source datasets. In both cases, multiple image datasets constructed by DatasetAgent are used to train various vision models for image classification, object detection, and image segmentation.

cs.CV↗

arXiv2025

Eu-doped CsSrCl$_3$ Large Nanocrystal Clusters with Self-Reduction Effect and Near-Unity Quantum Yield

Europium halide perovskites have emerged as promising candidates for environmental-friendly blue-emitting materials. However, their development is hindered by relative low photoluminescence quantum yields (PLQY, e.g. ~2-5% for intrinsic CsEuCl3) and poor stability against air. Here, we introduce a one-step-procedure for synthesizing Eu$^{2+}$-doped CsSrCl$_3$ large nanocrystal clusters (LNCs) with the effect of self-reduction, therefore eliminating the use of conventional reductant oleylamine (OAm) and ensuring phase purity. The CsSrCl$_3$:Eu LNCs shows photoluminescence emission centered at 430 nm with a full width at half-maximum (FWHM) of 25 nm and a PLQY of ~40%, which can be further enhanced to ~97% after passivating the surface defects by adding trioctylphosphine (TOP), the highest among all reported lead-free blue-emitting perovskite nanocrystals. The stability of CsSrCl$_3$:Eu can also be improved significantly by epitaxially growing ZnS shell on the surface. This work will shed more light on lanthanide and alkaline-earth metal (AEM)-based perovskites for nontoxic light-emitting materials.

cond-mat.mtrl-sci↗

arXiv2025

Generalized circle patterns on surfaces with cusps

Guo and Luo introduced generalized circle patterns on surfaces and proved their rigidity. In this paper, we prove the existence of Guo-Luo's generalized circle patterns with prescribed generalized intersection angles on surfaces with cusps, which partially answers a question raised by Guo-Luo and generalizes Bobenko-Springborn's hyperbolic circle patterns on closed surfaces to generalized hyperbolic circle patterns on surfaces with cusps. We further introduce the combinatorial Ricci flow and combinatorial Calabi flow for generalized circle patterns on surfaces with cusps, and prove the longtime existence and convergence of the solutions for these combinatorial curvature flows.

math.GT↗

arXiv2024

Intermittency of bubble deformation in turbulence

The deformation of finite-sized bubbles in intense turbulence exhibits complex geometries beyond simple spheroids as the bubbles exchange energy with the surrounding eddies across a wide range of scales. This study investigates deformation via the velocity of the most stretched tip of the deformed bubble in 3D, as the tip extension results from the compression of the rest of the interface by surrounding eddies. The results show that the power spectrum based on the tip velocity exhibits a scaling akin to that of the Lagrangian statistics of fluid elements, but decays with a distinct timescale and magnitude modulated by the Weber number based on the bubble size. This indicates that the interfacial energy is primarily siphoned from eddies of similar sizes as the bubble. Moreover, the tip velocity appears much more intermittent than the velocity increment, and its distribution near the extreme tails can be explained by the proposed model that accounts for the fact that small eddies with sufficient energy can contribute to extreme deformation. These findings provide a framework for understanding the energy transfer between deformable objects and multiscale eddies in intense turbulence.

physics.flu-dyn↗

arXiv2024

Discrete conformal structures on surfaces with boundary (II) -- Rigidity and Existence

In \cite{X-Z DCS1}, we introduced discrete conformal structures on surfaces with boundary via an axiomatic framework, and provided a classification of such discrete conformal structures. The present work focuses on the rigidity and existence of these discrete conformal structures on surfaces with boundary. As a direct consequence, the results by Guo-Luo in \cite{GL2} and Guo in \cite{Guo}, which deal with the rigidity and existence of discrete conformal structures on surfaces with boundary, are extended to a very general context.

math.DG↗