arXiv subjects

Tianlong Ma

Publications and source records attributed to Tianlong Ma.

At least 19 recordsLinked to original sources

arXiv2026

Irreducibility of interlace polynomials

The factorisation of graph polynomials often reflects combinatorial decomposition. For a nonempty loopless graph $G$, we first prove that the two-variable interlace polynomial $q(G;x,y)$, introduced by Arratia, Bollob\'as and Sorkin, is irreducible over $\mathbb{C}[x,y]$ if and only if $G$ is connected, exactly paralleling the classical irreducibility theorem for the Tutte polynomial. The loopless hypothesis is essential: we construct an infinite family of connected looped graphs whose two-variable interlace polynomials are reducible. For a nonempty graph $G$, we prove that Courcelle's multivariate interlace polynomial $C_G(u,v;\mathbf{x},\mathbf{y})$ is irreducible over $\mathbb{C}[u,v,x_a,y_a:a\in V(G)]$ if and only if $G$ is connected.

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arXiv2026

Proof of a Brown-Mol conjecture on subtree roots

The subtree polynomial of a tree is the generating function that enumerates its subtrees according to their orders. Brown and Mol conjectured that every subtree root of a tree of order $n\ge 2$ lies in the disk \[ \left\{z\in\mathbb C: |z|\le 1+\sqrt[n-1]{n-1} \right\}. \] We prove this conjecture by introducing a recursive comparison method based on an extremal problem over integer compositions. We further characterize the equality case: the upper bound is attained if and only if $n$ is even and the tree is the star; in this case the unique boundary root is $-1-\sqrt[n-1]{n-1}$. We also show that every nonzero subtree root $z$ satisfies \[ |z|>\sqrt[n-1]{n-1}-1. \] The lower bound is asymptotically sharp as $n\to\infty$. For odd $n$, although the upper bound is not attained, it is asymptotically sharp as $n\to\infty$.

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arXiv2026

Combinatorial interpretations of Tutte polynomials at the point $(2,-1)$

Let $G$ be a simple connected graph, and let $T_{G}(x,y)$ be the Tutte polynomial of $G$. Motivated by the works in \cite{Ma}, we, in this paper, introduce the even-left spanning forests of $G$ and odd $G$-partitionable permutations, and show that $T_{G}(2,-1)$ is equal to both the number of even-left spanning forests of $G$ and the number of odd $G$-partitionable permutations. In particular, for a complete graph $K_n$, we prove that $T_{K_{n}}(2,-1)$ is the number of alternating permutations on $\{1,2,\dots,n+1\}$, using two distinct techniques: a recurrence relation and an explicit bijection construction.

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arXiv2025

On the coefficients of interior and exterior polynomials of polymatroids

The Tutte polynomial is an important invariant of graphs and matroids. Chen and Guo \emph{[Adv. in Appl. Math. 166 (2025) 102868.]} proved that for a $(k+1)$-edge connected graph $G$ and for any $i$ with $0\leq i <\frac{3(k+1)}{2}$, $$[y^{g-i}]T_{G}(1,y)=\binom{|V(G)|+i-2}{i}-\sum_{j=0}^{i}\binom{|V(G)|+i-2-j}{i-j}|\mathcal{SC}_{j}(G)|,$$ where $g=|E(G)|-|V(G)|+1$, $\mathcal{SC}_{j}(G)$ is the set of all minimal edge cuts with $j$ edges, $T_{G}(x,y)$ is the Tutte polynomial of the graph $G$, and $[y^{g-i}]T_{G}(1,y)$ denotes the coefficient of $y^{g-i}$ in the polynomial $T_{G}(1,y)$. Recently, Ma, Guan and Jin \emph{[arXiv.2503.06095, 2025.]} generalized this result from graphs to matroids and obtained the dual result on coefficients of $T_M(x,1)$ of matroids $M$ at the same time. In 2013, as a generalization of $T_{G}(x,1)$ and $T_{G}(1,y)$ of graphs $G$ to hypergraphs, K\'{a}lm\'{a}n \emph{[Adv. Math. 244 (2013) 823-873.]} introduced interior and exterior polynomials for connected hypergraphs. Chen and Guo posed a problem that can one generalize these results of graphs to interior and exterior polynomials of hypergraphs? In this paper, we solve it in the affirmative by obtaining results for more general polymatroids, which include the case of hypergraphs and also generalize the results of matroids due to Ma, Guan and Jin. As an application, the sequence consisting of these coefficients on polymatroids is proven to be unimodal, while the unimodality of the whole coefficients of matroids was obtained in 2018 by Adiprasito, Huh and Katz using Hodge theory.

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arXiv2025

Coefficients of univariate Tutte polynomials with one variable fixed

It is well known that the 2-variable Tutte polynomial of a graph $G$ includes chromatic polynomial and flow polynomial of $G$, i.e. the cases of $y=0$ and $x=0$. In 2013, K\'{a}lm\'{a}n introduced the interior and exterior polynomials which generalized the cases of $y=1$ and $x=1$ of Tutte polynomials of graphs to hypergraphs, and further polymatroids. There have been some results on coefficients of these polynomials, which motivate us to study uniformly the coefficients of $T_M(x,t)$ and $T_M(t,y)$, where $T_M(x,y)$ denotes the Tutte polynomial of a matroid $M$ and $t$ is a fixed real number. In this paper, we introduce two mutually dual parameters $f_k(M)$ and $g_k(M)$ ($g_1(M)$ is the girth of $M$) for any nonnegative integer $k$, and obtain the following results: (1) Formulas for coefficients of the higher-degree terms (related to $g_2(M)$ and $f_2(M)$, respectively) of $T_M(x,t)$ and $T_M(t,y)$ in terms of circuits and hyperplanes of $M$; (2) when $0\leq t \leq 1$, coefficients of the more higher-degree terms (related to $g_1(M)$ and $f_1(M)$, respectively) of $T_M(x,t)$ and $T_M(t,y)$ are further simplified and characterized; (3) As applications, some known results in the cases $t=0$ and $t=1$ are derived and generalized, and the unimodality of these coefficients in (1) are proved when $t\leq 1$.

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arXiv2024

Cross-Domain Document Layout Analysis Using Document Style Guide

The document layout analysis (DLA) aims to decompose document images into high-level semantic areas (i.e., figures, tables, texts, and background). Creating a DLA framework with strong generalization capabilities is a challenge due to document objects are diversity in layout, size, aspect ratio, texture, etc. Many researchers devoted this challenge by synthesizing data to build large training sets. However, the synthetic training data has different styles and erratic quality. Besides, there is a large gap between the source data and the target data. In this paper, we propose an unsupervised cross-domain DLA framework based on document style guidance. We integrated the document quality assessment and the document cross-domain analysis into a unified framework. Our framework is composed of three components, Document Layout Generator (GLD), Document Elements Decorator(GED), and Document Style Discriminator(DSD). The GLD is used to document layout generates, the GED is used to document layout elements fill, and the DSD is used to document quality assessment and cross-domain guidance. First, we apply GLD to predict the positions of the generated document. Then, we design a novel algorithm based on aesthetic guidance to fill the document positions. Finally, we use contrastive learning to evaluate the quality assessment of the document. Besides, we design a new strategy to change the document quality assessment component into a document cross-domain style guide component. Our framework is an unsupervised document layout analysis framework. We have proved through numerous experiments that our proposed method has achieved remarkable performance.

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arXiv2024

Extreme coefficients of multiplicity Tutte polynomials

The multiplicity Tutte polynomial, which includes the arithmetic Tutte polynomial, is a generalization of the classical Tutte polynomial of matroids. In this paper, we obtain an expression of the general coefficient and the expressions of six extreme coefficients of multiplicity Tutte polynomials. In particular, an expression of the general coefficient and the expressions of corresponding extreme coefficients of classical Tutte polynomial of matroids are deduced.

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arXiv2023

Progressive Evidence Refinement for Open-domain Multimodal Retrieval Question Answering

Pre-trained multimodal models have achieved significant success in retrieval-based question answering. However, current multimodal retrieval question-answering models face two main challenges. Firstly, utilizing compressed evidence features as input to the model results in the loss of fine-grained information within the evidence. Secondly, a gap exists between the feature extraction of evidence and the question, which hinders the model from effectively extracting critical features from the evidence based on the given question. We propose a two-stage framework for evidence retrieval and question-answering to alleviate these issues. First and foremost, we propose a progressive evidence refinement strategy for selecting crucial evidence. This strategy employs an iterative evidence retrieval approach to uncover the logical sequence among the evidence pieces. It incorporates two rounds of filtering to optimize the solution space, thus further ensuring temporal efficiency. Subsequently, we introduce a semi-supervised contrastive learning training strategy based on negative samples to expand the scope of the question domain, allowing for a more thorough exploration of latent knowledge within known samples. Finally, in order to mitigate the loss of fine-grained information, we devise a multi-turn retrieval and question-answering strategy to handle multimodal inputs. This strategy involves incorporating multimodal evidence directly into the model as part of the historical dialogue and question. Meanwhile, we leverage a cross-modal attention mechanism to capture the underlying connections between the evidence and the question, and the answer is generated through a decoding generation approach. We validate the model's effectiveness through extensive experiments, achieving outstanding performance on WebQA and MultimodelQA benchmark tests.

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arXiv2023

Convolution formulas for multivariate arithmetic Tutte polynomials

The multivariate arithmetic Tutte polynomial of arithmetic matroids is a generalization of the multivariate Tutte polynomial of matroids. In this note, we give the convolution formulas for the multivariate arithmetic Tutte polynomial of the product of two arithmetic matroids. In particular, the convolution formulas for the multivariate arithmetic Tutte polynomial of an arithmetic matroid are obtained. Applying our results, several known convolution formulas including [5, Theorem 10.9 and Corollary 10.10] and [1, Theorems 1 and 4] are proved by a purely combinatorial proof. The proofs presented here are significantly shorter than the previous ones. In addition, we obtain a convolution formula for the characteristic polynomial of an arithmetic matroid.

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arXiv2023

On the maximum local mean order of sub-k-trees of a k-tree

For a k-tree T, a generalization of a tree, the local mean order of sub-k-trees of T is the average order of sub-k-trees of T containing a given k-clique. The problem whether the largest local mean order of a tree (i.e., a 1-tree) at a vertex always takes on at a leaf was asked by Jamison in 1984 and was answered by Wagner and Wang in 2016. In 2018, Stephens and Oellermann asked a similar problem: for any k-tree T, does the maximum local mean order of sub-k-trees containing a given k-clique occur at a k-clique that is not a major k-clique of T? In this paper, we give it an affirmative answer.

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arXiv2023

Progressive Scene Text Erasing with Self-Supervision

Scene text erasing seeks to erase text contents from scene images and current state-of-the-art text erasing models are trained on large-scale synthetic data. Although data synthetic engines can provide vast amounts of annotated training samples, there are differences between synthetic and real-world data. In this paper, we employ self-supervision for feature representation on unlabeled real-world scene text images. A novel pretext task is designed to keep consistent among text stroke masks of image variants. We design the Progressive Erasing Network in order to remove residual texts. The scene text is erased progressively by leveraging the intermediate generated results which provide the foundation for subsequent higher quality results. Experiments show that our method significantly improves the generalization of the text erasing task and achieves state-of-the-art performance on public benchmarks.

cs.CV↗

arXiv2023

Extremal trees, unicyclic and bicyclic graphs with respect to $p$-Sombor spectral radii

For a graph $G=(V,E)$ and $v_{i}\in V$, denote by $d_{v_{i}}$ (or $d_{i}$ for short) the degree of vertex $v_{i}$. The $p$-Sombor matrix $\textbf{S}_{\textbf{p}}(G)$ ($p\neq0$) of a graph $G$ is a square matrix, where the $(i,j)$-entry is equal to $\displaystyle (d_{i}^{p}+d_{j}^{p})^{\frac{1}{p}}$ if the vertices $v_{i}$ and $v_{j}$ are adjacent, and 0 otherwise. The $p$-Sombor spectral radius of $G$, denoted by $\displaystyle ρ(\textbf{S}_{\textbf{p}}(G))$, is the largest eigenvalue of the $p$-Sombor matrix $\textbf{S}_{\textbf{p}}(G)$. In this paper, we consider the extremal trees, unicyclic and bicyclic graphs with respect to the $p$-Sombor spectral radii. We characterize completely the extremal graphs with the first three maximum Sombor spectral radii, which answers partially a problem posed by Liu et al. in [MATCH Commun. Math. Comput. Chem. 87 (2022) 59-87].

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arXiv2022

Homogeneous Multi-modal Feature Fusion and Interaction for 3D Object Detection

Multi-modal 3D object detection has been an active research topic in autonomous driving. Nevertheless, it is non-trivial to explore the cross-modal feature fusion between sparse 3D points and dense 2D pixels. Recent approaches either fuse the image features with the point cloud features that are projected onto the 2D image plane or combine the sparse point cloud with dense image pixels. These fusion approaches often suffer from severe information loss, thus causing sub-optimal performance. To address these problems, we construct the homogeneous structure between the point cloud and images to avoid projective information loss by transforming the camera features into the LiDAR 3D space. In this paper, we propose a homogeneous multi-modal feature fusion and interaction method (HMFI) for 3D object detection. Specifically, we first design an image voxel lifter module (IVLM) to lift 2D image features into the 3D space and generate homogeneous image voxel features. Then, we fuse the voxelized point cloud features with the image features from different regions by introducing the self-attention based query fusion mechanism (QFM). Next, we propose a voxel feature interaction module (VFIM) to enforce the consistency of semantic information from identical objects in the homogeneous point cloud and image voxel representations, which can provide object-level alignment guidance for cross-modal feature fusion and strengthen the discriminative ability in complex backgrounds. We conduct extensive experiments on the KITTI and Waymo Open Dataset, and the proposed HMFI achieves better performance compared with the state-of-the-art multi-modal methods. Particularly, for the 3D detection of cyclist on the KITTI benchmark, HMFI surpasses all the published algorithms by a large margin.

cs.CV↗

arXiv2022

A Survey of Human-in-the-loop for Machine Learning

Human-in-the-loop aims to train an accurate prediction model with minimum cost by integrating human knowledge and experience. Humans can provide training data for machine learning applications and directly accomplish tasks that are hard for computers in the pipeline with the help of machine-based approaches. In this paper, we survey existing works on human-in-the-loop from a data perspective and classify them into three categories with a progressive relationship: (1) the work of improving model performance from data processing, (2) the work of improving model performance through interventional model training, and (3) the design of the system independent human-in-the-loop. Using the above categorization, we summarize major approaches in the field; along with their technical strengths/ weaknesses, we have simple classification and discussion in natural language processing, computer vision, and others. Besides, we provide some open challenges and opportunities. This survey intends to provide a high-level summarization for human-in-the-loop and motivates interested readers to consider approaches for designing effective human-in-the-loop solutions.

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arXiv2022

Tight toughness, isolated toughness and binding number bounds for the $\{K_2,C_n\}$-factors

The $\{K_2,C_n\}$-factor of a graph is a spanning subgraph whose each component is either $K_2$ or $C_n$. In this paper, a sufficient condition with regard to tight toughness, isolated toughness and binding number bounds to guarantee the existence of the $\{K_2,C_{2i+1}| i\geq 2 \}$-factor for any graph is obtained, which answers a problem due to Gao and Wang (J. Oper. Res. Soc. China (2021), https://doi.org/10.1007/s40305-021-00357-6).

math.CO↗

arXiv2022

A direct and elementary proof of the well-definedness of the interior and exterior polynomials of hypergraphs

T. Kálmán (A version of Tutte's polynomial for hypergraphs, Adv. Math. 244 (2013) 823-873.) introduced the interior and exterior polynomials which are generalizations of the Tutte polynomial $T(x,y)$ on plane points $(1/x,1)$ and $(1,1/y)$ to hypergraphs. The two polynomials are defined under a fixed ordering of hyperedges, and are proved to be independent of the ordering using techniques of polytopes. In this paper, similar to the Tutte's original proof we provide a direct and elementary proof for the well-definedness of the interior and exterior polynomials of hypergraphs.

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arXiv2021

Document Layout Analysis with Aesthetic-Guided Image Augmentation

Document layout analysis (DLA) plays an important role in information extraction and document understanding. At present, document layout analysis has reached a milestone achievement, however, document layout analysis of non-Manhattan is still a challenge. In this paper, we propose an image layer modeling method to tackle this challenge. To measure the proposed image layer modeling method, we propose a manually-labeled non-Manhattan layout fine-grained segmentation dataset named FPD. As far as we know, FPD is the first manually-labeled non-Manhattan layout fine-grained segmentation dataset. To effectively extract fine-grained features of documents, we propose an edge embedding network named L-E^3Net. Experimental results prove that our proposed image layer modeling method can better deal with the fine-grained segmented document of the non-Manhattan layout.

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arXiv2021

Fractional strong matching preclusion for Cartesian product graphs

The strong matching preclusion number of a graph, introduced by Park and Ihm in 2011, is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. As a generalization, the fractional strong matching preclusion number of a graph is the minimum number of edges and vertices whose deletion leaves the resulting graph without a fractional perfect matching. In this paper, we obtain the fractional strong matching preclusion number for Cartesian product graphs. As an application, the fractional strong matching preclusion number for torus networks is obtained.

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