arXiv subjects

Fengling Li

Publications and source records attributed to Fengling Li.

35 records · Page 2Linked to original sources

arXiv2025

New Aspects of Analyzing Amyloid Fibrils

This is a summary of mathematical tools we used in research of analyzing the structure of proteins with amyloid form \cite{xi2024Top}. We defined several geometry indicators on the discrete curve namely the hop distance, the discrete curvature and the discrete torsion. Then, we used these indicators to analyze the structure of amyloid fibrils by regarding its peptide chains as discrete curves in $\Rds^3$. We gave examples to show that these indicators give novel insights in the characterization analysis of the structure of amyloid fibrils, for example the discrete torsion can detect the hydrogen bonds interactions between layers of amyloid fibril. {Moreover,} the topological tool performs better than the root mean square deviation (RMSD) in quantifying the difference of the structure of amyloid fibrils, etc.

math.AT↗

arXiv2025

A three-variable transcendental invariant of planar knotoids via Gauss diagrams

As a generalization of the classical knots, knotoids are equivalence classes of immersions of the oriented unit interval in a surface. In recent years, a variety of invariants of spherical and planar knotoids have been constructed as extensions of invariants of classical and virtual knots. In this paper we introduce a three-variable transcendental invariant of planar knotoids which is defined over an index function of a Gauss diagram. We describe properties of this invariant and show that it is a Vassiliev invariant of order one. We also discuss the Gordian distance between planar knotoids and provide lower bounds on the Gordian distance of homotopic planar knotoids by using the transcendental invariant.

math.GT↗

arXiv2024

Multiscale Jones Polynomial and Persistent Jones Polynomial for Knot Data Analysis

Many structures in science, engineering, and art can be viewed as curves in 3-space. The entanglement of these curves plays a crucial role in determining the functionality and physical properties of materials. Many concepts in knot theory provide theoretical tools to explore the complexity and entanglement of curves in 3-space. However, classical knot theory primarily focuses on global topological properties and lacks the consideration of local structural information, which is critical in practical applications. In this work, two localized models based on the Jones polynomial, namely the multiscale Jones polynomial and the persistent Jones polynomial, are proposed. The stability of these models, especially the insensitivity of the multiscale and persistent Jones polynomial models to small perturbations in curve collections, is analyzed, thus ensuring their robustness for real-world applications.

math.GT↗

arXiv2024

Experts' cognition-driven ensemble deep learning for external validation of predicting pathological complete response to neoadjuvant chemotherapy from histological images in breast cancer

In breast cancer, neoadjuvant chemotherapy (NAC) provides a standard treatment option for patients who have locally advanced cancer and some large operable tumors. A patient will have better prognosis when he has achieved a pathological complete response (pCR) with the treatment of NAC. There has been a trend to directly predict pCR to NAC from histological images based on deep learning (DL). However, the DL-based predictive models numerically have better performances in internal validation than in external validation. In this paper, we aim to alleviate this situation with an intrinsic approach. We propose an experts' cognition-driven ensemble deep learning (ECDEDL) approach. Taking the cognition of both pathology and artificial intelligence experts into consideration to improve the generalization of the predictive model to the external validation, ECDEDL can intrinsically approximate the working paradigm of a human being which will refer to his various working experiences to make decisions. ECDEDL was validated with 695 WSIs collected from the same center as the primary dataset to develop the predictive model and perform the internal validation, and was also validated with 340 WSIs collected from other three centers as the external dataset to perform the external validation. In external validation, ECDEDL improves the AUCs of pCR prediction from 61.52(59.80-63.26) to 67.75(66.74-68.80) and the Accuracies of pCR prediction from 56.09(49.39-62.79) to 71.01(69.44-72.58). ECDEDL was quite effective for external validation of predicting pCR to NAC from histological images in breast cancer, numerically approximating the internal validation.

physics.med-ph↗

arXiv2024

Cross-Modal Retrieval: A Systematic Review of Methods and Future Directions

With the exponential surge in diverse multi-modal data, traditional uni-modal retrieval methods struggle to meet the needs of users seeking access to data across various modalities. To address this, cross-modal retrieval has emerged, enabling interaction across modalities, facilitating semantic matching, and leveraging complementarity and consistency between heterogeneous data. Although prior literature has reviewed the field of cross-modal retrieval, it suffers from numerous deficiencies in terms of timeliness, taxonomy, and comprehensiveness. This paper conducts a comprehensive review of cross-modal retrieval's evolution, spanning from shallow statistical analysis techniques to vision-language pre-training models. Commencing with a comprehensive taxonomy grounded in machine learning paradigms, mechanisms, and models, the paper delves deeply into the principles and architectures underpinning existing cross-modal retrieval methods. Furthermore, it offers an overview of widely-used benchmarks, metrics, and performances. Lastly, the paper probes the prospects and challenges that confront contemporary cross-modal retrieval, while engaging in a discourse on potential directions for further progress in the field. To facilitate the ongoing research on cross-modal retrieval, we develop a user-friendly toolbox and an open-source repository at https://cross-modal-retrieval.github.io.

cs.IR↗

arXiv2024

One-Step Abductive Multi-Target Learning with Diverse Noisy Samples and Its Application to Tumour Segmentation for Breast Cancer

Recent studies have demonstrated the effectiveness of the combination of machine learning and logical reasoning, including data-driven logical reasoning, knowledge driven machine learning and abductive learning, in inventing advanced technologies for different artificial intelligence applications. One-step abductive multi-target learning (OSAMTL), an approach inspired by abductive learning, via simply combining machine learning and logical reasoning in a one-step balanced multi-target learning way, has as well shown its effectiveness in handling complex noisy labels of a single noisy sample in medical histopathology whole slide image analysis (MHWSIA). However, OSAMTL is not suitable for the situation where diverse noisy samples (DiNS) are provided for a learning task. In this paper, giving definition of DiNS, we propose one-step abductive multi-target learning with DiNS (OSAMTL-DiNS) to expand the original OSAMTL to handle complex noisy labels of DiNS. Applying OSAMTL-DiNS to tumour segmentation for breast cancer in MHWSIA, we show that OSAMTL-DiNS is able to enable various state-of-the-art approaches for learning from noisy labels to achieve more rational predictions. We released a model pre-trained with OSAMTL-DiNS for tumour segmentation in HE-stained pre-treatment biopsy images in breast cancer, which has been successfully applied as a pre-processing tool to extract tumour-associated stroma compartment for predicting the pathological complete response to neoadjuvant chemotherapy in breast cancer.

cs.LG↗

arXiv2024

Split to Merge: Unifying Separated Modalities for Unsupervised Domain Adaptation

Large vision-language models (VLMs) like CLIP have demonstrated good zero-shot learning performance in the unsupervised domain adaptation task. Yet, most transfer approaches for VLMs focus on either the language or visual branches, overlooking the nuanced interplay between both modalities. In this work, we introduce a Unified Modality Separation (UniMoS) framework for unsupervised domain adaptation. Leveraging insights from modality gap studies, we craft a nimble modality separation network that distinctly disentangles CLIP's features into language-associated and vision-associated components. Our proposed Modality-Ensemble Training (MET) method fosters the exchange of modality-agnostic information while maintaining modality-specific nuances. We align features across domains using a modality discriminator. Comprehensive evaluations on three benchmarks reveal our approach sets a new state-of-the-art with minimal computational costs. Code: https://github.com/TL-UESTC/UniMoS

cs.CV↗

arXiv2024

Agile Multi-Source-Free Domain Adaptation

Efficiently utilizing rich knowledge in pretrained models has become a critical topic in the era of large models. This work focuses on adaptively utilizing knowledge from multiple source-pretrained models to an unlabeled target domain without accessing the source data. Despite being a practically useful setting, existing methods require extensive parameter tuning over each source model, which is computationally expensive when facing abundant source domains or larger source models. To address this challenge, we propose a novel approach which is free of the parameter tuning over source backbones. Our technical contribution lies in the Bi-level ATtention ENsemble (Bi-ATEN) module, which learns both intra-domain weights and inter-domain ensemble weights to achieve a fine balance between instance specificity and domain consistency. By slightly tuning source bottlenecks, we achieve comparable or even superior performance on a challenging benchmark DomainNet with less than 3% trained parameters and 8 times of throughput compared with SOTA method. Furthermore, with minor modifications, the proposed module can be easily equipped to existing methods and gain more than 4% performance boost. Code is available at https://github.com/TL-UESTC/Bi-ATEN.

cs.CV↗

arXiv2024

Domain-Agnostic Mutual Prompting for Unsupervised Domain Adaptation

Conventional Unsupervised Domain Adaptation (UDA) strives to minimize distribution discrepancy between domains, which neglects to harness rich semantics from data and struggles to handle complex domain shifts. A promising technique is to leverage the knowledge of large-scale pre-trained vision-language models for more guided adaptation. Despite some endeavors, current methods often learn textual prompts to embed domain semantics for source and target domains separately and perform classification within each domain, limiting cross-domain knowledge transfer. Moreover, prompting only the language branch lacks flexibility to adapt both modalities dynamically. To bridge this gap, we propose Domain-Agnostic Mutual Prompting (DAMP) to exploit domain-invariant semantics by mutually aligning visual and textual embeddings. Specifically, the image contextual information is utilized to prompt the language branch in a domain-agnostic and instance-conditioned way. Meanwhile, visual prompts are imposed based on the domain-agnostic textual prompt to elicit domain-invariant visual embeddings. These two branches of prompts are learned mutually with a cross-attention module and regularized with a semantic-consistency loss and an instance-discrimination contrastive loss. Experiments on three UDA benchmarks demonstrate the superiority of DAMP over state-of-the-art approaches.

cs.AI↗

arXiv2023

The $F$-polynomial invariant for knotoids

As a generalization of the classical knots, knotoids deal with the open ended knot diagrams in a surface. In recent years, many polynomial invariants for knotoids have appeared, such as the bracket polynomial, the index polynomial and the $n$th polynomial, etc. In this paper, we introduce a new polynomial invariant $F$-polynomial for knotoids and discuss some properties of the $F$-polynomial. Then, we construct a family of knotoid diagrams which can be distinguished from each other by the $F$-polynomial but cannnot be distinguished by the index polynomial and the $n$th polynomial.

math.GT↗

arXiv2023

Knot data analysis using multiscale Gauss link integral

In the past decade, topological data analysis (TDA) has emerged as a powerful approach in data science. The main technique in TDA is persistent homology, which tracks topological invariants over the filtration of point cloud data using algebraic topology. Although knot theory and related subjects are a focus of study in mathematics, their success in practical applications is quite limited due to the lack of localization and quantization. We address these challenges by introducing knot data analysis (KDA), a new paradigm that incorporating curve segmentation and multiscale analysis into the Gauss link integral. The resulting multiscale Gauss link integral (mGLI) recovers the global topological properties of knots and links at an appropriate scale but offers multiscale feature vectors to capture the local structures and connectivities of each curve segment at various scales. The proposed mGLI significantly outperforms other state-of-the-art methods in benchmark protein flexibility analysis, including earlier persistent homology-based methods. Our approach enables the integration of artificial intelligence (AI) and KDA for general curve-like objects and data.

math.GT↗

arXiv2022

Task-adaptive Asymmetric Deep Cross-modal Hashing

Supervised cross-modal hashing aims to embed the semantic correlations of heterogeneous modality data into the binary hash codes with discriminative semantic labels. Because of its advantages on retrieval and storage efficiency, it is widely used for solving efficient cross-modal retrieval. However, existing researches equally handle the different tasks of cross-modal retrieval, and simply learn the same couple of hash functions in a symmetric way for them. Under such circumstance, the uniqueness of different cross-modal retrieval tasks are ignored and sub-optimal performance may be brought. Motivated by this, we present a Task-adaptive Asymmetric Deep Cross-modal Hashing (TA-ADCMH) method in this paper. It can learn task-adaptive hash functions for two sub-retrieval tasks via simultaneous modality representation and asymmetric hash learning. Unlike previous cross-modal hashing approaches, our learning framework jointly optimizes semantic preserving that transforms deep features of multimedia data into binary hash codes, and the semantic regression which directly regresses query modality representation to explicit label. With our model, the binary codes can effectively preserve semantic correlations across different modalities, meanwhile, adaptively capture the query semantics. The superiority of TA-ADCMH is proved on two standard datasets from many aspects.

cs.IR↗

arXiv2019

A characteristics for a surface sum of two handlebodies along an annulus or a once-punctured torus to be a handlebody

The main results of the paper is that we give a characteristics for an annulus sum and a once-punctured torus sum of two handlebodies to be a handlebody as follows: 1. The annulus sum $H=H_1\cup_A H_2$ of two handlebodies $H_1$ and $H_2$ is a handlebody if and only if the core curve of $A$ is a longitude for either $H_1$ or $H_2$. 2. Let $H=H_1\cup_T H_2$ be a surface sum of two handlebodies $H_1$ and $H_2$ along a once-punctured torus $T$. Suppose that $T$ is incompressible in both $H_1$ and $H_2$. Then $H$ is a handlebody if and only if the there exists a collection $\{δ, σ\}$ of simple closed curves on $T$ such that either $\{δ, σ\}$ is primitive in $H_1$ or $H_2$, or $\{δ\}$ is primitive in $H_1$ and $\{σ\}$ is primitive in $H_2$.

math.GT↗

arXiv2019

A theory of orbit braids

This paper upbuilds the theoretical framework of orbit braids in $M\times I$ by making use of the orbit configuration space $F_G(M,n)$, which enriches the theory of ordinary braids, where $M$ is a connected topological manifold of dimension at least 2 with an effective action of a finite group $G$ and the action of $G$ on $I$ is trivial. Main points of our work include as follows. We introduce the orbit braid group $\mathcal{B}_n^{orb}(M,G)$, and show that it is isomorphic to a group with an additional endowed operation (called the extended fundamental group of $F_G(M,n)$), formed by the homotopy classes of some paths (not necessarily closed paths) in $F_G(M,n)$, which is an essential extension for fundamental groups. The orbit braid group $\mathcal{B}_n^{orb}(M,G)$ is large enough to contain the fundamental group of $F_G(M,n)$ and other various braid groups as its subgroups. Around the central position of $\mathcal{B}_n^{orb}(M,G)$, we obtain five short exact sequences weaved in a commutative diagram. We also analyze the essential relations among various braid groups associated to those configuration spaces $F_G(M,n), F(M/G,n)$, and $F(M,n)$. We finally consider how to give the presentations of orbit braid groups in terms of orbit braids as generators. We carry out our work by choosing $M=\mathbb{C}$ with typical actions of $\mathbb{Z}_p$ and $(\mathbb{Z}_2)^2$. We obtain the presentations of the corresponding orbit braid groups, from which we see that the generalized braid group $Br(B_n)$ actually agrees with an orbit braid group and $Br(D_n)$ is a subgroup of another orbit braid group. In addition, the notion of extended fundamental groups is also defined in a general way in the category of topology and some characteristics extracted from the discussions of orbit braids are given.

math.AT↗

arXiv2018

Density of roots of the Yamada polynomial of spatial graphs

We survey the construction and properties of the Yamada polynomial of spatial graphs and present the Yamada polynomial formulae for some classes of graphs. Then we construct an infinite family of spatial graphs for which roots of Yamada polynomials are dense in the complex plane.

math.GT↗

arXiv2018

On Yamada polynomial of spatial graphs obtained by edge replacements

We present formulae for computing the Yamada polynomial of spatial graphs obtained by replacing edges of plane graphs, such as cycle-graphs, theta-graphs, and bouquet-graphs, by spatial parts. As a corollary, it is shown that zeros of Yamada polynomials of some series of spatial graphs are dense in a certain region in the complex plane, described by a system of inequalities. Also, the relation between Yamada polynomial of graphs and the chain polynomial of edge-labelled graphs is obtained.

math.GT↗

arXiv2013

A proof of Lickorish and Wallace's theorem

In this paper, we give a simple proof of Lickorish and Wallace's theorem, which states that every closed orientable 3-manifold is obtained by surgery on some link in 3-sphere.

math.GT↗