arXiv subjects

Yongquan Zhang

Publications and source records attributed to Yongquan Zhang.

15 recordsLinked to original sources

arXiv2026

MedGEN-Bench: A Contextually Entangled Benchmark for Open-ended Multimodal Medical Generation

Medical vision-language models (VLMs) are increasingly expected to support clinical workflows through diagnostic text and relevant medical images. However, current medical visual benchmarks have three recurring limitations: query-image misalignment from queries weakly grounded in specific image instances, closed-ended formats that narrow answer space and encourage shortcut-based prediction, and text-centric output paradigms that limit evaluation of image-generation and image-editing capabilities. We introduce MedGEN-Bench, a benchmark for open-ended multimodal medical generation. The evaluation snapshot reported in this manuscript comprises 6,422 image-text pairs reviewed by clinical experts and models, spanning 6 canonical imaging modalities, 15 clinical tasks, and 27 named subtasks. It includes 1,100 Visual Question Answering (VQA) pairs, 3,872 Image Editing pairs, and 1,450 Contextual Multimodal Generation pairs. MedGEN-Bench centers on contextual entanglement: dependence of an instruction's intended output on the particular image instance rather than on task wording alone. The benchmark operationalizes this concept through image-grounded instructions and extends evaluation to open-ended multimodal outputs. Its tiered evaluation protocol combines reproducible reference-based fidelity and similarity measures with a structured, checklist-guided assessment by a medical VLM judge. We evaluate 10 compositional frameworks, 2 dedicated image-editing models, 3 unified models, and 5 VLMs. The results show image-output tasks remain unsaturated. Contextual augmentation increases mean image-instruction similarity from 0.273 to 0.372, while a 1,000-case medical-expert audit shows moderate agreement between judge scores and clinician ratings. Source code and dataset are available at https://yangjj007.github.io/medgen.

cs.CV↗

arXiv2026

USCNet: Transformer-Based Multimodal Fusion with Segmentation Guidance for Urolithiasis Classification

Kidney stone disease ranks among the most prevalent conditions in urology, and understanding the composition of these stones is essential for creating personalized treatment plans and preventing recurrence. Current methods for analyzing kidney stones depend on postoperative specimens, which prevents rapid classification before surgery. To overcome this limitation, we introduce a new approach called the Urinary Stone Segmentation and Classification Network (USCNet). This innovative method allows for precise preoperative classification of kidney stones by integrating Computed Tomography (CT) images with clinical data from Electronic Health Records (EHR). USCNet employs a Transformer-based multimodal fusion framework with CT-EHR attention and segmentation-guided attention modules for accurate classification. Moreover, a dynamic loss function is introduced to effectively balance the dual objectives of segmentation and classification. Experiments on an in-house kidney stone dataset show that USCNet demonstrates outstanding performance across all evaluation metrics, with its classification efficacy significantly surpassing existing mainstream methods. This study presents a promising solution for the precise preoperative classification of kidney stones, offering substantial clinical benefits. The source code has been made publicly available: https://github.com/ZhangSongqi0506/KidneyStone.

cs.CV↗

arXiv2025

Isoperiodic foliation of the stratum $Ω\mathcal{M}_1(1,1,-2)$

This paper describes the geometry and topology of leaves of the isoperiodic foliation of the stratum $Ω\mathcal{M}_1(1,1,-2)$. We prove that each leaf is a surface of infinite genus homeomorphic to the Loch Ness monster surface and supports a singular Euclidean structure whose singularities correspond to isoperiodic forms in the lower stratum $Ω\mathcal{M}_1(2,-2)$. Along the way we also characterize the possible groups arising as the Veech group of a leaf and give a description of the large-scale conformal geometry of the wall-and-chamber decomposition of the leaves.

math.GT↗

arXiv2025

Effective equidistribution of intersection points in hyperbolic manifolds

In this paper, we establish effective equidistribution of transverse intersection points between properly immersed totally geodesic submanifolds of complementary dimensions in a finite-volume hyperbolic manifold with respect to the hyperbolic volume measure, as the volume of the submanifolds tends to infinity.

math.DS↗

arXiv2025

Disk patterns, quasi-duality and the uniform bounded diameter conjecture

We show that the diameter of the image of the skinning map on the deformation space of an acylindrical reflection group is bounded by a constant depending only on the topological complexity of the components of its boundary, answering a conjecture of Minsky in the reflection group setting. This result can be interpreted as a uniform rigidity theorem for disk patterns. Our method also establishes a connection between the diameter of the skinning image and certain discrete extremal width on the Coxeter graph of the reflection group.

math.GT↗

arXiv2025

Circle packings, renormalizations and subdivision rules

In this paper, we use iterations of skinning maps on Teichmüller spaces to study circle packings and develop a renormalization theory for circle packings whose nerves satisfy certain subdivision rules. We characterize when the skinning map has bounded image. Under the corresponding condition, we prove that the renormalization operator $\mathfrak{R}$ is uniformly contracting. This allows us to give complete answers for the existence and moduli problems for such circle packings. The exponential contraction of $\mathfrak{R}^n$ means that despite the non-rigidity of such circle packings, they are geometrically inflexible. As an application, we show that any geometrically finite Kleinian circle packing is combinatorially rigid.

math.GT↗

arXiv2025

On quasiconformal non-equivalence of gasket Julia sets and limit sets

This paper studies quasiconformal non-equivalence of Julia sets and limit sets. We proved that any Julia set is quasiconformally different from the Apollonian gasket. We also proved that any Julia set of a quadratic rational map is quasiconformally different from the gasket limit set of a geometrically finite Kleinian group.

math.DS↗

arXiv2024

Geodesic planes in a geometrically finite end and the halo of a measured lamination

Recent works [MMO1, arXiv:1802.03853, arXiv:1802.04423, arXiv:2101.08956] have shed light on the topological behavior of geodesic planes in the convex core of a geometrically finite hyperbolic 3-manifolds $M$ of infinite volume. In this paper, we focus on the remaining case of geodesic planes outside the convex core of $M$, giving a complete classification of their closures in $M$. In particular, we show that the behavior is different depending on whether exotic roofs exist or not. Here an exotic roof is a geodesic plane contained in an end $E$ of $M$, which limits on the convex core boundary $\partial E$, but cannot be separated from the core by a support plane of $\partial E$. A necessary condition for the existence of exotic roofs is the existence of exotic rays for the bending lamination. Here an exotic ray is a geodesic ray that has finite intersection number with a measured lamination $\mathcal{L}$ but is not asymptotic to any leaf nor eventually disjoint from $\mathcal{L}$. We establish that exotic rays exist if and only if $\mathcal{L}$ is not a multicurve. The proof is constructive, and the ideas involved are important in the construction of exotic roofs. We also show that the existence of geodesic rays satisfying a stronger condition than being exotic, phrased in terms of only the hyperbolic surface $\partial E$ and the bending lamination, is sufficient for the existence of exotic roofs. As a result, we show that geometrically finite ends with exotic roofs exist in every genus. Moreover, in genus $1$, when the end is homotopic to a punctured torus, a generic one (in the sense of Baire category) contains uncountably many exotic roofs.

math.GT↗

arXiv2024

Semi-supervised Medical Image Segmentation Method Based on Cross-pseudo Labeling Leveraging Strong and Weak Data Augmentation Strategies

Traditional supervised learning methods have historically encountered certain constraints in medical image segmentation due to the challenging collection process, high labeling cost, low signal-to-noise ratio, and complex features characterizing biomedical images. This paper proposes a semi-supervised model, DFCPS, which innovatively incorporates the Fixmatch concept. This significantly enhances the model's performance and generalizability through data augmentation processing, employing varied strategies for unlabeled data. Concurrently, the model design gives appropriate emphasis to the generation, filtration, and refinement processes of pseudo-labels. The novel concept of cross-pseudo-supervision is introduced, integrating consistency learning with self-training. This enables the model to fully leverage pseudo-labels from multiple perspectives, thereby enhancing training diversity. The DFCPS model is compared with both baseline and advanced models using the publicly accessible Kvasir-SEG dataset. Across all four subdivisions containing different proportions of unlabeled data, our model consistently exhibits superior performance. Our source code is available at https://github.com/JustlfC03/DFCPS.

cs.CV↗

arXiv2023

FedPDC:Federated Learning for Public Dataset Correction

As people pay more and more attention to privacy protection, Federated Learning (FL), as a promising distributed machine learning paradigm, is receiving more and more attention. However, due to the biased distribution of data on devices in real life, federated learning has lower classification accuracy than traditional machine learning in Non-IID scenarios. Although there are many optimization algorithms, the local model aggregation in the parameter server is still relatively traditional. In this paper, a new algorithm FedPDC is proposed to optimize the aggregation mode of local models and the loss function of local training by using the shared data sets in some industries. In many benchmark experiments, FedPDC can effectively improve the accuracy of the global model in the case of extremely unbalanced data distribution, while ensuring the privacy of the client data. At the same time, the accuracy improvement of FedPDC does not bring additional communication costs.

cs.LG↗

arXiv2022

Elementary planes in the Apollonian orbifold

In this paper, we study the topological behavior of elementary planes in the Apollonian orbifold $M_A$, whose limit set is the classical Apollonian gasket. The existence of these elementary planes leads to the following failure of equidistribution: there exists a sequence of closed geodesic planes in $M_A$ limiting only on a finite union of closed geodesic planes. This contrasts with other acylindrical hyperbolic 3-manifolds analyzed in [MMO1, arXiv:1802.03853, arXiv:1802.04423]. On the other hand, we show that certain rigidity still holds: the area of an elementary plane in $M_A$ is uniformly bounded above, and the union of all elementary planes is closed. This is achieved by obtaining a complete list of elementary planes in $M_A$, indexed by their intersection with the convex core boundary. The key idea is to recover information on a closed geodesic plane in $M_A$ from its boundary data; requiring the plane to be elementary in turn puts restrictions on these data.

math.GT↗

arXiv2022

Train tracks, entropy, and the halo of a measured lamination

Let $\mathcal{L}$ be a measured geodesic lamination on a complete hyperbolic surface of finite area. Assuming $\mathcal{L}$ is not a multicurve, our main result establishes the existence of a geodesic ray which has finite intersection number with $\mathcal{L}$ but is not asymptotic to any leaf of $\mathcal{L}$ nor eventually disjoint from $\mathcal{L}$. In fact, we show that the endpoints of such rays, when lifted to the universal cover $\mathbb{H}^2$ of $X$, give an uncountable set $h\tilde{\mathcal{L}}\subset S^1$ (called the halo of $\tilde{\mathcal{L}}$), which is disjoint from the endpoints of leaves of the lifted lamination $\tilde{\mathcal{L}}$.

math.GT↗

arXiv2022

Existence of an exotic plane in an acylindrical 3-manifold

Let $P$ be a geodesic plane in a convex cocompact, acylindrical hyperbolic 3-manifold $M$. Assume that $P^*=M^*\cap P$ is nonempty, where $M^*$ is the interior of the convex core of $M$. Does this condition imply that $P$ is either closed or dense in $M$? A positive answer would furnish an analogue of Ratner's theorem in the infinite volume setting. In arXiv:1802.03853 it is shown that $P^*$ is either closed or dense in $M^*$. Moreover, there are at most countably many planes with $P^*$ closed, and in all previously known examples, $P$ was also closed in $M$. In this note we show more exotic behavior can occur: namely, we give an explicit example of a pair $(M,P)$ such that $P^*$ is closed in $M^*$ but $P$ is not closed in $M$. In particular, the answer to the question above is no. Thus Ratner's theorem fails to generalize to planes in acylindrical 3-manifolds, without additional restrictions.

math.GT↗

arXiv2016

Smale's mean value conjecture for finite Blaschke products

Motivated by a dictionary between polynomials and finite Blaschke products, we study both Smale's mean value conjecture and its dual conjecture for finite Blaschke products in this paper. Our result on the dual conjecture for finite Blaschke products allows us to improve a bound obtained by V. Dubinin and T. Sugawa for the dual mean value conjecture for polynomials.

math.CV↗

arXiv2015

On the Feasibility of Distributed Kernel Regression for Big Data

In modern scientific research, massive datasets with huge numbers of observations are frequently encountered. To facilitate the computational process, a divide-and-conquer scheme is often used for the analysis of big data. In such a strategy, a full dataset is first split into several manageable segments; the final output is then averaged from the individual outputs of the segments. Despite its popularity in practice, it remains largely unknown that whether such a distributive strategy provides valid theoretical inferences to the original data. In this paper, we address this fundamental issue for the distributed kernel regression (DKR), where the algorithmic feasibility is measured by the generalization performance of the resulting estimator. To justify DKR, a uniform convergence rate is needed for bounding the generalization error over the individual outputs, which brings new and challenging issues in the big data setup. Under mild conditions, we show that, with a proper number of segments, DKR leads to an estimator that is generalization consistent to the unknown regression function. The obtained results justify the method of DKR and shed light on the feasibility of using other distributed algorithms for processing big data. The promising preference of the method is supported by both simulation and real data examples.

stat.ML↗