arXiv subjects

Fei He

Publications and source records attributed to Fei He.

At least 19 recordsLinked to original sources

arXiv2026

Quantum-state texture measure and texture transformation

Quantum-state texture quantifies structural irregularities of a state in a selected basis and has emerged as a valuable resource for gate characterization in universal circuits. Consequently, a class of contractive distance based texture measures and a framework for constructing convex-roof extended texture measure have been proposed. Here, we extend this theory in several directions. We examine the convertibility of a pure state to any state under texture-free operations, and fully solve the deterministic transformation problem between any two states in the qubit case. We then propose two classes of texture measures: convex-function-based measures and texture cost defined via minimal cost of texture contained in pure states. Moreover, we show that every texture monotone gives rise to a non-negative function which admits the same properties as the function used in the convex-roof extension---thus providing a converse to that construction. Our work thereby offers a relatively comprehensive resource-theoretic formulation of quantum-state texture.

quant-ph↗

arXiv2026

An Evidence-Aware Framework for EEG Microstate Analysis: Improved Sensitivity to Alzheimer's Disease and Ageing

Electroencephalography (EEG) microstate analysis commonly converts each scalp topography into a winner-take-all hard label and summarises the resulting sequence using duration, occurrence, coverage, transitions, and symbolic complexity. Although interpretable, this readout discards evidence strength, assignment ambiguity, and low-confidence periods. We introduce a template evidence trajectory framework that retains, at each sampled Global Field Power (GFP) peak, the evidence for all templates or subject-specific topographic communities. Conventional hard labels are treated as a compressed readout of this multivariate trajectory. We derive two evidence-aware extensions of classical descriptors: high-evidence episode duration and episode rate, which quantify temporal clustering and fragmentation of strong state evidence, and null-state Lempel-Ziv complexity (LZC), which explicitly encodes insufficient-evidence periods. We evaluated the framework across four resting-state EEG datasets spanning Alzheimer's disease and age-related variation. Fixed-state models included K-means, AAHC, and HMMs at K = 4 and K = 7, together with adaptive subject-specific Leiden and Infomap communities. Across 32 dataset-model cases, trajectory-derived duration effects exceeded matched hard-label effects in all cases at the representative setting and in 30-32 cases across a broader parameter grid. Null-state LZC improved over traditional LZC in most cases, while classification showed modest but consistent gains for trajectory or combined features. Retaining template evidence therefore provides a more sensitive readout of EEG topographic state dynamics while remaining compatible with conventional microstate analysis.

q-bio.NC↗

arXiv2026

NL-FRA: A MATLAB package for nonlinear frequency response analysis

Nonlinear Output Frequency Response Functions (NOFRFs) provide a one-dimensional frequency-domain representation of nonlinear dynamics, enabling direct decomposition of an output spectrum into contributions from different orders of nonlinearity. NL-FRA (NonLinear Frequency Response Analysis) is an open-source MATLAB package implementing a data-driven Least Squares (LS) method for estimating NOFRFs directly from system input-output data. It provides an integrated workflow for NOFRF estimation, validation, and visualisation, together with nonlinear transmissibility analysis. The package supports different types of inputs, i.e. general band-limited, multi-one and harmonic inputs, and includes routines for identifying the frequency ranges over which each nonlinear order contributes to the output. Furthermore, since the LS approach estimates NOFRFs directly from input-output data, it can be applied to experimental measurements or data generated using any suitable dynamic model of the system. The software facilitates interpretable nonlinear frequency-domain analysis for applications including fault diagnosis, condition and structural health monitoring, and biomedical engineering.

eess.SY↗

arXiv2026

Spectral bounds for $f$-Laplace-type operators with applications to Betti numbers on gradient Ricci shrinkers

We study the spectrum of the $f$-Laplacian on complete gradient Ricci shrinkers. Upper and lower bounds for the $k$-th eigenvalue are established in terms of the volume growth rate. Both bounds are shown to be sharp in the exponent. The method extends to $f$-Laplace-type operators on vector bundles; as an application we obtain explicit upper bounds for the Betti numbers.

math.DG↗

arXiv2026

Connectivity Estimation using Stochastic Graph Heat Modelling

A growing number of techniques leverage the spatial structures that underlie many real-world datasets. Despite these advances, the complementary task of estimating spatial structures and understanding their role within these techniques has often been overlooked. In neurophysiological data analysis specifically, numerous methods exist to estimate brain connectivity, but most are not explicitly model-based, dynamic, multivariate, or directed. To address these limitations, we previously introduced noise-driven heat modelling on graphs for neurophysiological connectivity estimation. In this study, we extend this framework by relaxing earlier noise assumptions and adding regularisation to improve robustness. We also develop a simulation procedure to characterise and evaluate our technique in a controlled setting. Finally, we demonstrate that the technique is able to capture meaningful spatial structure across two experiments, each using two real-world datasets. The explicit model formulation of our connectivity estimator has the potential to improve the interpretability of graph-based techniques across a wide range of applications. The code implementing our method is available at https://github.com/sgoerttler/Heat_Connectivity.

stat.ML↗

arXiv2026

Topology of gradient Ricci shrinkers via weighted $L^2$ cohomology

This paper proves several topological results for smooth gradient Ricci shrinkers. We establish upper bounds for the Betti numbers, a vanishing theorem for cohomology, and a dichotomy for the number of ends. We also prove a full Hodge theorem for a large class of shrinkers. The methods are based on weighted $L^2$ cohomology and extend to self-shrinkers of the mean curvature flow.

math.DG↗

arXiv2026

A Dynamical Systems and System Identification Framework for Phase Amplitude Coupling Analysis

Phase-amplitude coupling (PAC), a form of cross-frequency coupling, is involved in diverse cognitive functions and neural communication, making its accurate detection and characterisation essential yet challenging. Most existing methods infer PAC from variations in instantaneous phase and amplitude profiles, but are limited by sensitivity to filter bandwidths, inconsistent performance across noise levels and data lengths, and vulnerability to spurious couplings. Here, we formulate PAC as a nonlinear dynamical-systems phenomenon characterised by quadratic phase coupling (QPC), and propose a nonlinear system identification framework that directly models the dynamics generating PAC. Rather than relying on filtered phase and amplitude fluctuations, the proposed method identifies a generative nonlinear model, enabling noise-free simulation of the estimated dynamics and model-based characterisation of coupling strength and preferred phase. It also provides dynamically grounded criteria for identifying harmonic- and intermodulation-related false detections, remains robust under high noise, and yields consistent characterisation despite changes in slow-frequency power. In simulations and rat hippocampal local field potentials (LFP) recordings, the proposed method produced more sharply localised and frequency-specific PAC estimates than benchmark filtering-based methods, while preserving detailed preferred-phase information. In simulations, it rejected harmonic-related spurious coupling, remained robust at a signal-to-noise ratio (SNR) of 2 and reasonably robust at an SNR of 1, and reliably characterised PAC using 5-second analysis windows. These results establish nonlinear system identification as a complementary dynamical framework for detecting and characterising PAC, with particular advantages for noisy and short-duration neural recordings susceptible to spurious coupling.

q-bio.NC↗

arXiv2026

Dr.Occ: Depth- and Region-Guided 3D Occupancy from Surround-View Cameras for Autonomous Driving

3D semantic occupancy prediction is crucial for autonomous driving perception, offering comprehensive geometric scene understanding and semantic recognition. However, existing methods struggle with geometric misalignment in view transformation due to the lack of pixel-level accurate depth estimation, and severe spatial class imbalance where semantic categories exhibit strong spatial anisotropy. To address these challenges, we propose Dr. Occ, a depth- and region-guided occupancy prediction framework. Specifically, we introduce a depth-guided 2D-to-3D View Transformer (D$^2$-VFormer) that effectively leverages high-quality dense depth cues from MoGe-2 to construct reliable geometric priors, thereby enabling precise geometric alignment of voxel features. Moreover, inspired by the Mixture-of-Experts (MoE) framework, we propose a region-guided Expert Transformer (R/R$^2$-EFormer) that adaptively allocates region-specific experts to focus on different spatial regions, effectively addressing spatial semantic variations. Thus, the two components make complementary contributions: depth guidance ensures geometric alignment, while region experts enhance semantic learning. Experiments on the Occ3D--nuScenes benchmark demonstrate that Dr. Occ improves the strong baseline BEVDet4D by 7.43% mIoU and 3.09% IoU under the full vision-only setting.

cs.CV↗

arXiv2026

Full-span reversible space-time birefringence

Birefringence, the polarization-dependent splitting of light in anisotropic crystals, enables diverse optical phenomena and advanced functionalities such as optical communication, nonlinear optics, and quantum optics. However, conventional methods for controlling birefringence typically rely on engineering the optical crystal structure or applying external stimuli such as electric fields, mechanical stress or thermal variations, which are often constrained by limited tunability, challenges in integration with compact photonic devices or slow response time. Here, we introduce a new degree of freedom to manipulate the birefringence of light propagation in optical crystals through programming the spatiotemporal spectral phase of the incident light wave. We demonstrate this approach achieves continuous tuning of birefringence across a spectrum more than 100 times broader than that achievable with conventional birefringence tuning, spanning from positive through zero to negative values, irrespective of the crystal's optical sign and without inherent physical limitations. This unique optical behavior provides a versatile platform for investigating the complex dynamics of wave flow in anisotropic media, while the broad tunability of this space-time birefringence will spur innovations in ultrafast optical manipulation, optical computation, and quantum information processing-applications that demand rapid and flexible device reconfiguration.

physics.optics↗

arXiv2026

TF-UNet: Resolving Complex Speckles for Single-Shot Reconstruction of 512^2-Matrix Images Using a Micron-Sized Optical Fiber

Tapered optical fibers (TFs), with diameters gradually reduced from hundreds of microns to the micron scale, offer key advantages over conventional flat optical fibers (FFs), including uniform illumination, efficient long-range signal collection, and minimal invasiveness for applications in high-sensitivity biosensing, optogenetics, and photodynamic therapy. However, high-fidelity, single-shot imaging through a single TF remains underexplored due to intermodal coupling from the tapering geometry, which distorts output speckle patterns and poses challenges for image reconstruction using existing deep learning methods. Here, we propose a physics-inspired TF-UNet architecture that augments skip connections with hierarchical grouped-MLP fusion to effectively capture non-local, cross-scale dependencies caused by intermodal coupling in TFs. We experimentally validate our method on both FFs and TFs, demonstrating that TF-UNet outperforms standard U-Net variants in structural and perceptual fidelity while maintaining competitive PSNR at quadratic complexity. Our study offers a promising approach for deep learning-based imaging through micron-sized, ultrafine optical fibers, enabling scanning-free single-shot reconstruction on a 512x512 reconstruction matrix, and further validating the framework on biologically meaningful neuronal and vascular datasets for physically interpretable characterization.

physics.optics↗

arXiv2026

SegRap2025: A Benchmark of Gross Tumor Volume and Lymph Node Clinical Target Volume Segmentation for Radiotherapy Planning of Nasopharyngeal Carcinoma

Accurate delineation of Gross Tumor Volume (GTV), Lymph Node Clinical Target Volume (LN CTV), and Organ-at-Risk (OAR) from Computed Tomography (CT) scans is essential for precise radiotherapy planning in Nasopharyngeal Carcinoma (NPC). Building upon SegRap2023, which focused on OAR and GTV segmentation using single-center paired non-contrast CT (ncCT) and contrast-enhanced CT (ceCT) scans, the SegRap2025 challenge aims to enhance the generalizability and robustness of segmentation models across imaging centers and modalities. SegRap2025 comprises two tasks: Task01 addresses GTV segmentation using paired CT from the SegRap2023 dataset, with an additional external testing set to evaluate cross-center generalization, and Task02 focuses on LN CTV segmentation using multi-center training data and an unseen external testing set, where each case contains paired CT scans or a single modality, emphasizing both cross-center and cross-modality robustness. This paper presents the challenge setup and provides a comprehensive analysis of the solutions submitted by ten participating teams. For GTV segmentation task, the top-performing models achieved average Dice Similarity Coefficient (DSC) of 74.61% and 56.79% on the internal and external testing cohorts, respectively. For LN CTV segmentation task, the highest average DSC values reached 60.24%, 60.50%, and 57.23% on paired CT, ceCT-only, and ncCT-only subsets, respectively. SegRap2025 establishes a large-scale multi-center, multi-modality benchmark for evaluating the generalization and robustness in radiotherapy target segmentation, providing valuable insights toward clinically applicable automated radiotherapy planning systems. The benchmark is available at: https://hilab-git.github.io/SegRap2025_Challenge.

eess.IV↗

arXiv2026

AlignDrive: Aligned Lateral-Longitudinal Planning for End-to-End Autonomous Driving

Practical autonomous driving requires models that generalize by reasoning through spatial-temporal possibilities to exclude unsafe outcomes. While state-of-the-art (SOTA) methods use parallel planning architectures, they fail to explicitly couple speed decisions with agent behavior along the driving path, leading to suboptimal coordination. To address this, we propose a cascaded framework that transforms longitudinal planning from an independent prediction task into a path-conditioned reasoning process. On the model side, we introduce an anchor-based regression design that conditions longitudinal prediction on the lateral drive path, and reformulate longitudinal planning as 1D displacement prediction along the path. This reduces geometric uncertainty and sharpens the model's focus on interaction-driven dynamics. On the data side, we introduce a planning-oriented data augmentation strategy that simulates rare safety-critical events by programmatically inserting agents and relabeling longitudinal targets to enforce collision avoidance. Evaluated on the challenging Bench2Drive benchmark, our method achieves SOTA performance with a driving score of 89.07 and a success rate of 73.18%, demonstrating significantly improved coordination and safety. Further evaluation on Fail2Drive confirms strong generalization to rare edge cases where parallel formulations typically fail. Project page:https://yanhaowu.github.io/AlignDrive/.

cs.RO↗

arXiv2025

Structural Abstraction and Refinement for Probabilistic Programs

In this paper, we present structural abstraction refinement, a novel framework for verifying the threshold problem of probabilistic programs. Our approach represents the structure of a Probabilistic Control-Flow Automaton (PCFA) as a Markov Decision Process (MDP) by abstracting away statement semantics. The maximum reachability of the MDP naturally provides a proper upper bound of the violation probability, termed the structural upper bound. This introduces a fresh ``structural'' characterization of the relationship between PCFA and MDP, contrasting with the traditional ``semantical'' view, where the MDP reflects semantics. The method uniquely features a clean separation of concerns between probability and computational semantics that the abstraction focuses solely on probabilistic computation and the refinement handles only the semantics aspect, where the latter allows non-random program verification techniques to be employed without modification. Building upon this feature, we propose a general counterexample-guided abstraction refinement (CEGAR) framework, capable of leveraging established non-probabilistic techniques for probabilistic verification. We explore its instantiations using trace abstraction. Our method was evaluated on a diverse set of examples against state-of-the-art tools, and the experimental results highlight its versatility and ability to handle more flexible structures swiftly.

cs.FL↗

arXiv2025

Combining Example-Based and Rule-Based Program Transformations to Resolve Build Conflicts

Merge conflicts often arise when developers integrate changes from different software branches. The conflicts can result from overlapping edits in programs (i.e., textual conflicts) or cause build and test errors (i.e., build and test conflicts). They degrade software quality and hinder programmer productivity. While several tools detect build conflicts, few offer meaningful support for resolving them. To overcome limitations of existing tools, we introduce BuCoR (Build Conflict Resolver), a new conflict resolver. BuCoR first detects conflicts by comparing three versions related to a merging scenario: base b, left l, and right r. To resolve conflicts, it employs two complementary strategies: example-based transformation (BuCoR-E) and rule-based transformation (BuCoR-R). BuCoR-R applies predefined rules to resolve conflicts in frequently suggested or conventional ways. BuCoR-E mines branch versions (l and r) for exemplar edits applied to fix related build errors. From these examples, it infers and generalizes program transformation patterns to resolve conflicts in project-specific or unconventional ways. We evaluated BuCoR on 88 real-world build conflicts spanning 21 distinct conflict types. BuCoR generated at least one solution for 65 cases and correctly resolved 34 conflicts. We observed that this hybrid approach--combining context-aware, example-based learning with structured, rule-based resolution--can effectively help resolve conflicts. Our research sheds light on future directions for more intelligent and automated merge tools.

cs.SE↗

arXiv2025

Boundary effects in biological planar networks: pentagonsdominate Pyropia marginal cells

The topological and geometrical features at the boundary zone of planar polygonal networks remain poorly understood. Based on observations and mathematical proofs, we propose that marginal cells in the thalli of Pyropia haitanensis, a two-dimensional (2D) biological polygonal network, have an average edge number of approximately five. We demonstrate that this number is maintained by specific division patterns. Furthermore, we observe that both marginal cells and inner cells follow the trends predicted by the Lewis law and Aboav-Weaire law, but each cell type requires its own set of correlation parameters to more accurately describe its topological and geometrical features. The boundary effects are also evident in the differences between marginal cells and inner cells in terms of the distributions of interior angles and edge lengths. Similar to inner cells, cell division tends to occur in marginal cells with large sizes and transects a pair of unconnected edges. In particular, this study finds that the division of marginal cells preferentially transects the marginal edge. These specific topological and geometrical features of marginal cells and division patterns may inform the development of modelling algorithms for boundary conditions in biological 2D cellular networks.

q-bio.OT↗

arXiv2025

Complete $k$-partite entanglement measure

The $k$-partite entanglement, which focus on at most how many particles in the global system are entangled but separable from other particles, is complementary to the $k$-entanglement that reflects how many splitted subsystems are entangled under partitions of the systems in characterizing multipartite entanglement. Very recently, the theory of the complete $k$-entanglement measure has been established in [Phys. Rev. A 110, 012405 (2024)]. Here we investigate whether we can define the complete measure of the $k$-partite entanglement. Consequently, with the same spirit as that of the complete $k$-entanglement measure, we present the axiomatic postulates that a complete $k$-partite entanglement measure should require. Furthermore, we present two classes of $k$-partite entanglement measures and show that one is complete while the other one is unified but not complete except for the case of $k=2$.

quant-ph↗

arXiv2025

Retrieving Filter Spectra in CNN for Explainable Sleep Stage Classification

Despite significant advances in deep learning-based sleep stage classification, the clinical adoption of automatic classification models remains slow. One key challenge is the lack of explainability, as many models function as black boxes with millions of parameters. In response, recent work has increasingly focussed on enhancing model explainability. This study contributes to these efforts by introducing an explainability tool for spectral processing of individual EEG channels. Specifically, this tools retrieves the filter spectrum of low-level convolutional feature extraction and compares it with the classification-relevant spectral information in the data. We apply our tool on the EEGNet and MSA-CNN models using the ISRUC-S3 and Sleep-EDF-20 datasets. The tool reveals that spectral processing plays a significant role in the lower frequency bands. In addition, comparing the correlation between filter spectrum and data-derived spectral information with univariate performance indicates that the model naturally prioritises the most informative channels in a multimodal setting. We specify how these insights can be leveraged to enhance model performance. The code for the filter spectrum retrieval and its analysis is available at https://github.com/sgoerttler/MSA-CNN.

eess.SP↗

arXiv2025

MSA-CNN: A Lightweight Multi-Scale CNN with Attention for Sleep Stage Classification

Recent advancements in machine learning-based signal analysis, coupled with open data initiatives, have fuelled efforts in automatic sleep stage classification. Despite the proliferation of classification models, few have prioritised reducing model complexity, which is a crucial factor for practical applications. In this work, we introduce Multi-Scale and Attention Convolutional Neural Network (MSA-CNN), a lightweight architecture featuring as few as ~10,000 parameters. MSA-CNN leverages a novel multi-scale module employing complementary pooling to eliminate redundant filter parameters and dense convolutions. Model complexity is further reduced by separating temporal and spatial feature extraction and using cost-effective global spatial convolutions. This separation of tasks not only reduces model complexity but also mirrors the approach used by human experts in sleep stage scoring. We evaluated both small and large configurations of MSA-CNN against nine state-of-the-art baseline models across three public datasets, treating univariate and multivariate models separately. Our evaluation, based on repeated cross-validation and re-evaluation of all baseline models, demonstrated that the large MSA-CNN outperformed all baseline models on all three datasets in terms of accuracy and Cohen's kappa, despite its significantly reduced parameter count. Lastly, we explored various model variants and conducted an in-depth analysis of the key modules and techniques, providing deeper insights into the underlying mechanisms. The code for our models, baselines, and evaluation procedures is available at https://github.com/sgoerttler/MSA-CNN.

cs.LG↗