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Qing Liu

Publications and source records attributed to Qing Liu.

At least 127 records · Page 7Linked to original sources
arXiv2023

Hamilton-Jacobi equations in metric spaces

These are lecture notes for our minicourse at OIST Summer Graduate School "Analysis and Partial Differential Equations" on June 12-17, 2023. We give an overview and collect a few important results concerning the well-posedness of Hamilton-Jacobi equations in metric spaces, especially several recently proposed notions of metric viscosity solutions to the eikonal equation. Basic knowledge about metric spaces and a review of viscosity solution theory in the Euclidean spaces are also presented.

math.AP↗
arXiv2023

A second-order operator for horizontal quasiconvexity in the Heisenberg group and application to convexity preserving for horizontal curvature flow

This paper is concerned with a PDE approach to horizontally quasiconvex (h-quasiconvex) functions in the Heisenberg group based on a nonlinear second order elliptic operator. We discuss sufficient conditions and necessary conditions for upper semicontinuous, h-quasiconvex functions in terms of the viscosity subsolution to the associated elliptic equation. Since the notion of h-quasiconvexity is equivalent to the horizontal convexity (h-convexity) of the function's sublevel sets, we further adopt these conditions to study the h-convexity preserving property for horizontal curvature flow in the Heisenberg group. Under the comparison principle, we show that the curvature flow starting from a star-shaped h-convex set preserves the h-convexity during the evolution.

math.AP↗
arXiv2023

SmartMask: Context Aware High-Fidelity Mask Generation for Fine-grained Object Insertion and Layout Control

The field of generative image inpainting and object insertion has made significant progress with the recent advent of latent diffusion models. Utilizing a precise object mask can greatly enhance these applications. However, due to the challenges users encounter in creating high-fidelity masks, there is a tendency for these methods to rely on more coarse masks (e.g., bounding box) for these applications. This results in limited control and compromised background content preservation. To overcome these limitations, we introduce SmartMask, which allows any novice user to create detailed masks for precise object insertion. Combined with a ControlNet-Inpaint model, our experiments demonstrate that SmartMask achieves superior object insertion quality, preserving the background content more effectively than previous methods. Notably, unlike prior works the proposed approach can also be used even without user-mask guidance, which allows it to perform mask-free object insertion at diverse positions and scales. Furthermore, we find that when used iteratively with a novel instruction-tuning based planning model, SmartMask can be used to design detailed layouts from scratch. As compared with user-scribble based layout design, we observe that SmartMask allows for better quality outputs with layout-to-image generation methods. Project page is available at https://smartmask-gen.github.io

cs.CV↗
arXiv2023

Perceptual Artifacts Localization for Image Synthesis Tasks

Recent advancements in deep generative models have facilitated the creation of photo-realistic images across various tasks. However, these generated images often exhibit perceptual artifacts in specific regions, necessitating manual correction. In this study, we present a comprehensive empirical examination of Perceptual Artifacts Localization (PAL) spanning diverse image synthesis endeavors. We introduce a novel dataset comprising 10,168 generated images, each annotated with per-pixel perceptual artifact labels across ten synthesis tasks. A segmentation model, trained on our proposed dataset, effectively localizes artifacts across a range of tasks. Additionally, we illustrate its proficiency in adapting to previously unseen models using minimal training samples. We further propose an innovative zoom-in inpainting pipeline that seamlessly rectifies perceptual artifacts in the generated images. Through our experimental analyses, we elucidate several practical downstream applications, such as automated artifact rectification, non-referential image quality evaluation, and abnormal region detection in images. The dataset and code are released.

cs.CV↗
arXiv2023

A representation formula for viscosity solutions of nonlocal Hamilton--Jacobi equations and applications

This paper is concerned with geometric motion of a closed surface whose velocity depends on a nonlocal quantity of the enclosed region. Using the level set formulation, we study a class of nonlocal Hamilton--Jacobi equations and establish a control-based representation formula for solutions. We also apply the formula to discuss the fattening phenomenon and large-time asymptotics of the solutions.

math.AP↗
arXiv2023

Uncovering the System Vulnerability and Criticality of Human Brain under Dynamical Neuropathological Events in Alzheimer's Disease

Background: Despite the striking efforts in investigating neurobiological factors behind the acquisition of amyloid-\b{eta} (A), protein tau (T), and neurodegeneration ([N]) biomarkers, the mechanistic pathways of how AT[N] biomarkers spreading throughout the brain remain elusive. Objectives: To disentangle the massive heterogeneities in AD progressions and identify vulnerable/critical brain regions to AD pathology. Methods: In this work, we characterized the interaction of AT[N] biomarkers and their propagation across brain networks using a novel bistable reaction-diffusion model, which allows us to establish a new systems biology underpinning of Alzheimer's disease (AD) progression. We applied our model to large-scale longitudinal neuroimages from the ADNI database and studied the systematic vulnerability and criticality of brains. Results: Our model yields long term prediction that is statistically significant linear correlated with temporal imaging data, produces clinically consistent risk prediction, and captures the Braak-like spreading pattern of AT[N] biomarkers in AD development. Conclusion: Our major findings include (i) tau is a stronger indicator of regional risk compared to amyloid, (ii) temporal lobe exhibits higher vulnerability to AD-related pathologies, (iii) proposed critical brain regions outperform hub nodes in transmitting disease factors across the brain, and (iv) comparing the spread of neuropathological burdens caused by amyloid-\b{eta} and tau diffusions, disruption of metabolic balance is the most determinant factor contributing to the initiation and progression of Alzheimer's disease.

q-bio.QM↗
arXiv2023

Discontinuous eikonal equations in metric measure spaces

In this paper, we study the eikonal equation in metric measure spaces, where the inhomogeneous term is allowed to be discontinuous, unbounded and merely $p$-integrable in the domain with a finite $p$. For continuous eikonal equations, it is known that the notion of Monge solutions is equivalent to the standard definition of viscosity solutions. Generalizing the notion of Monge solutions in our setting, we establish uniqueness and existence results for the associated Dirichlet boundary problem. The key in our approach is to adopt a new metric, based on the optimal control interpretation, which integrates the discontinuous term and converts the eikonal equation to a standard continuous form. We also discuss the Holder continuity of the unique solution with respect to the original metric under regularity assumptions on the space and the inhomogeneous term.

math.AP↗
arXiv2023

Thinking Like an Expert:Multimodal Hypergraph-of-Thought (HoT) Reasoning to boost Foundation Modals

Reasoning ability is one of the most crucial capabilities of a foundation model, signifying its capacity to address complex reasoning tasks. Chain-of-Thought (CoT) technique is widely regarded as one of the effective methods for enhancing the reasoning ability of foundation models and has garnered significant attention. However, the reasoning process of CoT is linear, step-by-step, similar to personal logical reasoning, suitable for solving general and slightly complicated problems. On the contrary, the thinking pattern of an expert owns two prominent characteristics that cannot be handled appropriately in CoT, i.e., high-order multi-hop reasoning and multimodal comparative judgement. Therefore, the core motivation of this paper is transcending CoT to construct a reasoning paradigm that can think like an expert. The hyperedge of a hypergraph could connect various vertices, making it naturally suitable for modelling high-order relationships. Inspired by this, this paper innovatively proposes a multimodal Hypergraph-of-Thought (HoT) reasoning paradigm, which enables the foundation models to possess the expert-level ability of high-order multi-hop reasoning and multimodal comparative judgement. Specifically, a textual hypergraph-of-thought is constructed utilizing triple as the primary thought to model higher-order relationships, and a hyperedge-of-thought is generated through multi-hop walking paths to achieve multi-hop inference. Furthermore, we devise a visual hypergraph-of-thought to interact with the textual hypergraph-of-thought via Cross-modal Co-Attention Graph Learning for multimodal comparative verification. Experimentations on the ScienceQA benchmark demonstrate the proposed HoT-based T5 outperforms CoT-based GPT3.5 and chatGPT, which is on par with CoT-based GPT4 with a lower model size.

cs.CL↗
arXiv2023

A Recipe for Unbiased Background Modeling in Deep Wide-Field Astronomical Images

Unbiased sky background modeling is crucial for the analysis of deep wide-field images, but it remains a major challenge in low surface brightness astronomy. Traditional image processing algorithms are often designed to produce artificially flat backgrounds, erasing astrophysically meaningful structures. In this paper, we present three ideas that can be combined to produce wide-field astronomical data that preserve accurate representations of the background sky: (1) Use of all-sky infrared/sub-mm data to remove the large-scale time-varying components while leaving the scattered light from Galactic cirrus intact, with the assumptions of (a) the underlying background has little power on small scales, and (b) the Galactic cirrus in the field is optically thin on large scales; (2) Censoring of frames contaminated by anomalously prominent wings in the wide-angle point-spread function; and (3) Incorporation of spatial covariance in image stacking that controls the local background consistency. We demonstrate these methods using example datasets obtained with the Dragonfly Telephoto Array, but these general techniques are prospective to be applied to improve sky models in data obtained from other wide-field imaging surveys, including those from the upcoming Vera Rubin Telescope.

astro-ph.IM↗
arXiv2023

Novel $π$-type vortex in a nanoscale extreme type-II superconductor: Induced by quantum-size effect

By numerically solving the Bogoliubov-de Gennes equations, we report a novel $π$-type vortex state whose order parameter near the core undergoes an extraordinary $π$-phase change for a quantum-confined extreme type-II $s$-wave superconductor. Its supercurrent behaves as the cube of the radial coordinate near the core, and its local density of states spectrum exhibits a significant negative-shifted zero-bias peak. Such $π$-type vortex state is induced by quantum-size effect, and can survive thermal smearing at temperatures up to a critical value $T_τ$. The Anderson's approximation indicates that the $π$-type vortex may remain stable under sufficiently week magnetic field in the case less deep in the type-II limit. Moreover, we find that its appearance is governed by the sample size and $k_Fξ_0$ with $k_F$ the Fermi wave number and $ξ_0$ the zero-temperature coherence length. Similar effects may be expected in quantum-confined ultracold superfluid Fermi gasses, or even high-$T_c$ superconductors with proper $k_Fξ_0$ value.

cond-mat.supr-con↗
arXiv2023

A novel multi-step method for the partial pole assignment in symmetric quadratic pencil with time delay

In this paper, we study the partial pole assignment problem in symmetric quadratic pencil with time delay. A novel multi-step method is proposed to solve this problem, resulting in the undesired eigenvalues being moved to desired values, and the remaining eigenvalues unchanged. By establishing a new matrix equality relation and using a multi-step method, the problem is transformed into solving linear systems with low order. Specifically, assuming that there are $p$ undesired eigenvalues requiring reassigned, the size of the linear system we finally solved is $p^2$. Notably, the method demonstrates high efficiency for large systems with only a few poles requiring reassigned. Numerical examples are provided to illustrate the effectiveness of the proposed method

math.NA↗
arXiv2023

Performance analysis of multi-shot shadow estimation

Shadow estimation is an efficient method for predicting many observables of a quantum state with a statistical guarantee. In the multi-shot scenario, one performs projective measurement on the sequentially prepared state for $K$ times after the same unitary evolution, and repeats this procedure for $M$ rounds of random sampled unitary. As a result, there are $MK$ times measurements in total. Here we analyze the performance of shadow estimation in this multi-shot scenario, which is characterized by the variance of estimating the expectation value of some observable $O$. We find that in addition to the shadow-norm $\|O \|_{\mathrm{shadow}}$ introduced in [Huang et.al.~Nat.~Phys.~2020\cite{huang2020predicting}], the variance is also related to another norm, and we denote it as the cross-shadow-norm $\|O \|_{\mathrm{Xshadow}}$. For both random Pauli and Clifford measurements, we analyze and show the upper bounds of $\|O \|_{\mathrm{Xshadow}}$. In particular, we figure out the exact variance formula for Pauli observable under random Pauli measurements. Our work gives theoretical guidance for the application of multi-shot shadow estimation.

quant-ph↗
arXiv2023

Photoswap: Personalized Subject Swapping in Images

In an era where images and visual content dominate our digital landscape, the ability to manipulate and personalize these images has become a necessity. Envision seamlessly substituting a tabby cat lounging on a sunlit window sill in a photograph with your own playful puppy, all while preserving the original charm and composition of the image. We present Photoswap, a novel approach that enables this immersive image editing experience through personalized subject swapping in existing images. Photoswap first learns the visual concept of the subject from reference images and then swaps it into the target image using pre-trained diffusion models in a training-free manner. We establish that a well-conceptualized visual subject can be seamlessly transferred to any image with appropriate self-attention and cross-attention manipulation, maintaining the pose of the swapped subject and the overall coherence of the image. Comprehensive experiments underscore the efficacy and controllability of Photoswap in personalized subject swapping. Furthermore, Photoswap significantly outperforms baseline methods in human ratings across subject swapping, background preservation, and overall quality, revealing its vast application potential, from entertainment to professional editing.

cs.CV↗
arXiv2023

Towards Open-World Segmentation of Parts

Segmenting object parts such as cup handles and animal bodies is important in many real-world applications but requires more annotation effort. The largest dataset nowadays contains merely two hundred object categories, implying the difficulty to scale up part segmentation to an unconstrained setting. To address this, we propose to explore a seemingly simplified but empirically useful and scalable task, class-agnostic part segmentation. In this problem, we disregard the part class labels in training and instead treat all of them as a single part class. We argue and demonstrate that models trained without part classes can better localize parts and segment them on objects unseen in training. We then present two further improvements. First, we propose to make the model object-aware, leveraging the fact that parts are "compositions", whose extents are bounded by the corresponding objects and whose appearances are by nature not independent but bundled. Second, we introduce a novel approach to improve part segmentation on unseen objects, inspired by an interesting finding -- for unseen objects, the pixel-wise features extracted by the model often reveal high-quality part segments. To this end, we propose a novel self-supervised procedure that iterates between pixel clustering and supervised contrastive learning that pulls pixels closer or pushes them away. Via extensive experiments on PartImageNet and Pascal-Part, we show notable and consistent gains by our approach, essentially a critical step towards open-world part segmentation.

cs.CV↗
arXiv2023

Quantum Uncertainty Principles for Measurements with Interventions

Heisenberg's uncertainty principle implies fundamental constraints on what properties of a quantum system can we simultaneously learn. However, it typically assumes that we probe these properties via measurements at a single point in time. In contrast, inferring causal dependencies in complex processes often requires interactive experimentation - multiple rounds of interventions where we adaptively probe the process with different inputs to observe how they affect outputs. Here we demonstrate universal uncertainty principles for general interactive measurements involving arbitrary rounds of interventions. As a case study, we show that they imply an uncertainty trade-off between measurements compatible with different causal dependencies.

quant-ph↗
arXiv2023

TOT: Topology-Aware Optimal Transport For Multimodal Hate Detection

Multimodal hate detection, which aims to identify harmful content online such as memes, is crucial for building a wholesome internet environment. Previous work has made enlightening exploration in detecting explicit hate remarks. However, most of their approaches neglect the analysis of implicit harm, which is particularly challenging as explicit text markers and demographic visual cues are often twisted or missing. The leveraged cross-modal attention mechanisms also suffer from the distributional modality gap and lack logical interpretability. To address these semantic gaps issues, we propose TOT: a topology-aware optimal transport framework to decipher the implicit harm in memes scenario, which formulates the cross-modal aligning problem as solutions for optimal transportation plans. Specifically, we leverage an optimal transport kernel method to capture complementary information from multiple modalities. The kernel embedding provides a non-linear transformation ability to reproduce a kernel Hilbert space (RKHS), which reflects significance for eliminating the distributional modality gap. Moreover, we perceive the topology information based on aligned representations to conduct bipartite graph path reasoning. The newly achieved state-of-the-art performance on two publicly available benchmark datasets, together with further visual analysis, demonstrate the superiority of TOT in capturing implicit cross-modal alignment.

cs.CL↗
arXiv2023

Crowd Counting with Sparse Annotation

This paper presents a new annotation method called Sparse Annotation (SA) for crowd counting, which reduces human labeling efforts by sparsely labeling individuals in an image. We argue that sparse labeling can reduce the redundancy of full annotation and capture more diverse information from distant individuals that is not fully captured by Partial Annotation methods. Besides, we propose a point-based Progressive Point Matching network (PPM) to better explore the crowd from the whole image with sparse annotation, which includes a Proposal Matching Network (PMN) and a Performance Restoration Network (PRN). The PMN generates pseudo-point samples using a basic point classifier, while the PRN refines the point classifier with the pseudo points to maximize performance. Our experimental results show that PPM outperforms previous semi-supervised crowd counting methods with the same amount of annotation by a large margin and achieves competitive performance with state-of-the-art fully-supervised methods.

cs.CV↗
arXiv2023

Extended Line Emission in the BCG of Abell 2390

We report CFHT/SITELLE imaging Fourier Transform Spectrograph observations of the Brightest Cluster Galaxy (BCG) of galaxy cluster Abell 2390 at z=0.228. The BCG displays a prominent cone of emission in H$α$, H$β$, [NII], and [OII] to the North-West with PA = 42$^o$, 4.4 arcsec in length (15.9 kpc), which is associated with elongated and asymmetric Chandra soft X-ray emission. The H$α$ flux map also contains a "hook" of H$α$ and [NII] emission resulting in a broadened northern edge to the cone. Using SITELLE/LUCI software we extract emission line flux, velocity, velocity dispersion, and continuum maps, and utilize them to derive flux ratio maps to determine ionization mechanisms and dynamical information in the BCG's emission line region. The Baldwin-Phillips-Terlevich diagnostics on the BCG cone indicate a composite ionization origin of photoionization due to star formation and shock. Strong LINER-like emission is seen in the nuclear region which hosts an AGN. As Abell 2390 is a cool-core cluster, we suggest that the cooling flow is falling onto the central BCG and interacting with the central AGN. The AGN produces jets that inflate "bubbles" of plasma in the ICM, as is often observed in local galaxy clusters. Furthermore, combining signs of AGN activities from radio, optical emission line and X-ray data over a large range of physical scale, we find evidence for three possible episodes of AGN activity in different epochs associated with the Abell 2390 BCG.

astro-ph.GA↗