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Jinrong Hu

Publications and source records attributed to Jinrong Hu.

At least 19 recordsLinked to original sources
arXiv2026

Centro-sectional measures for log-concave functions

We introduce centro-sectional measures with parameters q,m for log-concave functions on Rn, defined in terms of the q-th moments of their Radon transforms with respect to the Haar measure on m-dimensional subspaces, where m=1,...,n-1, and establish the corresponding variational formulas. Our measures generalize the notion of dual curvature measure if q=1, and are related to the Sine transform if q=2. In line with the coarea formula for log-concave functions as BV functions, the variational formulas give rise to the Euclidean centro-sectional measures and the spherical centro-sectional measures. In the symmetric setting, we solve the associated even functional centro-sectional Minkowski problem, which asks which pairs of measures can arise as the centro-sectional measures of an even log-concave function.

math.AP↗
arXiv2026

Capillary John ellipsoid theorem with applications to capillary curvature problems

In this paper, we apply a capillary John ellipsoid theorem for capillary convex bodies in the Euclidean half-space $\overline{\mathbb{R}^{n+1}_{+}}$. This theorem yields a non-collapsing estimate for capillary hypersurfaces, which provides a new approach to obtaining $C^{0}$ estimates for solutions to some capillary curvature problems (including the capillary $L_{p}$ Christoffel-Minkowski problem and the capillary $L_{p}$ curvature problem), based on the corresponding gradient estimates. As an application, we study the capillary $L_{p}$ dual Minkowski problem. A gradient estimate, together with the non-collapsing estimate and a $C^2$ estimate, yields existence for every $1 1$, with uniqueness up to dilation. We further obtain existence and uniqueness for $p>q$ without an upper restriction on $q$.

math.AP↗
arXiv2026

Smooth solutions to the chord log-Minkowski problem

In integral geometry generalized with Aleksandrov's variational theory, Lutwak-Xi-Yang-Zhang [Comm. Pure Appl. Math. 77 (2024)] recently opened the door to researching the cone-chord measures and their log-Minkowski problem stemming from the chord integrals, named as the chord log-Minkowski problem. In the smooth category, the solvability of the chord log-Minkowski problem amounts to dealing with a nonlocal {M}onge-{A}mpère equation involving a Riesz potential. In this paper, to study the chord log-Minkowski problem, we first present some novel results on the boundary regularity of the Riesz potential. Based on these results, we obtain the regularity and existence for the chord log-Minkowski problem from the perspective of a nonlocal {M}onge-{A}mpère equation and a nonlocal Gauss curvature flow equation.

math.AP↗
arXiv2026

Discard the Dross and Select the Essential: Pre-query Sample Selection for Black-box Membership Inference Attacks

Black-box membership inference attacks (MIAs) rely on target-model queries to infer whether candidate samples were used for training. However, membership signals are highly non-uniform across samples: some candidate samples support strong member/non-member separability, whereas many others provide little useful signal. Consequently, indiscriminate querying can incur substantial query cost and increase query-induced exposure, with limited marginal benefit for inference. This raises a key question: which candidate samples are worth querying for black-box MIAs? To address this question, we propose PSS-MIA, a pre-query sample selection framework which can be embedded with any existing MIA methods. PSS-MIA proceeds in two stages: it first ranks candidate samples and selects a subset expected to support stronger membership inference, then queries the selected samples and uses the returned outputs for an existing black-box MIA, thereby reducing query cost and query-induced exposure. In the first stage, we propose Loss-Gap Ranking (LGR), which ranks candidate samples by estimating the strength of their membership signal using loss gaps computed from reference models. Experiments on CIFAR-10, CIFAR-100, and CINIC-10 with five representative black-box MIA methods demonstrate that PSS-MIA with LGR consistently outperforms all other compared methods. Moreover, under a 0.1% FPR constraint, PSS-MIA can save at least 83.1%, 60.6%, and 80.4% of the query budget for the three datasets, respectively.

cs.CR↗
arXiv2025

Teacher Encoder-Student Decoder Denoising Guided Segmentation Network for Anomaly Detection

Visual anomaly detection is a highly challenging task, often categorized as a one-class classification and segmentation problem. Recent studies have demonstrated that the student-teacher (S-T) framework effectively addresses this challenge. However, most S-T frameworks rely solely on pre-trained teacher networks to guide student networks in learning multi-scale similar features, overlooking the potential of the student networks to enhance learning through multi-scale feature fusion. In this study, we propose a novel model named PFADSeg, which integrates a pre-trained teacher network, a denoising student network with multi-scale feature fusion, and a guided anomaly segmentation network into a unified framework. By adopting a unique teacher-encoder and student-decoder denoising mode, the model improves the student network's ability to learn from teacher network features. Furthermore, an adaptive feature fusion mechanism is introduced to train a self-supervised segmentation network that synthesizes anomaly masks autonomously, significantly increasing detection performance. Rigorous evaluations on the widely-used MVTec AD dataset demonstrate that PFADSeg exhibits excellent performance, achieving an image-level AUC of 98.9%, a pixel-level mean precision of 76.4%, and an instance-level mean precision of 78.7%.

cs.CV↗
arXiv2025

Effective resource allocation to combat invasions of the spotted lanternfly (Lycorma delicatula) and similar pests

The spotted lanternfly is rapidly establishing itself as a major insect pest with global implications. Despite significant management efforts, its spread continues in invaded regions, and refined management strategies are required. A recent study introduced a model that generalized the results of empirical control efficacy studies by incorporating population dynamics and incomplete delivery. In particular, a generalized population growth formula was derived, providing the minimum proportion of a population that must be treated with a given control to induce population decline. However, this model could not address the more relevant question of how best to deploy a control to minimize population growth. Here, we extend this model and formula to address this question in various settings. When the effect of control is proportional to effort, we show that exhaustive sequential deployment of stage-specific controls, ordered by efficacy, is optimal. When control effects exhibit diminishing returns with effort, we derive a formula for when to switch controls, providing an effective strategy in situations where management resources may vary or be cut at any time. We also use numerical global optimization methods to obtain strategies when resources are fixed a priori. Both strategies outperform random deployment, which can result in disastrous outcomes. Our results demonstrate that adopting an effective strategy for deploying stage-specific controls is essential for managing the spotted lanternfly. However, we found no papers addressing this topic in the lanternfly literature, nor information on whether such strategies are used. Given the limited resources available to combat the lanternfly, it is critical that they are used effectively. The approach introduced here, along with other optimization methods used in related fields, can contribute to this goal.

q-bio.OT↗
arXiv2025

Capillary $L_p$ Minkowski Flows

We study the long-time existence and asymptotic behavior of a class of anisotropic capillary Gauss curvature flows. As an application, we provide a flow approach to the existence of smooth solutions to the capillary even $L_p$ Minkowski problem in the Euclidean half-space for all $p \in (-n-1, \infty)$ and capillary $L_p$ Minkowski problem for $p > n+1$.

math.AP↗
arXiv2025

The $L_{p}$ dual Christoffel-Minkowski problem for $1<p<q\leq k+1$ with $1\leq k\leq n$

In this paper, we investigate an $L_{p}$ Christoffel-Minkowski-type problem that prescribes a class of $L_p$ geometric measures, which are mixtures of the $k$-th area measure and the $q$-th dual curvature measure. By establishing a gradient estimate, we obtain the existence of an even, smooth, strictly convex solution to this problem for $1 < p < q \leq k + 1$, where $1 \leq k \leq n$ and $n \geq 1$.

math.AP↗
arXiv2025

The $L_{p}$-Brunn-Minkowski inequalities for variational functionals with $0\leq p<1$

The infinitesimal forms of the $L_{p}$-Brunn-Minkowski inequalities for variational functionals, such as the $q$-capacity, the torsional rigidity, and the first eigenvalue of the Laplace operator, are investigated for $p \geq 0$. These formulations yield Poincaré-type inequalities related to these functionals. As an application, the $L_{p}$-Brunn-Minkowski inequalities for torsional rigidity with $0 \leq p < 1$ are confirmed for small $C^{2}$-perturbations of the unit ball.

math.AP↗
arXiv2025

The dual Minkowski problem for positive indices

We derive the stability result of the dual curvature measure with near constant density in the even case. As an application, the existence and uniqueness of solutions to the even dual Minkowski problem for positive indices in $\mathbb{R}^{n+1}$ are obtained with $n\geq 1$, provided the density of the given measure is close to 1 in the $C^α$ norm with $α\in (0,1)$.

math.AP↗
arXiv2025

LLM-MedQA: Enhancing Medical Question Answering through Case Studies in Large Language Models

Accurate and efficient question-answering systems are essential for delivering high-quality patient care in the medical field. While Large Language Models (LLMs) have made remarkable strides across various domains, they continue to face significant challenges in medical question answering, particularly in understanding domain-specific terminologies and performing complex reasoning. These limitations undermine their effectiveness in critical medical applications. To address these issues, we propose a novel approach incorporating similar case generation within a multi-agent medical question-answering (MedQA) system. Specifically, we leverage the Llama3.1:70B model, a state-of-the-art LLM, in a multi-agent architecture to enhance performance on the MedQA dataset using zero-shot learning. Our method capitalizes on the model's inherent medical knowledge and reasoning capabilities, eliminating the need for additional training data. Experimental results show substantial performance gains over existing benchmark models, with improvements of 7% in both accuracy and F1-score across various medical QA tasks. Furthermore, we examine the model's interpretability and reliability in addressing complex medical queries. This research not only offers a robust solution for medical question answering but also establishes a foundation for broader applications of LLMs in the medical domain.

cs.CL↗
arXiv2024

A Self-Learning Multimodal Approach for Fake News Detection

The rapid growth of social media has resulted in an explosion of online news content, leading to a significant increase in the spread of misleading or false information. While machine learning techniques have been widely applied to detect fake news, the scarcity of labeled datasets remains a critical challenge. Misinformation frequently appears as paired text and images, where a news article or headline is accompanied by a related visuals. In this paper, we introduce a self-learning multimodal model for fake news classification. The model leverages contrastive learning, a robust method for feature extraction that operates without requiring labeled data, and integrates the strengths of Large Language Models (LLMs) to jointly analyze both text and image features. LLMs are excel at this task due to their ability to process diverse linguistic data drawn from extensive training corpora. Our experimental results on a public dataset demonstrate that the proposed model outperforms several state-of-the-art classification approaches, achieving over 85% accuracy, precision, recall, and F1-score. These findings highlight the model's effectiveness in tackling the challenges of multimodal fake news detection.

cs.CL↗
arXiv2024

The generalized Gaussian log-Minkowski problem

The generalized Gaussian distribution that stems from information theory is studied. The log-Minkowski problem associated with generalized Gaussian distribution shall be introduced and solved.

math.MG↗
arXiv2024

Uncertainty-Aware Explainable Recommendation with Large Language Models

Providing explanations within the recommendation system would boost user satisfaction and foster trust, especially by elaborating on the reasons for selecting recommended items tailored to the user. The predominant approach in this domain revolves around generating text-based explanations, with a notable emphasis on applying large language models (LLMs). However, refining LLMs for explainable recommendations proves impractical due to time constraints and computing resource limitations. As an alternative, the current approach involves training the prompt rather than the LLM. In this study, we developed a model that utilizes the ID vectors of user and item inputs as prompts for GPT-2. We employed a joint training mechanism within a multi-task learning framework to optimize both the recommendation task and explanation task. This strategy enables a more effective exploration of users' interests, improving recommendation effectiveness and user satisfaction. Through the experiments, our method achieving 1.59 DIV, 0.57 USR and 0.41 FCR on the Yelp, TripAdvisor and Amazon dataset respectively, demonstrates superior performance over four SOTA methods in terms of explainability evaluation metric. In addition, we identified that the proposed model is able to ensure stable textual quality on the three public datasets.

cs.IR↗
arXiv2024

X-Transfer: A Transfer Learning-Based Framework for GAN-Generated Fake Image Detection

Generative adversarial networks (GANs) have remarkably advanced in diverse domains, especially image generation and editing. However, the misuse of GANs for generating deceptive images, such as face replacement, raises significant security concerns, which have gained widespread attention. Therefore, it is urgent to develop effective detection methods to distinguish between real and fake images. Current research centers around the application of transfer learning. Nevertheless, it encounters challenges such as knowledge forgetting from the original dataset and inadequate performance when dealing with imbalanced data during training. To alleviate this issue, this paper introduces a novel GAN-generated image detection algorithm called X-Transfer, which enhances transfer learning by utilizing two neural networks that employ interleaved parallel gradient transmission. In addition, we combine AUC loss and cross-entropy loss to improve the model's performance. We carry out comprehensive experiments on multiple facial image datasets. The results show that our model outperforms the general transferring approach, and the best metric achieves 99.04%, which is increased by approximately 10%. Furthermore, we demonstrate excellent performance on non-face datasets, validating its generality and broader application prospects.

cs.CV↗