arXiv subjects

Ziqi Yu

Publications and source records attributed to Ziqi Yu.

11 recordsLinked to original sources

arXiv2026

The Art of Calling the Winner by Asking Just Enough Questions: Competitive Preference Elicitation with Next-Best Queries

We study active elicitation of agent preferences for collectively choosing among $m$ alternatives using prominent voting rules. We focus on the next-best query model, in which an agent responds to a query by revealing their next favorite alternative, and measure the competitive ratio, which is the worst-case ratio between the number of queries made by the active elicitation algorithm and the minimum number of queries needed to reveal the winning alternative(s) in hindsight. We show that sublinear competitive ratios are achievable for many positional scoring rules, whereas every Condorcet-consistent rule has competitive ratio linear in $m$. For Borda count, we develop two complementary techniques: level-wise pruning, whose analysis extends to general concave scoring rules, and multi-scale score thresholding, which gives an $O(\sqrt m)$ worst-case guarantee for Borda. We also demonstrate strong empirical performance of level-wise pruning on real data.

cs.GT↗

arXiv2026

Unifying Proportional Fairness in Centroid and Non-Centroid Clustering

Proportional fairness criteria inspired by democratic ideals of proportional representation have received growing attention in the clustering literature. Prior work has investigated them in two separate paradigms. Chen et al. [ICML 2019] study centroid clustering, in which each data point's loss is determined by its distance to a representative point (centroid) chosen in its cluster. Caragiannis et al. [NeurIPS 2024] study non-centroid clustering, in which each data point's loss is determined by its maximum distance to any other data point in its cluster. We generalize both paradigms to introduce semi-centroid clustering, in which each data point's loss is a combination of its centroid and non-centroid losses, and study two proportional fairness criteria -- the core and, its relaxation, fully justified representation (FJR). Our main result is a novel algorithm which achieves a constant approximation to the core, in polynomial time, even when the distance metrics used for centroid and non-centroid loss measurements are different. We also derive improved results for more restricted loss functions and the weaker FJR criterion, and establish lower bounds in each case.

cs.GT↗

arXiv2025

A note on the bounded orbit conjecture

If $f:\mathbb{R}^2\rightarrow \mathbb{R}^2$ is an orientation reversing fixed point free homeomorphism on the plane $\mathbb{R}^2$ with no unbounded orbit, then $f$ has infinitely many periodic orbits.

math.DS↗

arXiv2024

Linearizations of periodic point free distal homeomorphisms on the annulus

Let $\mathbb{A}$ be an annulus in the plane $\mathbb R^2$ and $g:\mathbb{A}\rightarrow \mathbb{A}$ be a boundary components preserving homeomorphism which is distal and has no periodic points. In \cite{SXY}, the authors show that there is a continuous decomposition $\mathcal P$ of $\mathbb{A}$ into $g$-invariant circles such that all the restrictions of $g$ on them share a common irrational rotation number (also called the rotation number of $g$) and all these circles are linearly ordered by the inclusion relation on the sets of bounded components of their complements in $\mathbb R^2$. In this note, we show that if the decomposition $\mathcal P$ above has a continuous section, then $g$ can be linearized, that is it is topologically conjugate to a rigid rotation on $\mathbb{A}$. For every irrational number $\alpha\in (0, 1)$, we show the existence of such a distal homeomorphism $g$ on $\mathbb{A}$ that it cannot be linearized and its rotation number is $\alpha$.

math.DS↗

arXiv2023

HiFi-Syn: Hierarchical Granularity Discrimination for High-Fidelity Synthesis of MR Images with Structure Preservation

Synthesizing medical images while preserving their structural information is crucial in medical research. In such scenarios, the preservation of anatomical content becomes especially important. Although recent advances have been made by incorporating instance-level information to guide translation, these methods overlook the spatial coherence of structural-level representation and the anatomical invariance of content during translation. To address these issues, we introduce hierarchical granularity discrimination, which exploits various levels of semantic information present in medical images. Our strategy utilizes three levels of discrimination granularity: pixel-level discrimination using a Brain Memory Bank, structure-level discrimination on each brain structure with a re-weighting strategy to focus on hard samples, and global-level discrimination to ensure anatomical consistency during translation. The image translation performance of our strategy has been evaluated on three independent datasets (UK Biobank, IXI, and BraTS 2018), and it has outperformed state-of-the-art algorithms. Particularly, our model excels not only in synthesizing normal structures but also in handling abnormal (pathological) structures, such as brain tumors, despite the variations in contrast observed across different imaging modalities due to their pathological characteristics. The diagnostic value of synthesized MR images containing brain tumors has been evaluated by radiologists. This indicates that our model may offer an alternative solution in scenarios where specific MR modalities of patients are unavailable. Extensive experiments further demonstrate the versatility of our method, providing unique insights into medical image translation.

eess.IV↗

arXiv2023

On the Existence of EFX (and Pareto-Optimal) Allocations for Binary Chores

We study the problem of allocating a group of indivisible chores among agents while each chore has a binary marginal. We focus on the fairness criteria of envy-freeness up to any item (EFX) and investigate the existence of EFX allocations. We show that when agents have additive binary cost functions, there exist EFX and Pareto-optimal (PO) allocations that can be computed in polynomial time. To the best of our knowledge, this is the first setting of a general number of agents that admits EFX and PO allocations, before which EFX and PO allocations have only been shown to exist for three bivalued agents. We further consider more general cost functions: cancelable and general monotone (both with binary marginal). We show that EFX allocations exist and can be computed for binary cancelable chores, but EFX is incompatible with PO. For general binary marginal functions, we propose an algorithm that computes (partial) envy-free (EF) allocations with at most $n-1$ unallocated items.

cs.GT↗

arXiv2023

EFX Allocations Exist for Binary Valuations

We study the fair division problem and the existence of allocations satisfying the fairness criterion envy-freeness up to any item (EFX). The existence of EFX allocations is a major open problem in the fair division literature. We consider binary valuations where the marginal gain of the value by receiving an extra item is either $0$ or $1$. Babaioff et al. [2021] proved that EFX allocations always exist for binary and submodular valuations. In this paper, by using completely different techniques, we extend this existence result to general binary valuations that are not necessarily submodular, and we present a polynomial time algorithm for computing an EFX allocation.

cs.CE↗

arXiv2022

MouseGAN++: Unsupervised Disentanglement and Contrastive Representation for Multiple MRI Modalities Synthesis and Structural Segmentation of Mouse Brain

Segmenting the fine structure of the mouse brain on magnetic resonance (MR) images is critical for delineating morphological regions, analyzing brain function, and understanding their relationships. Compared to a single MRI modality, multimodal MRI data provide complementary tissue features that can be exploited by deep learning models, resulting in better segmentation results. However, multimodal mouse brain MRI data is often lacking, making automatic segmentation of mouse brain fine structure a very challenging task. To address this issue, it is necessary to fuse multimodal MRI data to produce distinguished contrasts in different brain structures. Hence, we propose a novel disentangled and contrastive GAN-based framework, named MouseGAN++, to synthesize multiple MR modalities from single ones in a structure-preserving manner, thus improving the segmentation performance by imputing missing modalities and multi-modality fusion. Our results demonstrate that the translation performance of our method outperforms the state-of-the-art methods. Using the subsequently learned modality-invariant information as well as the modality-translated images, MouseGAN++ can segment fine brain structures with averaged dice coefficients of 90.0% (T2w) and 87.9% (T1w), respectively, achieving around +10% performance improvement compared to the state-of-the-art algorithms. Our results demonstrate that MouseGAN++, as a simultaneous image synthesis and segmentation method, can be used to fuse cross-modality information in an unpaired manner and yield more robust performance in the absence of multimodal data. We release our method as a mouse brain structural segmentation tool for free academic usage at https://github.com/yu02019.

eess.IV↗

arXiv2022

The structures of pointwise recurrent quasi-graph maps

We show that a continuous map $f$ from a quasi-graph $G$ to itself is pointwise recurrent if and only if one of the following two statements holds: (1) $X$ is a simple closed curve and $f$ is topologically conjugate to an irrational rotation on the unit circle $\mathbb S^1$; (2) $f$ is a perodic homeomorphism.

math.DS↗

arXiv2022

The structure of pointwise recurrent expansive homeomorphisms

Let $X$ be a compact metric space and let $f:X\rightarrow X$ be a homeomorphism on $X$. We show that if $f$ is both pointwise recurrent and expansive, then the dynamical system $(X, f)$ is topologically conjugate to a subshift of some symbolic system. Moreover, if $f$ is pointwise positively recurrent, then the subshift is semisimple; a counterexample is given to show the necessity of positive recurrence to ensure the semisimilicity.

math.DS↗

arXiv2020

Towards Data-Efficient Learning: A Benchmark for COVID-19 CT Lung and Infection Segmentation

Purpose: Accurate segmentation of lung and infection in COVID-19 CT scans plays an important role in the quantitative management of patients. Most of the existing studies are based on large and private annotated datasets that are impractical to obtain from a single institution, especially when radiologists are busy fighting the coronavirus disease. Furthermore, it is hard to compare current COVID-19 CT segmentation methods as they are developed on different datasets, trained in different settings, and evaluated with different metrics. Methods: To promote the development of data-efficient deep learning methods, in this paper, we built three benchmarks for lung and infection segmentation based on 70 annotated COVID-19 cases, which contain current active research areas, e.g., few-shot learning, domain generalization, and knowledge transfer. For a fair comparison among different segmentation methods, we also provide standard training, validation and testing splits, evaluation metrics and, the corresponding code. Results: Based on the state-of-the-art network, we provide more than 40 pre-trained baseline models, which not only serve as out-of-the-box segmentation tools but also save computational time for researchers who are interested in COVID-19 lung and infection segmentation. We achieve average Dice Similarity Coefficient (DSC) scores of 97.3\%, 97.7\%, and 67.3\% and average Normalized Surface Dice (NSD) scores of 90.6\%, 91.4\%, and 70.0\% for left lung, right lung, and infection, respectively. Conclusions: To the best of our knowledge, this work presents the first data-efficient learning benchmark for medical image segmentation and the largest number of pre-trained models up to now. All these resources are publicly available, and our work lays the foundation for promoting the development of deep learning methods for efficient COVID-19 CT segmentation with limited data.

eess.IV↗