arXiv subjects

Ting Yang

Publications and source records attributed to Ting Yang.

At least 19 recordsLinked to original sources

arXiv2026

Slice Fueter-regular functions on arbitrary domains in octonions

This paper is concerned with a class of generalized slice Fueter-regular functions on arbitrary domains in O with local stem functions. Some classical theorems such as the maximum modulus principle will be generalized to our setting. Some new phenomena such as the conditional uniqueness of stem vectors will be discovered by means of new technical tools, e.g., the CCL equivalence relation and the Bers-Vekua continuation. And a natural connection between the theory of slice Fueter-regular functions and that of Riemann domains will be revealed via the quotient space under the CCL equivalence relation.

math.CV↗

arXiv2026

FedCRF: A Federated Cross-domain Recommendation Method with Semantic-driven Deep Knowledge Fusion

As user behavior data becomes increasingly scattered across different platforms, achieving cross-domain knowledge fusion while preserving privacy has become a critical issue in recommender systems. Existing PPCDR methods usually rely on overlapping users or items as a bridge, making them inapplicable to non-overlapping scenarios. They also suffer from limitations in the collaborative modeling of global and local semantics. To this end, this paper proposes a Federated Cross-domain Recommendation method with deep knowledge Fusion (FedCRF). Using textual semantics as a cross-domain bridge, FedCRF achieves cross-domain knowledge transfer via federated semantic learning under the non-overlapping scenario. Specifically, FedCRF constructs global semantic clusters on the server side to extract shared semantic information, and designs a FGSAT module on the client side to dynamically adapt to local data distributions and alleviate cross-domain distribution shift. Meanwhile, it builds a semantic graph based on textual features to learn representations that integrate both structural and semantic information, and introduces contrastive learning constraints between global and local semantic representations to enhance semantic consistency and promote deep knowledge fusion. In this framework, only item semantic representations are shared, while user interaction data remains locally stored, effectively mitigating privacy leakage risks. Experimental results on multiple real-world datasets show that FedCRF significantly outperforms existing methods in terms of Recall@20 and NDCG@20, validating its effectiveness and superiority in non-overlapping cross-domain recommendation scenarios.

cs.IR↗

arXiv2026

On the Enestrom-Kakeya Theorem for polynomials of an octonionic variable

To study the zeros of octonionic polynomials, we generalize the well-known Enestrom-Kakeya Theorem to the case of octonions. In this paper, we first deal with octonionic polynomials with nonnegative and monotonic coefficients, and prove that its zero set is contained within the closed sphere of octonion space. Then, we also consider the octonionic polynomials which the coefficients muduli is monotonic and the real parts of the coefficients is monotonic respectively, and get some results.

math.AG↗

arXiv2026

Growth theorems for slice Dirac-regular mappings over Clifford algebras

In this paper, we define a class of slice Dirac-regular mappings of several variables over Clifford algebras, based on the concept of O(3)-stem mappings. We prove that the slice mappings vanish under the slice Dirac operator, which is equivalent to its O(3)-stem mappings satisfy the generalized version of the Cauchy-Riemann equation. Moreover, we establish the growth theorem for slice Dirac-regular starlike mappings in the slice cones of Clifford algebras, as well as for slice Dirac-regular k-fold symmetric mappings.

math.CV↗

arXiv2026

A Low-Complexity Framework for Multi-access Coded Caching Systems with Arbitrary User-cache Access Topology

This paper studies the multi-access coded caching (MACC) problem with arbitrary user-cache access topology, which extends existing MACC models that rely on highly structured and combinatorially designed topologies. We consider a MACC system consisting of a single server, $\Lambda$ cache-nodes, and $K$ user-nodes. The server stores $N$ equal-size files, each cache-node has a storage capacity of $M$ files, and each user-node $k\in[K]$ can access an arbitrary subset of cache-nodes $\mathcal{A}_k\subseteq[\Lambda]$ and retrieve the cached content stored in cache-nodes $\mathcal{A}_k$. The objective is to design a universal framework for the MACC delivery problem. Decoding conflicts among the requested packets are captured by a conflict graph, and the design of the delivery is reduced to a graph coloring problem, where achieving a lower transmission load corresponds to coloring the graph using fewer colors. Under this formulation, the classical DSatur algorithm achieves a transmission load close to the index-coding (IC) converse bound, thereby providing a practical benchmark. However, its computational complexity becomes prohibitive for large-scale graphs. To overcome this limitation, we develop a learning-driven approach using graph neural networks (GNNs) that efficiently constructs coded multicast transmissions with performance close to the theoretical bounds and generalizes across different user-cache access topologies and numbers of users. In addition, we extend the IC converse bound to MACC systems with arbitrary access topology and propose a low-complexity greedy approximation that closely matches the IC converse bound. Numerical results demonstrate that the proposed approach achieves performance close to the DSatur algorithm and the IC converse bound, while significantly reducing computational complexity, making it well-suited for large-scale MACC systems.

cs.IT↗

arXiv2026

MedDialogRubrics: A Comprehensive Benchmark and Evaluation Framework for Multi-turn Medical Consultations in Large Language Models

Medical conversational AI (AI) plays a pivotal role in the development of safer and more effective medical dialogue systems. However, existing benchmarks and evaluation frameworks for assessing the information-gathering and diagnostic reasoning abilities of medical large language models (LLMs) have not been rigorously evaluated. To address these gaps, we present MedDialogRubrics, a novel benchmark comprising 5,200 synthetically constructed patient cases and over 60,000 fine-grained evaluation rubrics generated by LLMs and subsequently refined by clinical experts, specifically designed to assess the multi-turn diagnostic capabilities of LLM. Our framework employs a multi-agent system to synthesize realistic patient records and chief complaints from underlying disease knowledge without accessing real-world electronic health records, thereby mitigating privacy and data-governance concerns. We design a robust Patient Agent that is limited to a set of atomic medical facts and augmented with a dynamic guidance mechanism that continuously detects and corrects hallucinations throughout the dialogue, ensuring internal coherence and clinical plausibility of the simulated cases. Furthermore, we propose a structured LLM-based and expert-annotated rubric-generation pipeline that retrieves Evidence-Based Medicine (EBM) guidelines and utilizes the reject sampling to derive a prioritized set of rubric items ("must-ask" items) for each case. We perform a comprehensive evaluation of state-of-the-art models and demonstrate that, across multiple assessment dimensions, current models face substantial challenges. Our results indicate that improving medical dialogue will require advances in dialogue management architectures, not just incremental tuning of the base-model.

cs.CL↗

arXiv2025

GK-SMOTE: A Hyperparameter-free Noise-Resilient Gaussian KDE-Based Oversampling Approach

Imbalanced classification is a significant challenge in machine learning, especially in critical applications like medical diagnosis, fraud detection, and cybersecurity. Traditional oversampling techniques, such as SMOTE, often fail to handle label noise and complex data distributions, leading to reduced classification accuracy. In this paper, we propose GK-SMOTE, a hyperparameter-free, noise-resilient extension of SMOTE, built on Gaussian Kernel Density Estimation (KDE). GK-SMOTE enhances class separability by generating synthetic samples in high-density minority regions, while effectively avoiding noisy or ambiguous areas. This self-adaptive approach uses Gaussian KDE to differentiate between safe and noisy regions, ensuring more accurate sample generation without requiring extensive parameter tuning. Our extensive experiments on diverse binary classification datasets demonstrate that GK-SMOTE outperforms existing state-of-the-art oversampling techniques across key evaluation metrics, including MCC, Balanced Accuracy, and AUPRC. The proposed method offers a robust, efficient solution for imbalanced classification tasks, especially in noisy data environments, making it an attractive choice for real-world applications.

cs.LG↗

arXiv2025

Law of the iterated logarithm for supercritical non-local spatial branching processes

Suppose that $X=(X_{t})_{t\ge 0}$ is either a general supercritical non-local branching Markov process, or a general supercritical non-local superprocess, on a Luzin space. Here, by ``supercritical" we mean that the mean semigroup of $X$ exhibits a Perron-Frobenius type behaviour with a positive principal eigenvalue. In this paper, we study the almost sure behaviour of a family of martingales naturally associated with the real or complex-valued eigenpairs of the mean semigroup. Under a fourth-moment condition, we establish limit theorems of the iterated logarithm type for these martingales. In particular, we discover three regimes, each resulting in different scaling factors and limits. Furthermore, we obtain a law of the iterated logarithm for the linear functional $\langle \mathrm{Re}(f),X_{t}\rangle$ where $f$ is a sum of finite terms of eigenfunctions and $\mathrm{Re}(f)$ denotes its real part. In the context of branching Markov processes, our results improve on existing literature by complementing the known results for multitype branching processes in Asmussen [Trans. Amer. Math. Soc. 231 (1) (1977) 233--248] and generalizing the recent work of Hou, Ren and Song [arXiv: 2505.12691v1, arXiv: 2505.12691v2] to allow for non-local branching mechanisms. For superprocesses, as far as we know, our results are new.

math.PR↗

arXiv2025

Towards Open-Ended Emotional Support Conversations in LLMs via Reinforcement Learning with Future-Oriented Rewards

Emotional Support Conversation (ESC) systems aim to alleviate users' emotional difficulties and provide long-term, systematic support for emotional well-being. However, most large language model (LLM)-based ESC systems rely on predefined strategies, which limits their effectiveness in complex, real-life scenarios. To enable flexible responses to diverse emotional problem scenarios, this paper introduces a novel end-to-end framework (RLFF-ESC) that directly learns enduring emotionally supportive response skills using reinforcement learning. For sustained emotional support, we first employ an LLM-based multi-agent mechanism to simulate future dialogue trajectories and collect future-oriented rewards. We then train a future-oriented reward model, which is subsequently used to train the emotional support policy model. Additionally, we incorporate an explicit reasoning process during response generation to further enhance the quality, relevance, and contextual appropriateness of the system's responses. We evaluate the backbone policy model on Qwen2.5-7B-Instruct-1M and LLaMA3.1-8B-Instruct models, testing the proposed RLFF-ESC framework across two public ESC datasets. Experimental results demonstrate that RLFF-ESC consistently outperforms existing baselines in terms of goal completion and response quality.

cs.AI↗

arXiv2025

Collaborative governance of cyber violence: A two-phase, multi-scenario four-party evolutionary game and SBI1I2R public opinion dissemination

Cyber violence severely disrupts public order in both cyberspace and the real world. Existing studies have gradually advocated collaborative governance but rely on macro-level theoretical analyses. This study integrates micro- and macro-level perspectives to propose a two-stage, multi-scenario governance mechanism for cyber violence. In the first phase, a multi-scenario evolutionary game model with four parties involved in cyber violence was developed based on evolutionary game theory. Matlab simulations show that under strong government regulation, moderate levels of punishment implemented by the government against the online media that adopt misguidance strategies can achieve the most desirable stable state. In the second phase, the role of bystanders was introduced by integrating communication dynamics theory, and emotional factors were considered alongside game strategies. This led to the development of a new SBI1I2R model for public opinion dissemination in cyber violence. Netlogo simulations found that increasing the "correct guidance" strategy by the online media reduces the influence of cyber violence supporters and the time it takes for their nodes to drop to zero, but does not significantly shorten the time for the peak to occur. Comparatively, collaborative intervention between the online media and the government was most effective in curbing public opinion, followed by the government's independent "strong regulation." Relying solely on the online media's "correct guidance" produced the weakest effect. Finally, this mechanism was applied to a case study, and a multi-stage, multi-scenario analysis based on life cycle theory enhanced its practical applicability.

cs.MA↗

arXiv2025

Monocle: Hybrid Local-Global In-Context Evaluation for Long-Text Generation with Uncertainty-Based Active Learning

Assessing the quality of long-form, model-generated text is challenging, even with advanced LLM-as-a-Judge methods, due to performance degradation as input length increases. To address this issue, we propose a divide-and-conquer approach, which breaks down the comprehensive evaluation task into a series of localized scoring tasks, followed by a final global assessment. This strategy allows for more granular and manageable evaluations, ensuring that each segment of the text is assessed in isolation for both coherence and quality, while also accounting for the overall structure and consistency of the entire piece. Moreover, we introduce a hybrid in-context learning approach that leverages human annotations to enhance the performance of both local and global evaluations. By incorporating human-generated feedback directly into the evaluation process, this method allows the model to better align with human judgment. Finally, we develop an uncertainty-based active learning algorithm that efficiently selects data samples for human annotation, thereby reducing annotation costs in practical scenarios. Experimental results show that the proposed evaluation framework outperforms several representative baselines, highlighting the effectiveness of our approach.

cs.CL↗

arXiv2025

Hua-Chen New Theory of Economic Optimization

Between 1957-1985, Chinese mathematician Loo-Keng Hua pioneered economic optimization theory through three key contributions: establishing economic stability's fundamental theorem, proving the uniqueness of equilibrium solutions in economic systems, and developing a consumption-integrated model 50 days before his death. Since 1988, Mu-Fa Chen has been working on Hua's theory. He introduced stochastics, namely Markov chains, to economic optimization theory. He updated and developed Hua's model and came up with a new model (Chen's model) which has become the starting point of a new economic optimization theory. Chen's theory can be applied to economic stability test, bankruptcy prediction, product ranking and classification, economic prediction and adjustment, economic structure optimization. Chen's theory can also provide efficient algorithms that are programmable and intelligent. {Stochastics} is the cornerstone of Chen's theory. There is no overlap between Chen's theory, and the existing mathematical economy theory and the economics developments that were awarded Nobel Prizes in Economics between 1969 and 2024. The distinguished features of Chen's theory from the existing theories are quantitative, calculable, predictable, optimizable, programmable and can be intelligent. This survey provides a theoretical overview of the newly published monograph \cite{5rw24}. Specifically, the invariant of the economic structure matrix, also known as the Chen's invariant, was first published in this survey.

econ.TH↗

arXiv2025

Fluctuations of the linear functionals for supercritical non-local branching superprocesses

Suppose $\{X_{t}:t\ge 0\}$ is a supercritical superprocess on a Luzin space $E$, with a non-local branching mechanism and probabilities $\mathbb{P}_{\delta_{x}}$, when initiated from a unit mass at $x\in E$. By ``supercritical", we mean that the first moment semigroup of $X_{t}$ exhibits a Perron-Frobenius type behaviour characterized by an eigentriplet $(\lambda_{1},\varphi,\widetilde{\varphi})$, where the principal eigenvalue $\lambda_{1}$ is greater than $0$. Under a second moment condition, we prove that $X_{t}$ satisfies a law of large numbers. The main purpose of this paper is to further investigate the fluctuations of the linear functional $\mathrm{e}^{-\lambda_{1}t}\langle f,X_{t}\rangle$ around the limit given by the law of large numbers. To this end, we introduce a parameter $\epsilon(f)$ for a bounded measurable function $f$, which determines the exponent term of the decay rate for the first moment of the fluctuation. Qualitatively, the second-order behaviour of $\langle f,X_{t}\rangle$ depends on the sign of $\epsilon(f)-\lambda_{1}/2$. We prove that, for a suitable test function $f$, the fluctuation of the associated linear functional exhibits distinct asymptotic behaviours depending on the magnitude of $\epsilon(f)$: If $\epsilon(f)\ge \lambda_{1}/2$, the fluctuation converges in distribution to a Gaussian limit under appropriate normalization; If $\epsilon(f)<\lambda_{1}/2$, the fluctuation converges to an $L^{2}$ limit with a larger normalization factor. In particular, when the test function is chosen as the right eigenfunction $\varphi$, we establish a functional central limit theorem. As an application, we consider a multitype superdiffusion in a bounded domain. For this model, we derive limit theorems for the fluctuations of arbitrary linear functionals.

math.PR↗

arXiv2025

Targetless 6DoF Calibration of LiDAR and 2D Scanning Radar Based on Cylindrical Occupancy

Owing to the capability for reliable and all-weather long-range sensing, the fusion of LiDAR and Radar has been widely applied to autonomous vehicles for robust perception. In practical operation, well manually calibrated extrinsic parameters, which are crucial for the fusion of multi-modal sensors, may drift due to the vibration. To address this issue, we present a novel targetless calibration approach, termed LiRaCo, for the extrinsic 6DoF calibration of LiDAR and Radar sensors. Although both types of sensors can obtain geometric information, bridging the geometric correspondences between multi-modal data without any clues of explicit artificial markers is nontrivial, mainly due to the low vertical resolution of scanning Radar. To achieve the targetless calibration, LiRaCo leverages a spatial occupancy consistency between LiDAR point clouds and Radar scans in a common cylindrical representation, considering the increasing data sparsity with distance for both sensors. Specifically, LiRaCo expands the valid Radar scanned pixels into 3D occupancy grids to constrain LiDAR point clouds based on spatial consistency. Consequently, a cost function involving extrinsic calibration parameters is formulated based on the spatial overlap of 3D grids and LiDAR points. Extrinsic parameters are finally estimated by optimizing the cost function. Comprehensive quantitative and qualitative experiments on two real outdoor datasets with different LiDAR sensors demonstrate the feasibility and accuracy of the proposed method. The source code will be publicly available.

cs.RO↗

arXiv2025

FDLLM: A Dedicated Detector for Black-Box LLMs Fingerprinting

Large Language Models (LLMs) are rapidly transforming the landscape of digital content creation. However, the prevalent black-box Application Programming Interface (API) access to many LLMs introduces significant challenges in accountability, governance, and security. LLM fingerprinting, which aims to identify the source model by analyzing statistical and stylistic features of generated text, offers a potential solution. Current progress in this area is hindered by a lack of dedicated datasets and the need for efficient, practical methods that are robust against adversarial manipulations. To address these challenges, we introduce FD-Dataset, a comprehensive bilingual fingerprinting benchmark comprising 90,000 text samples from 20 famous proprietary and open-source LLMs. Furthermore, we present FDLLM, a novel fingerprinting method that leverages parameter-efficient Low-Rank Adaptation (LoRA) to fine-tune a foundation model. This approach enables LoRA to extract deep, persistent features that characterize each source LLM. Through our analysis, we find that LoRA adaptation promotes the aggregation of outputs from the same LLM in representation space while enhancing the separation between different LLMs. This mechanism explains why LoRA proves particularly effective for LLM fingerprinting. Extensive empirical evaluations on FD-Dataset demonstrate FDLLM's superiority, achieving a Macro F1 score 22.1% higher than the strongest baseline. FDLLM also exhibits strong generalization to newly released models, achieving an average accuracy of 95% on unseen models. Notably, FDLLM remains consistently robust under various adversarial attacks, including polishing, translation, and synonym substitution. Experimental results show that FDLLM reduces the average attack success rate from 49.2% (LM-D) to 23.9%.

cs.CR↗

arXiv2025

PoVF: Empowering Decentralized Blockchain Systems with Verifiable Function Consensus

Consensus mechanism is the core technology for blockchain to ensure that transactions are executed in sequence. It also determines the decentralization, security, and efficiency of blockchain. Existing mechanisms all have certain centralization issues and fail to ensure the decentralization of blockchain networks. A decentralized and efficient mechanism is required to improve blockchain systems. This paper proposes a fair consensus mechanism called Proof of Verifiable Functions (PoVF), based on the verifiability and unpredictability of verifiable functions. PoVF provides a sufficiently fair mechanism, ensuring that all nodes in blockchain network have equal opportunity to participate in consensus. In addition, a structure called "Delay buffer" is proposed to ensure transactions are executed sequentially. It delay the selection of blocks to avoid blockchain forks caused by broadcasting and transaction execution confusion. According to our security analysis, PoVF is provably secure and has the ability to resist potential adversaries. According to the experiments, PoVF-based blockchain can process up to 4000 transactions per second with nodes configured with only 4-core CPUs. This paper uses the Gini coefficient to measure the decentralization of blockchains, and the PoVF-based blockchain achieves the lowest Gini coefficient of 0.39 among all sampled blockchains. PoVF has been shown to provide sufficient efficiency while ensuring decentralization and security through experiments.

cs.CR↗

arXiv2024

Navigating User Experience of ChatGPT-based Conversational Recommender Systems: The Effects of Prompt Guidance and Recommendation Domain

Conversational recommender systems (CRS) enable users to articulate their preferences and provide feedback through natural language. With the advent of large language models (LLMs), the potential to enhance user engagement with CRS and augment the recommendation process with LLM-generated content has received increasing attention. However, the efficacy of LLM-powered CRS is contingent upon the use of prompts, and the subjective perception of recommendation quality can differ across various recommendation domains. Therefore, we have developed a ChatGPT-based CRS to investigate the impact of these two factors, prompt guidance (PG) and recommendation domain (RD), on the overall user experience of the system. We conducted an online empirical study (N = 100) by employing a mixed-method approach that utilized a between-subjects design for the variable of PG (with vs. without) and a within-subjects design for RD (book recommendations vs. job recommendations). The findings reveal that PG can substantially enhance the system's explainability, adaptability, perceived ease of use, and transparency. Moreover, users are inclined to perceive a greater sense of novelty and demonstrate a higher propensity to engage with and try recommended items in the context of book recommendations as opposed to job recommendations. Furthermore, the influence of PG on certain user experience metrics and interactive behaviors appears to be modulated by the recommendation domain, as evidenced by the interaction effects between the two examined factors. This work contributes to the user-centered evaluation of ChatGPT-based CRS by investigating two prominent factors and offers practical design guidance.

cs.HC↗

arXiv2024

Fluctuations of the additive martingales related to super-Brownian motion

Let $(W_{t}(\lambda))_{t\ge 0}$, parametrized by $\lambda\in\mathbb{R}$, be the additive martingale related to a supercritical super-Brownian motion on the real line and let $W_{\infty}(\lambda)$ be its limit. Under a natural condition for the martingale limit to be non-degenerate, we investigate the rate at which the martingale approaches its limit. Indeed, assuming certain moment conditions on the branching mechanism, we show that the tail martingale $W_{\infty}(\lambda)-W_{t}(\lambda)$, properly normalized, converges in distribution to a non-degenerate random variable, and we identify the limit laws. We find that, for parameters with small absolute value, the fluctuations are affected by the behaviour of the branching mechanism $\psi$ around $0$. In fact, we prove that, in the case of small $|\lambda|$, when $\psi$ is secondly differentiable at $0$, the limit laws are scale mixtures of the standard normal laws, and when $\psi$ is `stable-like' near $0$ in some proper sense, the limit laws are scale mixtures of the stable laws. However, the effect of the branching mechanism is limited in the case of large $|\lambda|$. In the latter case, we show that the fluctuations and limit laws are determined by the limiting extremal process of the super-Brownian motion.

math.PR↗