arXiv subjects

Yan Cao

Publications and source records attributed to Yan Cao.

At least 55 records · Page 3Linked to original sources

arXiv2021

A note on Goldberg's conjecture on total chromatic numbers

Let $G=(V(G), E(G))$ be a multigraph with maximum degree $Δ(G)$, chromatic index $χ'(G)$ and total chromatic number $χ''(G)$. The Total Coloring conjecture proposed by Behzad and Vizing, independently, states that $χ''(G)\leq Δ(G)+μ(G) +1$ for a multigraph $G$, where $μ(G)$ is the multiplicity of $G$. Moreover, Goldberg conjectured that $χ''(G)=χ'(G)$ if $χ'(G)\geq Δ(G)+3$ and noticed the conjecture holds when $G$ is an edge-chromatic critical graph. By assuming the Goldberg-Seymour conjecture, we show that $χ''(G)=χ'(G)$ if $χ'(G)\geq \max\{ Δ(G)+2, |V(G)|+1\}$ in this note. Consequently, $χ''(G) = χ'(G)$ if $χ'(G) \ge Δ(G) +2$ and $G$ has a spanning edge-chromatic critical subgraph.

math.CO↗

arXiv2021

The Core Conjecture of Hilton and Zhao II: a Proof

A simple graph $G$ with maximum degree $Δ$ is overfull if $|E(G)|>Δ\lfloor |V(G)|/2\rfloor$. The core of $G$, denoted $G_Δ$, is the subgraph of $G$ induced by its vertices of degree $Δ$. Clearly, the chromatic index of $G$ equals $Δ+1$ if $G$ is overfull. Conversely, Hilton and Zhao in 1996 conjectured that if $G$ is a simple connected graph with $Δ\ge 3$ and $Δ(G_Δ)\le 2$, then $χ'(G)=Δ+1$ implies that $G$ is overfull or $G=P^*$, where $P^*$ is obtained from the Petersen graph by deleting a vertex. Cariolaro and Cariolaro settled the base case $Δ=3$ in 2003, and Cranston and Rabern proved the next case $Δ=4$ in 2019. In this paper, we give a proof of this conjecture for all $Δ\ge 4$.

math.CO↗

arXiv2021

Joint Landmark and Structure Learning for Automatic Evaluation of Developmental Dysplasia of the Hip

The ultrasound (US) screening of the infant hip is vital for the early diagnosis of developmental dysplasia of the hip (DDH). The US diagnosis of DDH refers to measuring alpha and beta angles that quantify hip joint development. These two angles are calculated from key anatomical landmarks and structures of the hip. However, this measurement process is not trivial for sonographers and usually requires a thorough understanding of complex anatomical structures. In this study, we propose a multi-task framework to learn the relationships among landmarks and structures jointly and automatically evaluate DDH. Our multi-task networks are equipped with three novel modules. Firstly, we adopt Mask R-CNN as the basic framework to detect and segment key anatomical structures and add one landmark detection branch to form a new multi-task framework. Secondly, we propose a novel shape similarity loss to refine the incomplete anatomical structure prediction robustly and accurately. Thirdly, we further incorporate the landmark-structure consistent prior to ensure the consistency of the bony rim estimated from the segmented structure and the detected landmark. In our experiments, 1,231 US images of the infant hip from 632 patients are collected, of which 247 images from 126 patients are tested. The average errors in alpha and beta angles are 2.221 degrees and 2.899 degrees. About 93% and 85% estimates of alpha and beta angles have errors less than 5 degrees, respectively. Experimental results demonstrate that the proposed method can accurately and robustly realize the automatic evaluation of DDH, showing great potential for clinical application.

eess.IV↗

arXiv2021

The overfullness of graphs with small minimum degree and large maximum degree

Given a simple graph $G$, denote by $Δ(G)$, $δ(G)$, and $χ'(G)$ the maximum degree, the minimum degree, and the chromatic index of $G$, respectively. We say $G$ is \emph{$Δ$-critical} if $χ'(G)=Δ(G)+1$ and $χ'(H)\le Δ(G)$ for every proper subgraph $H$ of $G$; and $G$ is \emph{overfull} if $|E(G)|>Δ\lfloor |V(G)|/2 \rfloor$. Since a maximum matching in $G$ can have size at most $\lfloor |V(G)|/2 \rfloor$, it follows that $χ'(G) = Δ(G) +1$ if $G$ is overfull. Conversely, let $G$ be a $Δ$-critical graph. The well known overfull conjecture of Chetwynd and Hilton asserts that $G$ is overfull provided $Δ(G) > |V(G)|/3$. In this paper, we show that any $Δ$-critical graph $G$ is overfull if $Δ(G) - 7δ(G)/4\ge(3|V(G)|-17)/4$.

math.CO↗

arXiv2021

An improvement to the vertex-splitting conjecture

For a simple graph $G$, denote by $n$, $Δ(G)$, and $χ'(G)$ its order, maximum degree, and chromatic index, respectively. A connected class 2 graph $G$ is edge-chromatic critical if $χ'(G-e)<Δ(G)+1$ for every edge $e$ of $G$. Define $G$ to be overfull if $|E(G)|>Δ(G) \lfloor n/2 \rfloor$. Clearly, overfull graphs are class 2 and any graph obtained from a regular graph of even order by splitting a vertex is overfull. Let $G$ be an $n$-vertex connected regular class 1 graph with $Δ(G) >n/3$. Hilton and Zhao in 1997 conjectured that if $G^*$ is obtained from $G$ by splitting one vertex of $G$ into two vertices, then $G^*$ is edge-chromatic critical, and they verified the conjecture for graphs $G$ with $Δ(G)\ge \frac{n}{2}(\sqrt{7}-1)\approx 0.82n$. The graph $G^*$ is easily verified to be overfull, and so the hardness of the conjecture lies in showing that the deletion of every of its edge decreases the chromatic index. Except in 2002, Song showed that the conjecture is true for a special class of graphs $G$ with $Δ(G)\ge \frac{n}{2}$, no other progress on this conjecture had been made. In this paper, we confirm the conjecture for graphs $G$ with $Δ(G) \ge 0.75n$.

math.CO↗

arXiv2020

Restricted cohomology of restricted Lie superalgebras

Suppose the ground field $\mathbb{F}$ is an algebraically closed field characteristic of $p>2$. In this paper, we investigate the restricted cohomology theory of restricted Lie superalgebras. Algebraic interpretations of low dimensional restricted cohomology of restricted Lie superalgebra are given. We show that there is a family of restricted model filiform Lie superalgebra $L_{p,p}^λ$ structures parameterized by elements $λ\in \mathbb{F}^{p}.$ We explicitly describe both the $1$-dimensional ordinary and restricted cohomology superspaces of $L_{p,p}^λ$ with coefficients in the $1$-dimensional trivial module and show that these superspaces are equal. We also describe the $2$-dimensional ordinary and restricted cohomology superspaces of $L_{p,p}^λ$ with coefficients in the $1$-dimensional trivial module and show that these superspaces are unequal.

math.RA↗

arXiv2020

Overfullness of critical class 2 graphs with a small core degree

Let $G$ be a simple graph, and let $n$, $Δ(G)$ and $χ' (G)$ be the order, the maximum degree and the chromatic index of $G$, respectively. We call $G$ overfull if $|E(G)|/\lfloor n/2\rfloor > Δ(G)$, and critical if $χ'(H) < χ'(G)$ for every proper subgraph $H$ of $G$. Clearly, if $G$ is overfull then $χ'(G) = Δ(G)+1$. The core of $G$, denoted by $G_Δ$, is the subgraph of $G$ induced by all its maximum degree vertices. Hilton and Zhao conjectured that for any critical class 2 graph $G$ with $Δ(G) \ge 4$, if the maximum degree of $G_Δ$ is at most two, then $G$ is overfull, which in turn gives $Δ(G) > n/2 +1$. We show that for any critical class 2 graph $G$, if the minimum degree of $G_Δ$ is at most two and $Δ(G) > n/2 +1$, then $G$ is overfull.

math.CO↗

arXiv2020

$Δ$-critical graphs with a vertex of degree 2

Let $G$ be a simple graph with maximum degree $Δ$. A classic result of Vizing shows that $χ'(G)$, the chromatic index of $G$, is either $Δ$ or $Δ+1$. We say $G$ is of \emph{Class 1} if $χ'(G)=Δ$, and is of \emph{Class 2} otherwise. A graph $G$ is \emph{$Δ$-critical} if $χ'(G)=Δ+1$ and $χ'(H)<Δ+1$ for every proper subgraph $H$ of $G$, and is \emph{overfull} if $|E(G)|>Δ\lfloor (|V(G)|-1)/2 \rfloor$. Clearly, overfull graphs are Class 2. Hilton and Zhao in 1997 conjectured that if $G$ is obtained from an $n$-vertex $Δ$-regular Class 1 graph with maximum degree greater than $n/3$ by splitting a vertex, then being overfull is the only reason for $G$ to be Class 2. This conjecture was only confirmed when $Δ\ge \frac{n}{2}(\sqrt{7}-1)\approx 0.82n$. In this paper, we improve the bound on $Δ$ from $\frac{n}{2}(\sqrt{7}-1)$ to $0.75n$. Considering the structure of $Δ$-critical graphs with a vertex of degree 2, we also show that for an $n$-vertex $Δ$-critical graph with $Δ\ge \frac{3n}{4}$, if it contains a vertex of degree 2, then it is overfull. We actually obtain a more general form of this result, which partially supports the overfull conjecture of Chetwynd and Hilton from 1986, which states that if $G$ is an $n$-vertex $Δ$-critical graph with $Δ>n/3$, then $G$ contains an overfull subgraph $H$ with $Δ(H)=Δ$. Our proof techniques are new and might shed some light on attacking both of the conjectures when $Δ$ is large.

math.CO↗

arXiv2020

Adaptive Dialog Policy Learning with Hindsight and User Modeling

Reinforcement learning methods have been used to compute dialog policies from language-based interaction experiences. Efficiency is of particular importance in dialog policy learning, because of the considerable cost of interacting with people, and the very poor user experience from low-quality conversations. Aiming at improving the efficiency of dialog policy learning, we develop algorithm LHUA (Learning with Hindsight, User modeling, and Adaptation) that, for the first time, enables dialog agents to adaptively learn with hindsight from both simulated and real users. Simulation and hindsight provide the dialog agent with more experience and more (positive) reinforcements respectively. Experimental results suggest that, in success rate and policy quality, LHUA outperforms competitive baselines from the literature, including its no-simulation, no-adaptation, and no-hindsight counterparts.

cs.AI↗

arXiv2020

Proof of the Core Conjecture of Hilton and Zhao

Let $G$ be a simple graph with maximum degree $Δ$. We call $G$ \emph{overfull} if $|E(G)|>Δ\lfloor |V(G)|/2\rfloor$. The \emph{core} of $G$, denoted $G_Δ$, is the subgraph of $G$ induced by its vertices of degree $Δ$. A classic result of Vizing shows that $χ'(G)$, the chromatic index of $G$, is either $Δ$ or $Δ+1$. It is NP-complete to determine the chromatic index for a general graph. However, if $G$ is overfull then $χ'(G)=Δ+1$. Hilton and Zhao in 1996 conjectured that if $G$ is a simple connected graph with $Δ\ge 3$ and $Δ(G_Δ)\le 2$, then $χ'(G)=Δ+1$ if and only if $G$ is overfull or $G=P^*$, where $P^*$ is obtained from the Petersen graph by deleting a vertex. This conjecture, if true, implies an easy approach for calculating $χ'(G)$ for graphs $G$ satisfying the conditions. The progress on the conjecture has been slow: it was only confirmed for $Δ=3,4$, respectively, in 2003 and 2017. In this paper, we confirm this conjecture for all $Δ\ge 4$.

math.CO↗

arXiv2019

An overlapping-free leaf segmentation method for plant point clouds

Automatic leaf segmentation, as well as identification and classification methods that built upon it, are able to provide immediate monitoring for plant growth status to guarantee the output. Although 3D plant point clouds contain abundant phenotypic features, plant leaves are usually distributed in clusters and are sometimes seriously overlapped in the canopy. Therefore, it is still a big challenge to automatically segment each individual leaf from a highly crowded plant canopy in 3D for plant phenotyping purposes. In this work, we propose an overlapping-free individual leaf segmentation method for plant point clouds using the 3D filtering and facet region growing. In order to separate leaves with different overlapping situations, we develop a new 3D joint filtering operator, which integrates a Radius-based Outlier Filter (RBOF) and a Surface Boundary Filter (SBF) to help to separate occluded leaves. By introducing the facet over-segmentation and facet-based region growing, the noise in segmentation is suppressed and labeled leaf centers can expand to their whole leaves, respectively. Our method can work on point clouds generated from three types of 3D imaging platforms, and also suitable for different kinds of plant species. In experiments, it obtains a point-level cover rate of 97% for Epipremnum aureum, 99% for Monstera deliciosa, 99% for Calathea makoyana, and 87% for Hedera nepalensis sample plants. At the leaf level, our method reaches an average Recall at 100.00%, a Precision at 99.33%, and an average F-measure at 99.66%, respectively. The proposed method can also facilitate the automatic traits estimation of each single leaf (such as the leaf area, length, and width), which has potential to become a highly effective tool for plant research and agricultural engineering.

cs.CV↗

arXiv2019

An Integrated Image Filter for Enhancing Change Detection Results

Change detection is a fundamental task in computer vision. Despite significant advances have been made, most of the change detection methods fail to work well in challenging scenes due to ubiquitous noise and interferences. Nowadays, post-processing methods (e.g. MRF, and CRF) aiming to enhance the binary change detection results still fall short of the requirements on universality for distinctive scenes, applicability for different types of detection methods, accuracy, and real-time performance. Inspired by the nature of image filtering, which separates noise from pixel observations and recovers the real structure of patches, we consider utilizing image filters to enhance the detection masks. In this paper, we present an integrated filter which comprises a weighted local guided image filter and a weighted spatiotemporal tree filter. The spatiotemporal tree filter leverages the global spatiotemporal information of adjacent video frames and meanwhile the guided filter carries out local window filtering of pixels, for enhancing the coarse change detection masks. The main contributions are three: (i) the proposed filter can make full use of the information of the same object in consecutive frames to improve its current detection mask by computations on a spatiotemporal minimum spanning tree; (ii) the integrated filter possesses both advantages of local filtering and global filtering; it not only has good edge-preserving property but also can handle heavily textured and colorful foreground regions; and (iii) Unlike some popular enhancement methods (MRF, and CRF) that require either a priori background probabilities or a posteriori foreground probabilities for every pixel to improve the coarse detection masks, our method is a versatile enhancement filter that can be applied after many different types of change detection methods, and is particularly suitable for video sequences.

cs.CV↗

arXiv2019

On Gupta's Co-density Conjecture

Let $G=(V,E)$ be a multigraph. The {\em cover index} $ξ(G)$ of $G$ is the greatest integer $k$ for which there is a coloring of $E$ with $k$ colors such that each vertex of $G$ is incident with at least one edge of each color. Let $δ(G)$ be the minimum degree of $G$ and let $Φ(G)$ be the {\em co-density} of $G$, defined by \[Φ(G)=\min \Big\{\frac{2|E^+(U)|}{|U|+1}:\,\, U \subseteq V, \,\, |U|\ge 3 \hskip 2mm {\rm and \hskip 2mm odd} \Big\},\] where $E^+(U)$ is the set of all edges of $G$ with at least one end in $U$. It is easy to see that $ξ(G) \le \min\{δ(G), \lfloor Φ(G) \rfloor\}$. In 1978 Gupta proposed the following co-density conjecture: Every multigraph $G$ satisfies $ξ(G)\ge \min\{δ(G)-1, \, \lfloor Φ(G) \rfloor\}$, which is the dual version of the Goldberg-Seymour conjecture on edge-colorings of multigraphs. In this note we prove that $ξ(G)\ge \min\{δ(G)-1, \, \lfloor Φ(G) \rfloor\}$ if $Φ(G)$ is not integral and $ξ(G)\ge \min\{δ(G)-2, \, \lfloor Φ(G) \rfloor-1\}$ otherwise. We also show that this co-density conjecture implies another conjecture concerning cover index made by Gupta in 1967.

math.CO↗

arXiv2019

Local superderivations on Cartan type Lie superalgebras

In this paper, we characterize the local superderivations on Cartan type Lie superalgebras over the complex field $\mathbb{C}$. Furthermore, we prove that every local superderivations on Cartan type simple Lie superalgebras is a superderivations. As an application, using the results on local superderivations we characterize the $2$-local superderivations on Cartan type Lie superalgebras. We prove that every $2$-local superderivations on Cartan type Lie superalgebras is a superderivations.

math.RA↗

arXiv2018

Super-biderivations of Cartan type Lie superalgebras

In this paper, we characterize the super-biderivations of Cartan type Lie superalgebras over the complex field $\mathbb{C}$. Furthermore, we prove that all super-biderivations of Cartan type simple Lie superalgebras are inner super-biderivations.

math.RA↗

arXiv2018

Scanning tunneling microscopic evidence of interface enhanced high-Tc superconductivity in Pb islands grown on SrTiO3

The discovery of the interface enhanced superconductivity in the single layer film of FeSe epitaxially grown on SrTiO3 substrates has triggered a flurry of activity in the field of superconductivity. It raised the hope to find more conventional high-Tc superconductors which are purely driven by the electron-phonon interaction at ambient pressure. Here we report the experimental evidence from the measurement of scanning tunneling spectroscopy for the interface enhanced high-Tc superconductivity in the Pb thin film islands grown on SrTiO3 substrates. The superconducting energy gap of the Pb film is found to depend on both the thickness and the volume of the islands. The largest superconducting energy gap is found to be about 10 meV, which is 7 times larger than that in the bulk Pb. The corresponding superconducting transition temperature, estimated by fitting the temperature dependence of the gap values using the BCS formula, is found to be 47 K, again 7 times higher than that of the bulk Pb.

cond-mat.supr-con↗

arXiv2018

Independence number of edge-chromatic critical graphs

Let $G$ be a simple graph with maximum degree $Δ(G)$ and chromatic index $χ'(G)$. A classic result of Vizing indicates that either $χ'(G )=Δ(G)$ or $χ'(G )=Δ(G)+1$. The graph $G$ is called $Δ$-critical if $G$ is connected, $χ'(G )=Δ(G)+1$ and for any $e\in E(G)$, $χ'(G-e)=Δ(G)$. Let $G$ be an $n$-vertex $Δ$-critical graph. Vizing conjectured that $α(G)$, the independence number of $G$, is at most $\frac{n}{2}$. The current best result on this conjecture, shown by Woodall, is that $α(G)<\frac{3n}{5}$. We show that for any given $\varepsilon\in (0,1)$, there exist positive constants $d_0(\varepsilon)$ and $D_0(\varepsilon)$ such that if $G$ is an $n$-vertex $Δ$-critical graph with minimum degree at least $d_0$ and maximum degree at least $D_0$, then $α(G)<(\frac{1}{2}+\varepsilon)n$. In particular, we show that if $G$ is an $n$-vertex $Δ$-critical graph with minimum degree at least $d$ and $Δ(G)\ge (d+2)^{5d+10}$, then \[ α(G) < \left. \begin{cases} \frac{7n}{12}, & \text{if $d= 3$; } \frac{4n}{7}, & \text{if $d= 4$; } \frac{d+2+\sqrt[3]{(d-1)d}}{2d+4+\sqrt[3]{(d-1)d}}n<\frac{4n}{7}, & \text{if $d\ge 19$. } \end{cases} \right. \]

math.CO↗

arXiv2017

Hamiltonicity of edge-chromatic critical graphs

Given a graph $G$, denote by $Δ$ and $χ^\prime$ the maximum degree and the chromatic index of $G$, respectively. A simple graph $G$ is called {\it edge-$Δ$-critical} if $χ^\prime(G)=Δ+1$ and $χ^\prime(H)\leΔ$ for every proper subgraph $H$ of $G$. We proved that every edge chromatic critical graph of order $n$ with maximum degree at least $\frac{2n}{3}+12$ is Hamiltonian.

math.CO↗