FRACTIONAL (g, f)-FACTORS OF GRAPHS

This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be induced.

Integrated causal inference modeling uncovers novel causal factors and potential therapeutic targets of Qingjin Yiqi granules for chronic fatigue syndrome

Objective:Chronic fatigue syndrome(CFS)is a prevalent symptom of post-coronavirus disease 2019(COVID-19)and is associated with unclear disease mechanisms.The herbal medicine Qingjin Yiqi granules(QJYQ)constitute a clinically approved formula for treating post-COVID-19;however,its potential as a drug target for treating CFS remains largely unknown.This study aimed to identify novel causal factors for CFS and elucidate the potential targets and pharmacological mechanisms of action of QJYQ in treating CFS.Methods:This prospective cohort analysis included 4,212 adults aged≥65 years who were followed up for 7 years with 435 incident CFS cases.Causal modeling and multivariate logistic regression analysis were performed to identify the potential causal determinants of CFS.A proteome-wide,two-sample Mendelian randomization(MR)analysis was employed to explore the proteins associated with the identified causal factors of CFS,which may serve as potential drug targets.Furthermore,we performed a virtual screening analysis to assess the binding affinity between the bioactive compounds in QJYQ and CFS-associated proteins.Results:Among 4,212 participants(47.5%men)with a median age of 69 years(interquartile range:69–70 years)enrolled in 2004,435 developed CFS by 2011.Causal graph analysis with multivariate logistic regression identified frequent cough(odds ratio:1.74,95%confidence interval[CI]:1.15–2.63)and insomnia(odds ratio:2.59,95%CI:1.77–3.79)as novel causal factors of CFS.Proteome-wide MR analysis revealed that the upregulation of endothelial cell-selective adhesion molecule(ESAM)was causally linked to both chronic cough(odds ratio:1.019,95%CI:1.012–1.026,P=2.75 e^(−05))and insomnia(odds ratio:1.015,95%CI:1.008–1.022,P=4.40 e^(−08))in CFS.The major bioactive compounds of QJYQ,ginsenoside Rb2(docking score:−6.03)and RG4(docking score:−6.15),bound to ESAM with high affinity based on virtual screening.Conclusions:Our integrated analytical framework combining epidemiological,genetic,and in silico data provides a novel strategy for elucidating complex disease mechanisms,such as CFS,and informing models of action of traditional Chinese medicines,such as QJYQ.Further validation in animal models is warranted to confirm the potential pharmacological effects of QJYQ on ESAM and as a treatment for CFS.

Carbon Emission Factors Prediction of Power Grid by Using Graph Attention Network

Advanced carbon emission factors of a power grid can provide users with effective carbon reduction advice,which is of immense importance in mobilizing the entire society to reduce carbon emissions.The method of calculating node carbon emission factors based on the carbon emissions flow theory requires real-time parameters of a power grid.Therefore,it cannot provide carbon factor information beforehand.To address this issue,a prediction model based on the graph attention network is proposed.The model uses a graph structure that is suitable for the topology of the power grid and designs a supervised network using the loads of the grid nodes and the corresponding carbon factor data.The network extracts features and transmits information more suitable for the power system and can flexibly adjust the equivalent topology,thereby increasing the diversity of the structure.Its input and output data are simple,without the power grid parameters.We demonstrated its effect by testing IEEE-39 bus and IEEE-118 bus systems with average error rates of 2.46%and 2.51%.

ON(g,f)-FACTORIZATIONS OF GRAPHS

Let G be a graph and g, f be two nonnegative integer-valued functions defined on the vertices set V(G) of G and g less than or equal to f. A (g, f)-factor of a graph G is a spanning subgraph F of G such that g(x)less than or equal to d(F)(x)less than or equal to f(x) for all x is an element of V(G). If G itself is a (g, f)-factor, then it is said that G is a (g, f)-graph. If the edges of G can be decomposed into some edge disjoint (g, f)-factors, then it is called that G is (g, f)-factorable. In this paper, one sufficient condition for a graph to be (g, f)-factorable is given.

OFDM叠加导频联合信道估计和检测方法

针对现有正交频分复用(Orthogonal Frequency Division Multiplexing,OFDM)系统信道估计和迭代检测算法中频谱效率低和鲁棒性差等问题,提出了一种基于酉近似消息传递和叠加导频的信道估计与联合检测方法。首先,在软调制/解调中叠加导频对正交幅度调制的星座点进行预处理,检测时将叠加的导频作为频域符号的先验分布,利用置信传播算法进行调制和解调,实现检测模型的简化。然后,应用因子图-消息传递算法对OFDM传输系统和信道进行建模和全局优化,引入酉变换加强信道估计算法的鲁棒性。最后,建立OFDM仿真环境对现有方法进行仿真分析。仿真结果表明,相对于现有的独立导频类算法,所提算法能够以相同复杂度显著提升OFDM系统的频谱效率和鲁棒性。

Predictive value of NLR, Fib4, and APRI in the occurrence of liver failure after hepatectomy in patients with hepatocellular carcinoma

BACKGROUND Neutrophil-lymphocyte ratio(NLR),fibrosis index based on four factors(Fib4),aspartate aminotransferase-to-platelet ratio index(APRI)can be used for prognostic evaluation of hepatocellular carcinoma.However,no study has established an individualized prediction model for the prognosis of hepatocellular carcinoma based on these factors.AIM To screen the factors that affect the prognosis of hepatocellular carcinoma and establish a nomogram model that predicts postoperative liver failure after hepatic resection in patients with hepatocellular carcinoma.METHODS In total,220 patients with hepatocellular carcinoma treated in our hospital from January 2022 to January 2023 were selected.They were divided into 154 participants in the modeling cohort,and 66 in the validation cohort.Comparative analysis of the changes in NLR,Fib4,and APRI levels in 154 patients with hepatocellular carcinoma before liver resection and at 3 mo,6 mo,and 12 mo postoperatively was conducted.Binary logistic regression to analyze the influencing factors on the occurrence of liver failure in hepatocellular carcinoma patients,roadmap prediction modeling,and validation,patient work characteristic curves(ROCs)to evaluate the predictive efficacy of the model,calibration curves to assess the consistency,and decision curve analysis(DCA)to evaluate the model’s validity were also conducted.RESULTS Binary logistic regression showed that Child-Pugh grading,Surgical site,NLR,Fib4,and APRI were all risk factors for liver failure after hepatic resection in patients with hepatocellular carcinoma.The modeling cohort built a column-line graph model,and the area under the ROC curve was 0.986[95%confidence in terval(CI):0.963-1.000].The patients in the validation cohort utilized the column-line graph to predict the probability of survival in the validation cohort and plotted the ROC curve with an area under the curve of the model of 0.692(95%CI:0.548-0.837).The deviation of the actual outcome curves from the calibration curves of the column-line plots generated by the modeling and validation cohorts was small,and the DCA confirmed the validity.CONCLUSION NLR,Fib4,and APRI independently influence posthepatectomy liver failure in patients with hepatocellular carcinoma.The column-line graph prediction model exhibited strong prognostic capability,with substantial concordance between predicted and actual events.

基于月面LTE基站OFDM测距的巡视器定位

针对目前的月面定位技术中成本高、观测时间长以及缺少可用定位信息的问题,开展了基于长期演进(LTE)基站的月面定位技术的研究,并引入了LTE技术,通过在月面布设基站为月面巡视器的实时定位提供了可行基础。提出了一种基于因子图优化的月面定位方法,通过融合月面基站的正交频分复用(OFDM)测距信息和巡视器自身的惯性导航信息,利用有限的月面基础设施,在较低成本的硬件条件下实现了月面巡视器的准确定位。仿真实验结果显示,该月面定位方法具有良好的准确性和鲁棒性。

The Factorization of Adjoint Polynomials of E^G（i）-class Graphs and Chromatically Equivalence Analysis

Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp＋（r-1）^G（i） the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r - 1 of S,, while the i-th vertex of each component of （r - 1）G be adjacented to r - 1 vertices of degree 1 of St, respectively. By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs Eτp＋（r-1）^G（i）∪（r - 1）K1 （1 ≤i≤p）. Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements.

ORTHOGONAL (g,f)-FACTORIZAFIONS OF BIPARTITE GRAPHS

Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two positive integer-valued functions defined on V(G) such that g(x) ≤ f(x) for every vertex x of V(G). Then a (g, f)-factor of G is a spanning subgraph H of G such that g(x) ≤ dH(x) 5 f(x) for each x ∈ V(H). A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {F1, F2,…… ， Fm } and H be a factorization and a subgraph of G, respectively. If F, 1 ≤ i ≤ m， has exactly one edge in common with H, then it is said that ■ is orthogonal to H. It is proved that every bipartite (mg + m - 1, mf - m + 1 )-graph G has a (g, f)-factorization orthogonal to k vertex disjoint m-subgraphs of G if 2-k ≤ g(x) for all x ∈ V(G). Furthermore, it is showed that the results in this paper are best possible.

K_(1,p)~k-FACTORIZATION OF COMPLETE BIPARTITE GRAPHS

In this paper, it is shown that a sufficient condition for the existence of a K 1,p k factorization of K m,n , whenever p is a prime number and k is a positive integer, is (1) m≤p kn,(2) n≤p km,(3)p kn-m≡p km-n ≡0(mod( p 2k -1 )) and (4) (p kn-m)(p km-n) ≡0(mod( p k -1)p k×(p 2k -1)(m+n)) .

Blind receiver for OFDM systems via sequential Monte Carlo in factor graphs

Estimation and detection algorithms for orthogonal frequency division multiplexing (OFDM) systems can be de-veloped based on the sum-product algorithms, which operate by message passing in factor graphs. In this paper, we apply the sampling method (Monte Carlo) to factor graphs, and then the integrals in the sum-product algorithm can be approximated by sums, which results in complexity reduction. The blind receiver for OFDM systems can be derived via Sequential Monte Carlo (SMC) in factor graphs, the previous SMC blind receiver can be regarded as the special case of the sum-product algorithms using sampling methods. The previous SMC blind receiver for OFDM systems needs generating samples of the channel vector assuming the channel has an a priori Gaussian distribution. In the newly-built blind receiver, we generate samples of the virtual-pilots instead of the channel vector, with channel vector which can be easily computed based on virtual-pilots. As the size of the vir-tual-pilots space is much smaller than the channel vector space, only small number of samples are necessary, with the blind de-tection being much simpler. Furthermore, only one pilot tone is needed to resolve phase ambiguity and differential encoding is not used anymore. Finally, the results of computer simulations demonstrate that the proposal can perform well while providing sig-nificant complexity reduction.

P_3-factor in Line Graphs of Trees

In this paper,we give a necessary and sufficient condition for the existence of P3-factors in the line graph of a tree.Then we present an algorithm to determine whether the line graph of a tree has a P3-factor.

On the ｛P_2,P_3｝-Factor of Cubic Graphs

Ler G = （ V, E） be a finite simple graph and Pn denote the path of order n. A spanning subgraph F is called a { P2, P3 }-factor of G if each component of F is isomorphic to P2 or P3. With the path-covering method, it is proved that any connected cubic graph with at least 5 vertices has a { P2, P3 }-factor F such that｜P3（F）｜P2（F）｜, where P2（F） and P3（F） denote the set of components of P2 and P3 in F, respectively.

K_(1,k)-FACTORIZATION OF BIPARTITE GRAPHS

In this paper, a necessary condition for a bipartite graph λK m,n to be K 1,k factorizable and a sufficient condition for kK m,n to have a K 1,k factorization whenever k is a prime number are given.

Vertex centrality of complex networks based on joint nonnegative matrix factorization and graph embedding

Finding crucial vertices is a key problem for improving the reliability and ensuring the effective operation of networks,solved by approaches based on multiple attribute decision that suffer from ignoring the correlation among each attribute or the heterogeneity between attribute and structure. To overcome these problems, a novel vertex centrality approach, called VCJG, is proposed based on joint nonnegative matrix factorization and graph embedding. The potential attributes with linearly independent and the structure information are captured automatically in light of nonnegative matrix factorization for factorizing the weighted adjacent matrix and the structure matrix, which is generated by graph embedding. And the smoothness strategy is applied to eliminate the heterogeneity between attributes and structure by joint nonnegative matrix factorization. Then VCJG integrates the above steps to formulate an overall objective function, and obtain the ultimately potential attributes fused the structure information of network through optimizing the objective function. Finally, the attributes are combined with neighborhood rules to evaluate vertex's importance. Through comparative analyses with experiments on nine real-world networks, we demonstrate that the proposed approach outperforms nine state-of-the-art algorithms for identification of vital vertices with respect to correlation, monotonicity and accuracy of top-10 vertices ranking.

On the Factorizations of (mg, mf)-graph

Let G be an (mg, mf)-graph, where g and f are integer-valued functions defined on V(G) and such that 0≤g(x)≤f(x) for each x ∈ V(G). It is proved that(1) If Z ≠ , both g and f may be not even, G has a (g, f)-factorization, where Z = {x ∈ V(G):mf(x)-dG(x)≤t(x) or dG(x)-mg(x)≤ t(x), t(x)=f(x)-g(x)>0}.(2) Let G be an m-regular graph with 2n vertices, m ≥ n. If (P1, P2,..., Pr) is a partition of m, P1 ≡m (mod 2), Pi≡0 (mod 2), i=2,..., r, then the edge set E(G) of G can be parted into r parts E1,E2,..., Er of E(G) such that G[Ei] is a Pi-factor of G.

(g,f)-FACTORS WITH SPECIAL PROPERTIES IN BIPARTITE (mg,mf)-GRAPHS

Let G be a bipartite graph and g and f be two positive integer-valued functions defined on vertex set V(G) of G such that g(x)≤f(x).In this paper,some sufficient conditions related to the connectivity and edge-connectivity for a bipartite (mg,mf)-graph to have a (g,f)-factor with special properties are obtained and some previous results are generalized.Furthermore,the new results are proved to be the best possible.

Overview and Graph Theory of the Immune System of Crustacean

In this paper,different kinds of enzymes,immune factors and regulatory factors of the immune system of crustaceans are summarized and then combed systematically and thoroughly. According to the mutual influence and effects of these factors,different symbolic forms are introduced to express the effects,and ultimately the whole node graph of the system is obtained. The graph theory can be used for further researches on the immune system of crustacean.

OFDM系统中基于因子图的信道估计算法

为提高正交频分复用(OFDM)系统的信道估计精度,根据频谱资源的无线信道特性,提出基于因子图的OFDM系统信道估计算法,包括二维联合信道估计算法和2个级联的一维信道估计算法。将时变频率选择性衰落信道建模为一阶自回归模型,使信道参数之间的交互信息近似为高斯分布,利用和积算法实现OFDM系统的联合信道估计和符号检测。仿真结果表明,该信道估计算法能够以较低的计算复杂度逼近最优的估计性能。