Graph Matrix Research Articles

Drug-Disease Association Prediction Using Heterogeneous Networks for Computational Drug Repositioning.

Drug repositioning, which involves the identification of new therapeutic indications for approved drugs, considerably reduces the time and cost of developing new drugs. Recent computational drug repositioning methods use heterogeneous networks to identify drug–disease associations. This review reveals existing network-based approaches for predicting drug–disease associations in three major categories: graph mining, matrix factorization or completion, and deep learning. We selected eleven methods from the three categories to compare their predictive performances. The experiment was conducted using two uniform datasets on the drug and disease sides, separately. We constructed heterogeneous networks using drug–drug similarities based on chemical structures and ATC codes, ontology-based disease–disease similarities, and drug–disease associations. An improved evaluation metric was used to reflect data imbalance as positive associations are typically sparse. The prediction results demonstrated that methods in the graph mining and matrix factorization or completion categories performed well in the overall assessment. Furthermore, prediction on the drug side had higher accuracy than on the disease side. Selecting and integrating informative drug features in drug–drug similarity measurement are crucial for improving disease-side prediction.

A note on Moore–Penrose inverse of Laplacian matrix of graphs

The aim of this paper is to present a study of the Moore–Penrose inverse [Formula: see text] of the Laplacian matrix of a simple and connected graph, particularly, for some families of graphs such as path, cycle, ladder, fan and wheel graphs. For this purpose, it is used diverse approaches and MP inverse of the Cartesian product of graphs, and are obtained new closed-form formulas of the [Formula: see text] of these families. A comparison of the computational efficiency of the new formulas versus traditional mathematical software is presented, showing the advantage of new formulas.

Maximum A Posteriori Inference of Random Dot Product Graphs via Conic Programming

We present a convex cone program to infer the latent probability matrix of a random dot product graph (RDPG). The optimization problem maximizes the Bernoulli maximum likelihood function with an added nuclear norm regularization term. The dual problem has a particularly nice form, related to the well-known semidefinite program relaxation of the maxcut problem. Using the primal-dual optimality conditions, we bound the entries and rank of the primal and dual solutions. Furthermore, we bound the optimal objective value and prove asymptotic consistency of the probability estimates of a slightly modified model under mild technical assumptions. Our experiments on synthetic RDPGs not only recover natural clusters, but also reveal the underlying low-dimensional geometry of the original data. We also demonstrate that the method recovers latent structure in the Karate Club Graph and synthetic U.S. Senate vote graphs and is scalable to graphs with up to a few hundred nodes.

Potential application of novel [formula omitted]-indices as molecular descriptors

A topological index or a descriptor is a graph invariant that describes the structure of a graph as a numerical value. This paper proposes eight novel indices called AL-indices, based on distance and degree, and analyzes their behavior to show that they can serve as potentially useful molecular descriptors. We find that among the proposed indices many have very good discriminative power when compared to the existing vertex-degree based indices and justifies the requirement of these new indices. Further, we propose a method to compute these indices and vertex-degree-based indices from a recently proposed graph matrix, referred to as neighborhood matrix.Computationally, we correlate the proposed indices’ efficiency against the octane isomers’ and polychlorobiphenyls’ physicochemical properties. We perform a comparative study of these indices with a few well-known vertex degree-based indices. Further, the proposed indices’ discriminative capacity is analyzed and shown to have higher discriminative power on the considered datasets. Among all the indices under study, four indices, namely AL4, AL5, AL7, and AL8 have shown the highest discriminative power on the set of octane isomers. While the indices AL4 and AL7 have the highest discriminative power on the set of PCB molecules compared to the other VDB indices.Among the proposed and considered indices, we show that the first index AL1 has a good correlation with the Acentric factor and entropy of octane isomer and with the total surface area, log-water-solubility, relative retention time, octanol–water-partition, and log-water-activity coefficient of PCBs.

On Spectra of Distance Randić Matrix of Graphs

On Spectra of Distance Randić Matrix of Graphs

The average search probabilities of discrete-time quantum walks

We study the average probability that a discrete-time quantum walk finds a marked vertex on a graph. We first show that, for a regular graph, the spectrum of the transition matrix is determined by the weighted adjacency matrix of an augmented graph. We then consider the average search probability on a distance regular graph, and find a formula in terms of the adjacency matrix of its vertex-deleted subgraph. In particular, for any family of the average search probability approaches 1/4 as the valency goes to infinity. We also present a more relaxed criterion, in terms of the intersection array, for this limit to be approached by distance regular graphs.

Bayesian Network Structure Learning Method Based on Causal Direction Graph for Protein Signaling Networks

Constructing the structure of protein signaling networks by Bayesian network technology is a key issue in the field of bioinformatics. The primitive structure learning algorithms of the Bayesian network take no account of the causal relationships between variables, which is unfortunately important in the application of protein signaling networks. In addition, as a combinatorial optimization problem with a large searching space, the computational complexities of the structure learning algorithms are unsurprisingly high. Therefore, in this paper, the causal directions between any two variables are calculated first and stored in a graph matrix as one of the constraints of structure learning. A continuous optimization problem is constructed next by using the fitting losses of the corresponding structure equations as the target, and the directed acyclic prior is used as another constraint at the same time. Finally, a pruning procedure is developed to keep the result of the continuous optimization problem sparse. Experiments show that the proposed method improves the structure of the Bayesian network compared with the existing methods on both the artificial data and the real data, meanwhile, the computational burdens are also reduced significantly.

Spektrum Laplace pada graf kincir angin berarah (Q_k^3)

Suppose that 0 = µ0 ≤ µ1 ≤ ... ≤ µn-1 are eigen values of a Laplacian matrix graph with n vertices and m(µ0), m(µ1), …, m(µn-1) are the multiplicity of each µ, so the Laplacian spectrum of a graph can be expressed as a matrix 2 × n whose line elements are µ0, µ1, …, µn-1 for the first row, and m(µ0), m(µ1), …, m(µn-1) for the second row. In this paper, we will discuss Laplacian spectrum of the directed windmill graph () with k ≥ 1. The determination of the Laplacian spectrum in this study is to determine the characteristic polynomial of the Laplacian matrix from the directed windmill graph () with k ≥ 1.
 Keywords: Characteristic polynomial, directed windmill graph, Laplacian matrix, Laplacian spectrum.MSC2020 :05C50

Total graph of a signed graph

The total graph is built by joining the graph to its line graph by means of the incidences. We introduce a similar construction for signed graphs. Under two similar defnitions of the line signed graph, we defne the corresponding total signed graph and we show that it is stable under switching. We consider balance, the frustration index and frustration number, and the largesteigenvalue. In the regular case we compute the spectrum of the adjacency matrix of the total graph and the spectra of certain compositions, and we determine some with exactly two main eigenvalues.

Examining the role of soft dimensions on the implementation of ISO 14000 environmental management systems: a graph-theoretic approach.

Organizations worldwide are now embracing different standards while approaching environmental management systems (EMS) to be environmentally and economically sustainable. The ISO 14001 EMS has captured much attention by offering efficient environmental practices organization-wide and throughout the supply chain. Human factors (HFs) are crucial behind implementing ISO 14001 EMS since research articles about ISO 14001 strongly emphasize different HFs. This study proposes a framework that solely focuses on those HFs. Influential HFs are extracted through content analysis of related literature and categorized into 5 main HFs. Opinions from experts in the relevant field about interrelationships and inheritances of the HFs are collected and converted into quantitative data. Incorporating the graph theoretic and matrix approach (GTMA), the data delivered permanent values corresponding to the main HFs and their best and worst possible values. Among the main HFs, EMS Training has been found to have the most scopes for improvement, followed by Employee Empowerment and EMS Teamwork. This study demonstrates a framework about how to assess the role of HFs behind internalizing ISO 14001 EMS and enables organizations to go for competitive benchmarking and to define and adjust goals for environmental management.

The spectral radius of signless Laplacian matrix and sum-connectivity index of graphs

The sum-connectivity index of a graph G is defined as the sum of weights over all edges uv of G, where du and dv are the degrees of the vertices u and v in G, respectively. The sum-connectivity index is one of the most important indices in chemical and mathematical fields. The spectral radius of a square matrix M is the maximum among the absolute values of the eigenvalues of M. Let q(G) be the spectral radius of the signless Laplacian matrix where D(G) is the diagonal matrix having degrees of the vertices on the main diagonal and A(G) is the (0, 1) adjacency matrix of G. The sum-connectivity index of a graph G and the spectral radius of the matrix Q(G) have been extensively studied. We investigate the relationship between the sum-connectivity index of a graph G and the spectral radius of the matrix Q(G). We prove that for some connected graphs with n vertices and m edges,

A Unifying Framework to Construct QC-LDPC Tanner Graphs of Desired Girth

This paper presents a unifying framework to construct low-density parity-check (LDPC) codes with associated Tanner graphs of desired girth. Towards this goal, we highlight the role that a certain square matrix that appears in the product of the parity-check matrix with its transpose has in the construction of codes with graphs of desired girth and further explore it in order to generate the set of necessary and sufficient conditions for a Tanner graph to have a given girth between 6 and 12. For each such girth, we present algorithms to construct codes of the desired girth and we show how to use them to compute the minimum necessary value of the lifting factor. For girth larger than 12, we show how to use multi-step graph lifting methods to deterministically modify codes in order to increase their girth. We also give a new perspective on LDPC protograph-based parity-check matrices by viewing them as rows of a parity-check matrix equal to the sum of certain permutation matrices and obtain an important connection between all protographs and those with variable nodes of degree 2. We also show that the results and methodology that we develop for the all-one protograph can be used and adapted to analyze the girth of the Tanner graph of any parity-check matrix and demonstrate how this can be done using a well-known irregular, multi-edge protograph specified by the NASA Consultative Committee for Space Data Systems (CCSDS). Throughout the paper, we exemplify our theoretical results with constructions of LDPC codes with Tanner graphs of any girth between 6 and 14 and give sufficient conditions for a multi-step lifted parity-check matrix to have girth between 14 and 22.

Adaptive event-triggered group consensus of multi-agent systems with non-identical nonlinear dynamics

The paper is concerned with mean-square group consensus for second-order multi-agent systems with non-identical dynamics, where the agents in the same group have the identical dynamics, the agents in the different groups have non-identical nonlinear dynamics. To reduce the update frequency of event-triggered controller, a novel adaptive dynamic event-triggered communication scheme is presented based on the local stochastic sampled information. The proposed event-triggered conditions of the position state and velocity state have be given separately owe to their state ranges may be different, which lead to the position state and velocity state with different event-triggered instants and release intervals. The event-triggered matrices and time-varying event-triggered parameters are introduced into event-triggered conditions, the given event-triggered conditions are detected only at discrete sampled times, which means Zeno behavior can be excluded. A novel distributed protocol is designed based on the neighboring agents information of the position state and velocity state at event-triggered instants. The group consensus issue can be transformed into the convergence problem of the augmented error system. Then some mean-square group consensus criteria can be derived with the help of tools from graph theory and matrix analysis, and the event-triggered matrices can be obtained by solving some linear matrix inequalities. Finally, two numerical examples are employed to show the validity and advantage of the proposed transmission scheme.

The spectra of random mixed graphs

A mixed graph is a graph that can be obtained from a simple undirected graph by replacing some of the edges by arcs in precisely one of the two possible directions. The Hermitian adjacency matrix of a mixed graph G of order n is the n×n matrix H(G)=(hij), where hij=−hji=i (with i=−1) if there exists an arc from vi to vj (but no arc from vj to vi), hij=hji=1 if there exists an edge (and no arcs) between vi and vj, and hij=hji=0 otherwise (if vi and vj are neither joined by an edge nor by an arc). Let λ1(G),λ2(G),…,λn(G) be eigenvalues of H(G). The k-th Hermitian spectral moment of G is defined as sk(H(G))=∑i=1nλik(G), where k≥0 is an integer. In this paper, we deal with the asymptotic behavior of the spectrum of the Hermitian adjacency matrix of random mixed graphs. We will present and prove a separation result between the largest and remaining eigenvalues of the Hermitian adjacency matrix, and as an application, we estimate the Hermitian spectral moments of random mixed graphs.

Community Detection in Semantic Networks: A Multi-View Approach.

The semantic social network is a complex system composed of nodes, links, and documents. Traditional semantic social network community detection algorithms only analyze network data from a single view, and there is no effective representation of semantic features at diverse levels of granularity. This paper proposes a multi-view integration method for community detection in semantic social network. We develop a data feature matrix based on node similarity and extract semantic features from the views of word frequency, keyword, and topic, respectively. To maximize the mutual information of each view, we use the robustness of L21-norm and F-norm to construct an adaptive loss function. On this foundation, we construct an optimization expression to generate the unified graph matrix and output the community structure with multiple views. Experiments on real social networks and benchmark datasets reveal that in semantic information analysis, multi-view is considerably better than single-view, and the performance of multi-view community detection outperforms traditional methods and multi-view clustering algorithms.

Pathological Voice Detection Using Joint Subsapce Transfer Learning

A pathological voice detection system is designed to detect pathological characteristics of vocal cords from speech. Such systems are particularly susceptible to domain mismatch where the training and testing data come from the source and target domains, respectively. Due to the difference in speech disease etiology, recording environment, and device, etc., the feature distributions of source and target domain are quite different. Meanwhile, considering the high costs of annotating labels, it is hard to acquire labeled data in the target domain. This paper attempts to formulate cross-domain pathological voice detection as an unsupervised domain adaptation problem. Joint subspace transfer learning (JSTL) aims to find a projection matrix to transform source and target domain data into a common space. The maximum mean discrepancy function is used to measure the divergence across databases. Intra-class and inter-class distance act as regularization to guarantee the maximum separability between different classes. A graph matrix is constructed to help transfer knowledge from the relevant source data to the target data. Three popular pathological voice databases were selected in this paper. For six cross-database experiments, the accuracy of the method proposed increased by up to 15%. For different voice categories, the category of structural voice showed the most significant increase, nearly 20%.

Learning to recommend journals for submission based on embedding models

Due to the rapid development of electronic journals, selecting appropriate journals to publish research papers has become a significant challenge to researchers. Sometimes, even a high-quality paper may get rejected from the editor due to the mismatch between the topic of the paper and the scope of the journal. To address this issue, we present a framework of learning to recommend journals for submission based on embedding models to assist researchers in journal selection. Specifically, the journal recommendation problem is formulated in the context of multi-class classification, where the Bidirectional Encoder Representations from Transformers (BERT) is deployed to extract the text-level features of representing papers and the AutoEncoder (AE) network is adopted to obtain the feature representation of each journal from the relationship matrix of the paper-journal bipartite graph. The final recommendation of journals is made by using a scoring function and a Softmax classifier. Experimental results obtained on the closed dataset of 10 different journals and the DBLP dataset indicate that we proposed method outperforms several classical approaches in terms of accuracy, F1, MRR, etc. Furthermore, we introduce information entropy as an evaluation index and analyze the model performance from the perspective of prediction uncertainty. This study provides a new approach to the journal recommendation task, and researchers can choose the appropriate embedding methods according to the actual problem.

Structural properties of local integrals of motion across the many-body localization transition via a fast and efficient method for their construction

Many-body localization (MBL) is a novel prototype of ergodicity breaking due to the emergence of local integrals of motion (LIOMs) in a disordered interacting quantum system. To better understand the role played by the existence of such macroscopically LIOMs, we explore and study some of their structural properties across the MBL transition. We first, consider a one-dimensional XXZ spin chain in a disordered magnetic field and introduce and implement a non-perturbative, fast, and accurate method of constructing LIOMs. In contrast to already existing methods, our scheme allows obtaining LIOMs not only in the deep MBL phase but rather, near the transition point too. Then, we take the matrix representation of LIOM operators as an adjacency matrix of a directed graph whose elements describe the connectivity of ordered eigenbasis in the Hilbert-space. Our cluster size analysis for this graph shows that the MBL transition coincides with a percolation transition in the Hilbert-space. By performing finite-size scaling, we compare the critical disorder and correlation exponent $\nu$ both in the presence and absence of interaction. Finally, we also discuss how the distribution of diagonal elements of LIOM operators in a typical cluster signals the transition.

Interactions among antecedents of project outsourcing strategies: evidence from Chinese construction firms

PurposeOutsourcing is a common practice that is often adopted to reduce costs and enhance capabilities. The underlying logic of a firm's outsourcing strategy is not always evident due to multiple antecedents with interacting effects. This study identifies critical factors that influence outsourcing strategies and reveals their interactions with empirical evidence from Chinese construction firms.Design/methodology/approachThe quantitative decision-making trial and evaluation laboratory (DEMATEL) method was applied to analyze the interrelationships among the antecedents of project outsourcing strategies. First, 24 experts from 13 Chinese construction firms were invited to evaluate and score the influence of each factor on the other. Second, the graph theory and matrix tools of DEMATEL were used to quantitatively obtain the causality among factors and the prominence of each factor within the system.FindingsAmong the antecedents, a firm's pursuit of cost efficiency, identity, technological capability and contracting capability are the most prominent factors influencing project outsourcing strategies. For the interactions among these factors, this study reveals that the focal firm's technological capability significantly influences its contracting capability, and they jointly influence the firm's outsourcing practices, the selection of outsourcing vendors and, eventually, its pursuit of cost efficiency. Moreover, legal restrictions in the institutional environment strongly shape this capability–cost efficiency relationship.Originality/valueTwelve critical factors following different theoretical perspectives at varying levels of analysis were identified from the literature review. By revealing the interrelationships among these factors, this study develops a holistic framework that integrates the transaction cost and capability perspectives for understanding project outsourcing strategies embedded in different institutional environments.

On Seidel Laplacian matrix and energy of graphs

Abstract In this work, the Seidel Laplacian spectrum of graphs are determined. Then new bounds are presented for the Seidel Laplacian energy of regular graphs and graphs by using their Seidel Laplacian spectrum and other techniques. Further, the Seidel Laplacian energy of specific graphs are computed.