arXiv subjects

Liang Guo

Publications and source records attributed to Liang Guo.

At least 37 records · Page 2Linked to original sources

arXiv2025

Anatomically and Metabolically Informed Diffusion for Unified Denoising and Segmentation in Low-Count PET Imaging

Positron emission tomography (PET) image denoising, along with lesion and organ segmentation, are critical steps in PET-aided diagnosis. However, existing methods typically treat these tasks independently, overlooking inherent synergies between them as correlated steps in the analysis pipeline. In this work, we present the anatomically and metabolically informed diffusion (AMDiff) model, a unified framework for denoising and lesion/organ segmentation in low-count PET imaging. By integrating multi-task functionality and exploiting the mutual benefits of these tasks, AMDiff enables direct quantification of clinical metrics, such as total lesion glycolysis (TLG), from low-count inputs. The AMDiff model incorporates a semantic-informed denoiser based on diffusion strategy and a denoising-informed segmenter utilizing nnMamba architecture. The segmenter constrains denoised outputs via a lesion-organ-specific regularizer, while the denoiser enhances the segmenter by providing enriched image information through a denoising revision module. These components are connected via a warming-up mechanism to optimize multi-task interactions. Experiments on multi-vendor, multi-center, and multi-noise-level datasets demonstrate the superior performance of AMDiff.

eess.IV↗

arXiv2025

Relative higher index theory on quotients of Roe algebras and positive scalar curvature at infinity

In this paper, we employ quotients of Roe algebras as index containers for elliptic differential operators to study the existence problem of Riemannian metrics with positive scalar curvature on non-compact complete Riemannian manifolds. The non-vanishing of such an index locates the precise direction at infinity of the obstructions to positive scalar curvature, and may be viewed as a refinement of the positive scalar curvature problem. To achieve this, we formulate the relative coarse Baum-Connes conjecture and the relative coarse Novikov conjecture, together with their maximal versions, for general metric spaces as a program to compute the $K$-theory of the quotients of the Roe algebras relative to specific ideals. We show that if the metric space admits a relative fibred coarse embedding into Hilbert space or an $\ell^p$-space, certain cases of these conjectures can be verified, which yield obstructions to the existence of uniformly positive scalar curvature metrics in specified directions at infinity. As an application, we prove that the maximal coarse Baum-Connes conjecture holds for finite products of certain expander graphs that fail to admit fibred coarse embeddings into Hilbert space.

math.KT↗

arXiv2025

A nonstanadard analysis approach to limit operators and Fredholmness in Roe-like algebras

Let $(X,d)$ be a uniformly locally finite metric space, and $T$ an operator in the uniform Roe algebra $C_u^*(X)$ (or uniform quasi-local algebra $C_{ql}^*(X)$). In this paper, we introduce the concept of limit operators of $T$ on galaxies in the nonstandard extension of $X$, and prove that $T$ is a generalized Fredholm operator with respect to the ghost ideal in $C_u^*(X)$ (or $C_{ql}^*(X)$) if and only if all limit operators on afar galaxies are invertible, and their inverses are uniformly bounded. In particular, if $X$ has Yu's Property A, then $T$ is a Fredholm operator if and only if all limit operators on afar galaxies are invertible. Using techniques in nonstandard analysis, our result strengthens a work of Špakula--Willett \cite{SpW} on the characterization of Fredholmness by using less limit operators.

math.FA↗

arXiv2025

Joint Classification of Haze and Dust Events Using Factorial Hidden Markov Model Framework

Haze and dust pollution events have significant adverse impacts on human health and ecosystems. Their formation-impact interactions are complex, creating substantial modeling and computational challenges for joint classification. To address the state-space explosion faced by conventional Hidden Markov Models in multivariate dynamic settings, this study develops a classification framework based on the Factorial Hidden Markov Model. The framework assumes statistical independence across multiple latent chains and applies the Walsh-Hadamard transform to reduce computational and memory costs. A Gaussian copula decouples marginal distributions from dependence to capture nonlinear correlations among meteorological and pollution indicators. Algorithmically, mutual information weights the observational variables to increase the sensitivity of Viterbi decoding to salient features, and a single global weight hyperparameter balances emission and transition contributions in the decoding objective. In an empirical application, the model attains a Micro-F1 of 0.9459; for the low-frequency classes Dust prevalence below 1\% and Haze prevalence below 10\%, the F1-scores improve from 0.19 and 0.32 under a baseline FHMM to 0.75 and 0.68. The framework provides a scalable pathway for statistical modeling of complex air-pollution events and supplies quantitative evidence for decision-making in outdoor activity management and fine-grained environmental governance.

stat.AP↗

arXiv2025

Request-Only Optimization for Recommendation Systems

Deep Learning Recommendation Models (DLRMs) represent one of the largest machine learning applications on the planet. Industry-scale DLRMs are trained with petabytes of recommendation data to serve billions of users every day. To utilize the rich user signals in the long user history, DLRMs have been scaled up to unprecedented complexity, up to trillions of floating-point operations (TFLOPs) per example. This scale, coupled with the huge amount of training data, necessitates new storage and training algorithms to efficiently improve the quality of these complex recommendation systems. In this paper, we present a Request-Only Optimizations (ROO) training and modeling paradigm. ROO simultaneously improves the storage and training efficiency as well as the model quality of recommendation systems. We holistically approach this challenge through co-designing data (i.e., request-only data), infrastructure (i.e., request-only based data processing pipeline), and model architecture (i.e., request-only neural architectures). Our ROO training and modeling paradigm treats a user request as a unit of the training data. Compared with the established practice of treating a user impression as a unit, our new design achieves native feature deduplication in data logging, consequently saving data storage. Second, by de-duplicating computations and communications across multiple impressions in a request, this new paradigm enables highly scaled-up neural network architectures to better capture user interest signals, such as Generative Recommenders (GRs) and other request-only friendly architectures.

cs.IR↗

arXiv2025

Leveraging large language models for SQL behavior-based database intrusion detection

Database systems are extensively used to store critical data across various domains. However, the frequency of abnormal database access behaviors, such as database intrusion by internal and external attacks, continues to rise. Internal masqueraders often have greater organizational knowledge, making it easier to mimic employee behavior effectively. In contrast, external masqueraders may behave differently due to their lack of familiarity with the organization. Current approaches lack the granularity needed to detect anomalies at the operational level, frequently misclassifying entire sequences of operations as anomalies, even though most operations are likely to represent normal behavior. On the other hand, some anomalous behaviors often resemble normal activities, making them difficult for existing detection methods to identify. This paper introduces a two-tiered anomaly detection approach for Structured Query Language (SQL) using the Bidirectional Encoder Representations from Transformers (BERT) model, specifically DistilBERT, a more efficient, pre-trained version. Our method combines both unsupervised and supervised machine learning techniques to accurately identify anomalous activities while minimizing the need for data labeling. First, the unsupervised method uses ensemble anomaly detectors that flag embedding vectors distant from learned normal patterns of typical user behavior across the database (out-of-scope queries). Second, the supervised method uses fine-tuned transformer-based models to detect internal attacks with high precision (in-scope queries), using role-labeled classification, even on limited labeled SQL data. Our findings make a significant contribution by providing an effective solution for safeguarding critical database systems from sophisticated threats.

cs.CR↗

arXiv2025

Hilbert-Hadamard spaces and the equivariant coarse Novikov conjecture

The equivariant coarse Novikov conjectures stand among a handful profound $K$-theoretic conjectures in noncommutative geometry. Motivated by the quest to verify Novikov-type conjectures for groups of diffeomorphisms, we study in this paper the equivariant coarse Novikov conjectures for spaces that equivariantly and coarsely embed into admissible Hilbert-Hadamard spaces, which are a type of infinite-dimensional nonpositively curved spaces. The paper is split into two parts. We prove in the first part that for any metric space $X$ with bounded geometry and with a proper isometric action $α$ by a countable discrete group $Γ$, if $X$ admits an equivariant coarse embedding into an admissible Hilbert-Hadamard space and $Γ$ is torsion-free, then the equivariant coarse strong Novikov conjecture holds rationally for $(X, Γ, α)$. In the second part, we extend the result in the first part by dropping the torsion-free assumption on $Γ$. To this end, we introduce, for a proper $Γ$-space $X$ with equivariant bounded geometry, a new Novikov-type conjecture that we call the rational analytic equivariant coarse Novikov conjecture, which generalizes the rational analytic Novikov conjecture and asserts the rational injectivity of a certain assembly map associated with a coarse analog of the classifying space $EΓ$. We show that for a proper $Γ$-space $X$ with equivariant bounded geometry, if $X$ admits an equivariant coarse embedding into an admissible Hilbert-Hadamard space, then the rational analytic equivariant coarse Novikov conjecture holds for $(X,Γ,α)$, i.e., the assembly map is a rational injection.

math.KT↗

arXiv2025

Dose-aware Diffusion Model for 3D PET Image Denoising: Multi-institutional Validation with Reader Study and Real Low-dose Data

Reducing scan times, radiation dose, and enhancing image quality for lower-performance scanners, are critical in low-dose PET imaging. Deep learning techniques have been investigated for PET image denoising. However, existing models have often resulted in compromised image quality when achieving low-count/low-dose PET and have limited generalizability to different image noise-levels, acquisition protocols, and patient populations. Recently, diffusion models have emerged as the new state-of-the-art generative model to generate high-quality samples and have demonstrated strong potential for medical imaging tasks. However, for low-dose PET imaging, existing diffusion models failed to generate consistent 3D reconstructions, unable to generalize across varying noise-levels, often produced visually-appealing but distorted image details, and produced images with biased tracer uptake. Here, we develop DDPET-3D, a dose-aware diffusion model for 3D low-dose PET imaging to address these challenges. Collected from 4 medical centers globally with different scanners and clinical protocols, we evaluated the proposed model using a total of 9,783 18F-FDG studies with low-dose levels ranging from 1% to 50%. With a cross-center, cross-scanner validation, the proposed DDPET-3D demonstrated its potential to generalize to different low-dose levels, different scanners, and different clinical protocols. As confirmed with reader studies performed by board-certified nuclear medicine physicians, experienced readers judged the images to be similar or superior to the full-dose images and previous DL baselines based on qualitative visual impression. Lesion-level quantitative accuracy was evaluated using a Monte Carlo simulation study and a lesion segmentation network. The presented results show the potential to achieve low-dose PET while maintaining image quality. Real low-dose scans was also included for evaluation.

eess.IV↗

arXiv2025

Geometric Banach property (T) for metric spaces via Banach representations of Roe algebras

In this paper, we introduce a notion of geometric Banach property (T) for metric spaces, which jointly generalizes Banach property (T) for groups and geometric property (T) for metric spaces. Our framework is achieved by Banach representations of Roe algebras of metric spaces. We show that geometric Banach property (T) is a coarse geometric invariant, and it is equivalent to the existence of the Kazhdan projections in the Banach-Roe algebras. Further, we study the implications of this property for sequences of finite Cayley graphs, establishing two key results: 1. geometric Banach property (T) of such sequences implies Banach property (T) for their limit groups; 2. while the Banach coarse fixed point property implies geometric Banach property (T), the converse fails. Additionally, we provide a geometric characterization of V. Lafforgue's strong Banach property (T) for a residually finite group in terms of geometric Banach property (T) of its box spaces.

math.FA↗

arXiv2025

Twisted Roe algebras and their $K$-theory

In this paper, we introduce a notion of twisted Roe algebra and a twisted coarse Baum-Connes conjecture with coefficients. We will study the basic properties of twisted Roe algebras, including a coarse analogue of the imprimitivity theorem for metric spaces with a structure of coarse fibrations. We show that the twisted coarse Baum-Connes conjecture with coefficients holds for a metric space with a coarse fibration structure when the base space and the fiber satisfy the twisted coarse Baum-Connes conjecture with coefficients. As an application, the coarse Baum-Connes conjecture holds for a finitely generated group which is an extension of coarsely embeddable groups.

math.KT↗

arXiv2025

Dual Attention Driven Lumbar Magnetic Resonance Image Feature Enhancement and Automatic Diagnosis of Herniation

Lumbar disc herniation (LDH) is a common musculoskeletal disease that requires magnetic resonance imaging (MRI) for effective clinical management. However, the interpretation of MRI images heavily relies on the expertise of radiologists, leading to delayed diagnosis and high costs for training physicians. Therefore, this paper proposes an innovative automated LDH classification framework. To address these key issues, the framework utilizes T1-weighted and T2-weighted MRI images from 205 people. The framework extracts clinically actionable LDH features and generates standardized diagnostic outputs by leveraging data augmentation and channel and spatial attention mechanisms. These outputs can help physicians make confident and time-effective care decisions when needed. The proposed framework achieves an area under the receiver operating characteristic curve (AUC-ROC) of 0.969 and an accuracy of 0.9486 for LDH detection. The experimental results demonstrate the performance of the proposed framework. Our framework only requires a small number of datasets for training to demonstrate high diagnostic accuracy. This is expected to be a solution to enhance the LDH detection capabilities of primary hospitals.

eess.IV↗

arXiv2025

Fed-NDIF: A Noise-Embedded Federated Diffusion Model For Low-Count Whole-Body PET Denoising

Low-count positron emission tomography (LCPET) imaging can reduce patients' exposure to radiation but often suffers from increased image noise and reduced lesion detectability, necessitating effective denoising techniques. Diffusion models have shown promise in LCPET denoising for recovering degraded image quality. However, training such models requires large and diverse datasets, which are challenging to obtain in the medical domain. To address data scarcity and privacy concerns, we combine diffusion models with federated learning -- a decentralized training approach where models are trained individually at different sites, and their parameters are aggregated on a central server over multiple iterations. The variation in scanner types and image noise levels within and across institutions poses additional challenges for federated learning in LCPET denoising. In this study, we propose a novel noise-embedded federated learning diffusion model (Fed-NDIF) to address these challenges, leveraging a multicenter dataset and varying count levels. Our approach incorporates liver normalized standard deviation (NSTD) noise embedding into a 2.5D diffusion model and utilizes the Federated Averaging (FedAvg) algorithm to aggregate locally trained models into a global model, which is subsequently fine-tuned on local datasets to optimize performance and obtain personalized models. Extensive validation on datasets from the University of Bern, Ruijin Hospital in Shanghai, and Yale-New Haven Hospital demonstrates the superior performance of our method in enhancing image quality and improving lesion quantification. The Fed-NDIF model shows significant improvements in PSNR, SSIM, and NMSE of the entire 3D volume, as well as enhanced lesion detectability and quantification, compared to local diffusion models and federated UNet-based models.

eess.IV↗

arXiv2025

Derivative-Free Optimization via Finite Difference Approximation: An Experimental Study

Derivative-free optimization (DFO) is vital in solving complex optimization problems where only noisy function evaluations are available through an oracle. Within this domain, DFO via finite difference (FD) approximation has emerged as a powerful method. Two classical approaches are the Kiefer-Wolfowitz (KW) and simultaneous perturbation stochastic approximation (SPSA) algorithms, which estimate gradients using just two samples in each iteration to conserve samples. However, this approach yields imprecise gradient estimators, necessitating diminishing step sizes to ensure convergence, often resulting in slow optimization progress. In contrast, FD estimators constructed from batch samples approximate gradients more accurately. While gradient descent algorithms using batch-based FD estimators achieve more precise results in each iteration, they require more samples and permit fewer iterations. This raises a fundamental question: which approach is more effective -- KW-style methods or DFO with batch-based FD estimators? This paper conducts a comprehensive experimental comparison among these approaches, examining the fundamental trade-off between gradient estimation accuracy and iteration steps. Through extensive experiments in both low-dimensional and high-dimensional settings, we demonstrate a surprising finding: when an efficient batch-based FD estimator is applied, its corresponding gradient descent algorithm generally shows better performance compared to classical KW and SPSA algorithms in our tested scenarios.

cs.LG↗

arXiv2025

The maximal coarse Baum-Connes conjecture for spaces that admit an A-by-FCE coarse fibration structure

In this paper, we introduce a concept of A-by-FCE coarse fibration structure for metric spaces, which serves as a generalization of the A-by-CE structure for a sequence of group extensions proposed by Deng, Wang, and Yu. We prove that the maximal coarse Baum-Connes conjecture holds for metric spaces with bounded geometry that admit an A-by-FCE coarse fibration structure. As an application, the relative expanders constructed by Arzhantseva and Tessera, as well as the box spaces derived from an ``amenable-by-Haagerup'' group extension, admit the A-by-FCE coarse fibration structure. Consequently, the maximal coarse Baum-Connes conjecture holds for these spaces, which may not admit an FCE structure, i.e. fibred coarse embedding into Hilbert space.

math.KT↗

arXiv2024

Noise-aware Dynamic Image Denoising and Positron Range Correction for Rubidium-82 Cardiac PET Imaging via Self-supervision

Rb-82 is a radioactive isotope widely used for cardiac PET imaging. Despite numerous benefits of 82-Rb, there are several factors that limits its image quality and quantitative accuracy. First, the short half-life of 82-Rb results in noisy dynamic frames. Low signal-to-noise ratio would result in inaccurate and biased image quantification. Noisy dynamic frames also lead to highly noisy parametric images. The noise levels also vary substantially in different dynamic frames due to radiotracer decay and short half-life. Existing denoising methods are not applicable for this task due to the lack of paired training inputs/labels and inability to generalize across varying noise levels. Second, 82-Rb emits high-energy positrons. Compared with other tracers such as 18-F, 82-Rb travels a longer distance before annihilation, which negatively affect image spatial resolution. Here, the goal of this study is to propose a self-supervised method for simultaneous (1) noise-aware dynamic image denoising and (2) positron range correction for 82-Rb cardiac PET imaging. Tested on a series of PET scans from a cohort of normal volunteers, the proposed method produced images with superior visual quality. To demonstrate the improvement in image quantification, we compared image-derived input functions (IDIFs) with arterial input functions (AIFs) from continuous arterial blood samples. The IDIF derived from the proposed method led to lower AUC differences, decreasing from 11.09% to 7.58% on average, compared to the original dynamic frames. The proposed method also improved the quantification of myocardium blood flow (MBF), as validated against 15-O-water scans, with mean MBF differences decreased from 0.43 to 0.09, compared to the original dynamic frames. We also conducted a generalizability experiment on 37 patient scans obtained from a different country using a different scanner.

eess.IV↗

arXiv2024

Angular Momentum-Resolved Inelastic Electron Scattering for Nuclear Giant Resonances

Giant resonances (GRs) provide crucial insights into nuclear physics and astrophysics. Exciting GRs using particles like electrons is effective, yet the angular momentum (AM) transfer of electrons, including both intrinsic spin and orbital degrees of freedom in inelastic scattering, has never been studied. Here, we investigate AM transfer in GRs excited by plane-wave and vortex electrons, developing a comprehensive AM-resolved inelastic electron scattering theory. We find that even plane-wave electrons can model-independently extract transition strengths of higher multipolarity by selecting specific AM states of scattered electrons. Additionally, relativistic vortex electrons with orbital angular momentum (OAM) $\pm1$ can be efficiently generated. Vortex electrons can also be used to extract GR transition strength as in the plane-wave case, regardless of the position of nucleus relative to the beam axis. Furthermore, relativistic vortex electrons with larger OAM can be generated for on-axis nuclei due to AM conservation. Our method offers new perspectives for nuclear structure research and paves the way for generating vortex particles.

nucl-th↗

arXiv2024

EnviroExam: Benchmarking Environmental Science Knowledge of Large Language Models

In the field of environmental science, it is crucial to have robust evaluation metrics for large language models to ensure their efficacy and accuracy. We propose EnviroExam, a comprehensive evaluation method designed to assess the knowledge of large language models in the field of environmental science. EnviroExam is based on the curricula of top international universities, covering undergraduate, master's, and doctoral courses, and includes 936 questions across 42 core courses. By conducting 0-shot and 5-shot tests on 31 open-source large language models, EnviroExam reveals the performance differences among these models in the domain of environmental science and provides detailed evaluation standards. The results show that 61.3% of the models passed the 5-shot tests, while 48.39% passed the 0-shot tests. By introducing the coefficient of variation as an indicator, we evaluate the performance of mainstream open-source large language models in environmental science from multiple perspectives, providing effective criteria for selecting and fine-tuning language models in this field. Future research will involve constructing more domain-specific test sets using specialized environmental science textbooks to further enhance the accuracy and specificity of the evaluation.

cs.CL↗

arXiv2023

Higher index theory for spaces with an FCE-by-FCE structure

Let $(1\to N_n\to G_n\to Q_n\to 1)_{n\in\mathbb{N}}$ be a sequence of extensions of finite groups. Assume that the coarse disjoint unions of $(N_n)_{n \in \mathbb{N}}$, $(G_n)_{n \in \mathbb{N}}$ and $(Q_n)_{n \in \mathbb{N}}$ have bounded geometry. The sequence $(G_n)_{n\in\mathbb{N}}$ is said to have an \emph{FCE-by-FCE structure}, if the sequence $(N_n)_{n\in\mathbb{N}}$ and the sequence $(Q_n)_{n\in\mathbb{N}}$ admit \emph{a fibred coarse embedding} into Hilbert space. In this paper, we show that the coarse Novikov conjecture holds for spaces with an FCE-by-FCE structure.

math.KT↗