arXiv subjects

Li Wu

Publications and source records attributed to Li Wu.

At least 19 recordsLinked to original sources

arXiv2026

Index theory for singular Lagrangian systems and Bessel-type differential operators

The aim of the present manuscript is to develop an index theory for singular Lagrangian systems, with a particular focus on the important class of singular operators given by Bessel-type differential operators. The main motivation is to address several challenges posed by singular operators, which appear in a wide range of applications: celestial mechanics (for instance, perturbations in planetary motion), oscillatory systems with time-dependent forcing, electromagnetism (such as wave equations in nonuniform media), and quantum mechanics (notably certain Schrodinger equations with periodic potentials). We pursue two principal objectives. First, we establish a spectral flow formula and a Morse Index Theorem for gap-continuous paths of singular Sturm-Liouville operators. By means of these index formulas, we construct a Morse index theory for a broad class of Bessel-type differential operators and apply it to a family of asymptotic solutions of the gravitational $N$-body problem. Finally, our new index theory provides new insight into a phenomenon first observed by Rellich concerning the spectrum of one-parameter families of Sturm-Liouville operators with varying domains.

math.DS↗

arXiv2026

Morse Index, Stability and Spectral Bounds for Periodic Orbits in Reversible Lagrangian Systems

We prove quantitative stability and instability estimates for reversible periodic solutions of strictly Legendre-convex Lagrangian systems. If the configuration dimension is $n$, the fixed-period Morse index is $k$, and $k_D,ν_D$ are the Dirichlet index and nullity on a half-period, set \[ \widetilde k=k-2k_D-ν_D. \] Then the algebraic number $ν_+$ of positive real Floquet multipliers satisfies \[ ν_+\ge 2n-2\widetilde k, \] and we obtain corresponding bounds for the positive real spectrum away from $1$, allowing arbitrary Jordan chains at the unit multiplier. Hence at most $2\widetilde k$ Floquet multipliers can lie outside the positive real axis. In particular, when $k=0$ we recover the positive-real-spectrum theorem for reversible minimizers, while for nonconstant autonomous brake orbits the bounds improve by two. If, moreover, $n\ge2$ and the algebraic multiplicity of $1$ is two, an index-one brake orbit is transversely hyperbolic, with $n-1$ stable and $n-1$ unstable directions. Decoupled oscillators show that the refined bounds can be sharp even when the estimate based on $k$ alone is vacuous, and the Hénon--Heiles straight-line orbit provides a nonlinear illustration of the half-period mechanism.

math.DS↗

arXiv2026

Index theory for non-compact quantum graphs

We develop an index theory for variational problems on noncompact quantum graphs. The main results are a spectral flow formula, relating the net change of eigenvalues to the Maslov index of boundary data, and a Morse index theorem, equating the negative directions of the Lagrangian action with the total multiplicity of conjugate instants along the edges. These results extend classical tools in global analysis and symplectic geometry to graph based models, with applications to nonlinear wave equations such as the nonlinear Schroedinger equation. The spectral flow formula is proved by constructing a Lagrangian intersection theory in the Gelfand-Robbin quotients of the second variation of the action. This approach also recovers, in a unified way, the known formulas for heteroclinic, halfclinic, homoclinic, and bounded orbits of (non)autonomous Lagrangian systems.

math.FA↗

arXiv2026

Human-AI Co-reasoning for Clinical Diagnosis with Evidence-Integrated Language Agent

We present PULSE, a medical reasoning agent that combines a domain-tuned large language model with scientific literature retrieval to support diagnostic decision-making in complex real-world cases. To evaluate its capabilities, we curated a benchmark of 82 authentic endocrinology case reports encompassing a broad spectrum of disease types and incidence levels. In controlled experiments, we compared PULSE's performance against physicians with varying levels of expertise-from residents to senior specialists-and examined how AI assistance influenced human diagnostic reasoning. PULSE attained expert-competitive accuracy, outperforming residents and junior specialists while matching senior specialist performance at both Top@1 and Top@4 thresholds. Unlike physicians, whose accuracy declined with disease rarity, PULSE maintained stable performance across incidence tiers. The agent also exhibited adaptive reasoning, increasing output length with case difficulty in a manner analogous to the longer deliberation observed among expert clinicians. When used collaboratively, PULSE enabled physicians to correct initial errors and broaden diagnostic hypotheses, but also introduced risks of automation bias. The study explores both serial and concurrent collaboration workflows, revealing that PULSE offers robust support across common and rare presentations. These findings underscore both the promise and the limitations of language model-based agents in clinical diagnosis, and offer a framework for evaluating their role in real-world decision-making.

cs.CL↗

arXiv2026

Non-minimality and instability of brake orbits for natural Lagrangians on Riemannian manifolds

We investigate minimality and stability of periodic brake orbits in natural Lagrangian systems on smooth Riemannian manifolds. We prove that every non-constant periodic brake orbit is not a minimizer of the fixed-time action, for any conormal boundary condition. Under an orbit-cylinder hypothesis, its Morse index strictly increases in the free-time setting. As a consequence, strongly nondegenerate brake orbits fail to be linearly stable under a dimensional condition; in dimension at least three, nondegenerate mountain-pass brake orbits are spectrally unstable when the monodromy is semisimple. The key ingredient is a local index contribution at each brake instant. Using Seifert collar coordinates near the Hill boundary, we reduce the normal dynamics to a one-dimensional model, exhibiting a degeneracy inherent to brake symmetry. We illustrate the results by explicit Morse index computations for the planar anisotropic oscillator, the planar pendulum, and the planar Kepler problem; in the Kepler case, the ejection--collision orbit is treated via cotangent-lift Levi--Civita--Lissajous regularization.

math.DS↗

arXiv2025

Morse index theorem for heteroclinic, homoclinic and halfclinic orbits of Lagrangian systems

The purpose of this paper is to prove a new, more general version of the Morse index theorem for heteroclinic, homoclinic, and half-clinic solutions in general Lagrangian systems. In the final section, we compute the Morse index for specific heteroclinic and half-clinic solutions in classical mechanical models such as the mathematical pendulum, the Nagumo equation, and a four-dimensional competition-diffusion system.

math.DS↗

arXiv2025

CarbonEdge: Leveraging Mesoscale Spatial Carbon-Intensity Variations for Low Carbon Edge Computing

The proliferation of latency-critical and compute-intensive edge applications is driving increases in computing demand and carbon emissions at the edge. To better understand carbon emissions at the edge, we analyze granular carbon intensity traces at intermediate "mesoscales," such as within a single US state or among neighboring countries in Europe, and observe significant variations in carbon intensity at these spatial scales. Importantly, our analysis shows that carbon intensity variations, which are known to occur at large continental scales (e.g., cloud regions), also occur at much finer spatial scales, making it feasible to exploit geographic workload shifting in the edge computing context. Motivated by these findings, we propose \proposedsystem, a carbon-aware framework for edge computing that optimizes the placement of edge workloads across mesoscale edge data centers to reduce carbon emissions while meeting latency SLOs. We implement CarbonEdge and evaluate it on a real edge computing testbed and through large-scale simulations for multiple edge workloads and settings. Our experimental results on a real testbed demonstrate that CarbonEdge can reduce emissions by up to 78.7\% for a regional edge deployment in central Europe. Moreover, our CDN-scale experiments show potential savings of 49.5\% and 67.8\% in the US and Europe, respectively, while limiting the one-way latency increase to less than 5.5 ms.

cs.DC↗

arXiv2025

FailLite: Failure-Resilient Model Serving for Resource-Constrained Edge Environments

Model serving systems have become popular for deploying deep learning models for various latency-sensitive inference tasks. While traditional replication-based methods have been used for failure-resilient model serving in the cloud, such methods are often infeasible in edge environments due to significant resource constraints that preclude full replication. To address this problem, this paper presents FailLite, a failure-resilient model serving system that employs (i) a heterogeneous replication where failover models are smaller variants of the original model, (ii) an intelligent approach that uses warm replicas to ensure quick failover for critical applications while using cold replicas, and (iii) progressive failover to provide low mean time to recovery (MTTR) for the remaining applications. We implement a full prototype of our system and demonstrate its efficacy on an experimental edge testbed. Our results using 27 models show that FailLite can recover all failed applications with 175.5ms MTTR and only a 0.6% reduction in accuracy.

cs.DC↗

arXiv2025

ROFI: A Deep Learning-Based Ophthalmic Sign-Preserving and Reversible Patient Face Anonymizer

Patient face images provide a convenient mean for evaluating eye diseases, while also raising privacy concerns. Here, we introduce ROFI, a deep learning-based privacy protection framework for ophthalmology. Using weakly supervised learning and neural identity translation, ROFI anonymizes facial features while retaining disease features (over 98\% accuracy, $κ> 0.90$). It achieves 100\% diagnostic sensitivity and high agreement ($κ> 0.90$) across eleven eye diseases in three cohorts, anonymizing over 95\% of images. ROFI works with AI systems, maintaining original diagnoses ($κ> 0.80$), and supports secure image reversal (over 98\% similarity), enabling audits and long-term care. These results show ROFI's effectiveness of protecting patient privacy in the digital medicine era.

cs.CV↗

arXiv2025

The fibered rotation number for ergodic symplectic cocycles and its applications: I. Gap Labelling Theorem

Let $ (Θ,T,μ) $ be an ergodic topological dynamical system. The fibered rotation number for cocycles in $ Θ\times \mathrm{SL}(2,\mathbb{R}) $, acting on $ Θ\times \mathbb{R}\mathbb{P}^1 $ is well-defined and has wide applications in the study of the spectral theory of Schrödinger operators. In this paper, we will provide its natural generalization for higher dimensional cocycles in $ Θ\times\mathrm{SP}(2m,\mathbb{R}) $ or $ Θ\times \mathrm{HSP}(2m,\mathbb{C}) $, where $ \mathrm{SP}(2m,\mathbb{R}) $ and $ \mathrm{HSP}(2m,\mathbb{C}) $ respectively refer to the $ 2m $-dimensional symplectic or Hermitian-symplectic matrices. As a corollary, we establish the equivalence between the integrated density of states for generalized Schrödinger operators and the fibered rotation number; and the Gap Labelling Theorem via the Schwartzman group, as expected from the one dimensional case [AS1983, JM1982].

math.DS↗

arXiv2025

LLM-Driven Auto Configuration for Transient IoT Device Collaboration

Today's Internet of Things (IoT) has evolved from simple sensing and actuation devices to those with embedded processing and intelligent services, enabling rich collaborations between users and their devices. However, enabling such collaboration becomes challenging when transient devices need to interact with host devices in temporarily visited environments. In such cases, fine-grained access control policies are necessary to ensure secure interactions; however, manually implementing them is often impractical for non-expert users. Moreover, at run-time, the system must automatically configure the devices and enforce such fine-grained access control rules. Additionally, the system must address the heterogeneity of devices. In this paper, we present CollabIoT, a system that enables secure and seamless device collaboration in transient IoT environments. CollabIoT employs a Large language Model (LLM)-driven approach to convert users' high-level intents to fine-grained access control policies. To support secure and seamless device collaboration, CollabIoT adopts capability-based access control for authorization and uses lightweight proxies for policy enforcement, providing hardware-independent abstractions. We implement a prototype of CollabIoT's policy generation and auto configuration pipelines and evaluate its efficacy on an IoT testbed and in large-scale emulated environments. We show that our LLM-based policy generation pipeline is able to generate functional and correct policies with 100% accuracy. At runtime, our evaluation shows that our system configures new devices in ~150 ms, and our proxy-based data plane incurs network overheads of up to 2 ms and access control overheads up to 0.3 ms.

cs.CR↗

arXiv2025

CarbonFlex: Enabling Carbon-aware Provisioning and Scheduling for Cloud Clusters

Accelerating computing demand, largely from AI applications, has led to concerns about its carbon footprint. Fortunately, a significant fraction of computing demand comes from batch jobs that are often delay-tolerant and elastic, which enables schedulers to reduce carbon by suspending/resuming jobs and scaling their resources down/up when carbon is high/low. However, prior work on carbon-aware scheduling generally focuses on optimizing carbon for individual jobs in the cloud, and not provisioning and scheduling resources for many parallel jobs in cloud clusters. To address the problem, we present CarbonFlex, a carbon-aware resource provisioning and scheduling approach for cloud clusters. CarbonFlex leverages continuous learning over historical cluster-level data to drive near-optimal runtime resource provisioning and job scheduling. We implement CarbonFlex by extending AWS ParallelCluster to include our carbon-aware provisioning and scheduling algorithms. Our evaluation on publicly available industry workloads shows that CarbonFlex decreases carbon emissions by $\sim$57\% compared to a carbon-agnostic baseline and performs within 2.1\% of an oracle scheduler with perfect knowledge of future carbon intensity and job length.

cs.DC↗

arXiv2025

Hierarchical Context Transformer for Multi-level Semantic Scene Understanding

A comprehensive and explicit understanding of surgical scenes plays a vital role in developing context-aware computer-assisted systems in the operating theatre. However, few works provide systematical analysis to enable hierarchical surgical scene understanding. In this work, we propose to represent the tasks set [phase recognition --> step recognition --> action and instrument detection] as multi-level semantic scene understanding (MSSU). For this target, we propose a novel hierarchical context transformer (HCT) network and thoroughly explore the relations across the different level tasks. Specifically, a hierarchical relation aggregation module (HRAM) is designed to concurrently relate entries inside multi-level interaction information and then augment task-specific features. To further boost the representation learning of the different tasks, inter-task contrastive learning (ICL) is presented to guide the model to learn task-wise features via absorbing complementary information from other tasks. Furthermore, considering the computational costs of the transformer, we propose HCT+ to integrate the spatial and temporal adapter to access competitive performance on substantially fewer tunable parameters. Extensive experiments on our cataract dataset and a publicly available endoscopic PSI-AVA dataset demonstrate the outstanding performance of our method, consistently exceeding the state-of-the-art methods by a large margin. The code is available at https://github.com/Aurora-hao/HCT.

cs.CV↗

arXiv2025

A formula of local Maslov index and applications

In this paper, we explicitly express the local Maslov index by a Maslov index in finite dimensional case without symplectic reduction. Then we calculate the Maslov index for the path of pairs of Lagrangian subspaces in triangular form. In particular, we get the Maslov-type index of a given symplectic path in triangle form. As applications, we calculate the splitting numbers of the symplectic matrix in triangle form, dependence of iteration theory on triangular frames and mod 2 Maslov-type index for a real symplectic path. We study the continuity of families of bounded linear relations and families of bounded linear operators acting on closed linear subspaces as technique preparations.

math.FA↗

arXiv2024

UmambaTSF: A U-shaped Multi-Scale Long-Term Time Series Forecasting Method Using Mamba

Multivariate Time series forecasting is crucial in domains such as transportation, meteorology, and finance, especially for predicting extreme weather events. State-of-the-art methods predominantly rely on Transformer architectures, which utilize attention mechanisms to capture temporal dependencies. However, these methods are hindered by quadratic time complexity, limiting the model's scalability with respect to input sequence length. This significantly restricts their practicality in the real world. Mamba, based on state space models (SSM), provides a solution with linear time complexity, increasing the potential for efficient forecasting of sequential data. In this study, we propose UmambaTSF, a novel long-term time series forecasting framework that integrates multi-scale feature extraction capabilities of U-shaped encoder-decoder multilayer perceptrons (MLP) with Mamba's long sequence representation. To improve performance and efficiency, the Mamba blocks introduced in the framework adopt a refined residual structure and adaptable design, enabling the capture of unique temporal signals and flexible channel processing. In the experiments, UmambaTSF achieves state-of-the-art performance and excellent generality on widely used benchmark datasets while maintaining linear time complexity and low memory consumption.

cs.LG↗

arXiv2024

ARFA: An Asymmetric Receptive Field Autoencoder Model for Spatiotemporal Prediction

Spatiotemporal prediction aims to generate future sequences by paradigms learned from historical contexts. It is essential in numerous domains, such as traffic flow prediction and weather forecasting. Recently, research in this field has been predominantly driven by deep neural networks based on autoencoder architectures. However, existing methods commonly adopt autoencoder architectures with identical receptive field sizes. To address this issue, we propose an Asymmetric Receptive Field Autoencoder (ARFA) model, which introduces corresponding sizes of receptive field modules tailored to the distinct functionalities of the encoder and decoder. In the encoder, we present a large kernel module for global spatiotemporal feature extraction. In the decoder, we develop a small kernel module for local spatiotemporal information reconstruction. Experimental results demonstrate that ARFA consistently achieves state-of-the-art performance on popular datasets. Additionally, we construct the RainBench, a large-scale radar echo dataset for precipitation prediction, to address the scarcity of meteorological data in the domain.

cs.CV↗

arXiv2023

A generalized index theory for non-Hamiltonian system

Morse index theory provides an elegant and useful tool for describing several aspects of a Lagrangian system in terms of its variational properties. In the classical framework it provides an equality between the spectral properties of a second order selfadjoint differential operator arising by the second variation of the Lagrangian action functional and the oscillation properties of the space of solutions of the associated boundary value problem. These oscillation properties are described by means of the Maslov index, which is a symplectic invariant intimately related to the Hamiltonian nature of the problem. Driven by the desire to get an analogous result in the non-Hamiltonian context for the investigation of the dynamical properties of dissipative systems, in this paper we start to introduce a new topological invariant, the so-called degree-index, defined in terms of the Brouwer degree of a suitable determinant map of a boundary matrix, which provides one possible substitute of the Maslov index in this non-Hamiltonian framework and finally we prove the equality between the Morse index and the degree-index in this non-selfadjoint setting through a new abstract trace formula. In the last part of the paper we apply our theoretical results to some 1D reaction-diffusion systems.

math-ph↗

arXiv2023

Multi-view information fusion using multi-view variational autoencoders to predict proximal femoral strength

The aim of this paper is to design a deep learning-based model to predict proximal femoral strength using multi-view information fusion. Method: We developed new models using multi-view variational autoencoder (MVAE) for feature representation learning and a product of expert (PoE) model for multi-view information fusion. We applied the proposed models to an in-house Louisiana Osteoporosis Study (LOS) cohort with 931 male subjects, including 345 African Americans and 586 Caucasians. With an analytical solution of the product of Gaussian distribution, we adopted variational inference to train the designed MVAE-PoE model to perform common latent feature extraction. We performed genome-wide association studies (GWAS) to select 256 genetic variants with the lowest p-values for each proximal femoral strength and integrated whole genome sequence (WGS) features and DXA-derived imaging features to predict proximal femoral strength. Results: The best prediction model for fall fracture load was acquired by integrating WGS features and DXA-derived imaging features. The designed models achieved the mean absolute percentage error of 18.04%, 6.84% and 7.95% for predicting proximal femoral fracture loads using linear models of fall loading, nonlinear models of fall loading, and nonlinear models of stance loading, respectively. Compared to existing multi-view information fusion methods, the proposed MVAE-PoE achieved the best performance. Conclusion: The proposed models are capable of predicting proximal femoral strength using WGS features and DXA-derived imaging features. Though this tool is not a substitute for FEA using QCT images, it would make improved assessment of hip fracture risk more widely available while avoiding the increased radiation dosage and clinical costs from QCT.

cs.LG↗