Outer-connected open packing sets in graphs

A set [Formula: see text] of a graph [Formula: see text] is an [Formula: see text] [Formula: see text] [Formula: see text] of [Formula: see text] if no two vertices of [Formula: see text] have a common neighbor in [Formula: see text]. An open packing set [Formula: see text] is called an outer-connected open packing set (ocop-set) if either [Formula: see text] or [Formula: see text] is connected. The minimum and maximum cardinalities of an ocop-set are called the lower outer-connected open packing number and the outer-connected open packing number, respectively, and are denoted by [Formula: see text] and [Formula: see text], respectively. In this paper, we initiate a study on these parameters.

A molecular dynamics study on cooling rate effect on atomic structure of solidified silver nanoparticles

The atomic structures and solidification point of silver nanoparticles (SNPs) are studied in aseries of molecular dynamics simulations based on the empirical embedded atom methods (EAM). Thesolidification point is calculated from the extracted potential energy during the cooling process, whereasthe atomic structures are analyzed using the common neighbor (CN) method. The results indicate that thestructures of the solidified SNPs are very sensitive to both the applied cooling rate and the particle size. Wefind the critical cooling rate where a glassy structure is observed. Below the critical rate, polycrystallinenanoparticles are formed, where the percentage of the close-packed structures, i.e., FCC and HCP, decreaseswith increasing cooling rate. Moreover, the proportion of those structures is always larger with a biggerparticle size for an identical applied cooling rate. The findings in this study provide useful information formany practical applications where the nanostructure strongly affects thermal management and operationalefficiency.

Identifying protein complexes from protein–protein interaction networks based on the gene expression profile and core-attachment approach

Defining protein complexes in the cell is important for learning about cellular processes mechanisms as they perform many of the molecular functions in these processes. Most of the proposed algorithms predict a complex as a dense area in a Protein–Protein Interaction (PPI) network. Others, on the other hand, weight the network using gene expression or geneontology (GO). These approaches, however, eliminate the proteins and their edges that offer no gene expression data. This can lead to the loss of important topological relations. Therefore, in this study, a method based on the Gene Expression and Core-Attachment (GECA) approach was proposed for addressing these limitations. GECA is a new technique to identify core proteins using common neighbor techniques and biological information. Moreover, GECA improves the attachment technique by adding the proteins that have low closeness but high similarity to the gene expression of the core proteins. GECA has been compared with several existing methods and proved in most datasets to be able to achieve the highest F-measure. The evaluation of complexes predicted by GECA shows high biological significance.

Link Prediction and Node Classification Based on Multitask Graph Autoencoder

The goal of network representation learning is to extract deep-level abstraction from data features that can also be viewed as a process of transforming the high-dimensional data to low-dimensional features. Learning the mapping functions between two vector spaces is an essential problem. In this paper, we propose a new similarity index based on traditional machine learning, which integrates the concepts of common neighbor, local path, and preferential attachment. Furthermore, for applying the link prediction methods to the field of node classification, we have innovatively established an architecture named multitask graph autoencoder. Specifically, in the context of structural deep network embedding, the architecture designs a framework of high-order loss function by calculating the node similarity from multiple angles so that the model can make up for the deficiency of the second-order loss function. Through the parameter fine-tuning, the high-order loss function is introduced into the optimized autoencoder. Proved by the effective experiments, the framework is generally applicable to the majority of classical similarity indexes.

OPEN PACKING NUMBER FOR SOME CLASSES OF PERFECT GRAPHS

Let \(G\) be a graph with the vertex set \(V(G)\). A subset \(S\) of \(V(G)\) is an open packing set of \(G\) if every pair of vertices in \(S\) has no common neighbor in \(G.\) The maximum cardinality of an open packing set of \(G\) is the open packing number of \(G\) and it is denoted by \(\rho^o(G)\). In this paper, the exact values of the open packing numbers for some classes of perfect graphs, such as split graphs, \(\{P_4, C_4\}\)-free graphs, the complement of a bipartite graph, the trestled graph of a perfect graph are obtained.

Crystallization of FCC and BCC Liquid Metals Studied by Molecular Dynamics Simulation

The atomic structure variations on cooling, vitrification and crystallization processes in liquid metals face centered cubic (FCC) Cu are simulated in the present work in comparison with body centered cubic (BCC) Fe. The process is done on continuous cooling and isothermal annealing using a classical molecular-dynamics computer simulation procedure with an embedded-atom method potential at constant pressure. The structural changes are monitored with direct structure observation in the simulation cells containing from about 100 k to 1 M atoms. The crystallization process is analyzed under isothermal conditions by monitoring density and energy variation as a function of time. A common-neighbor cluster analysis is performed. The results of thermodynamic calculations on estimating the energy barrier for crystal nucleation and a critical nucleus size are compared with those obtained from simulation. The differences in crystallization of an FCC and a BCC metal are discussed.

Proximity Measures as Graph Convolution Matrices for Link Prediction in Biological Networks

MotivationLink prediction is an important and well-studied problem in computational biology, with a broad range of applications including disease gene prioritization, drug-disease associations, and drug response in cancer. The general principle in link prediction is to use the topological characteristics and the attributes–if available– of the nodes in the network to predict new links that are likely to emerge/disappear. Recently, graph representation learning methods, which aim to learn a low-dimensional representation of topological characteristics and the attributes of the nodes, have drawn increasing attention to solve the link prediction problem via learnt low-dimensional features. Most prominently, Graph Convolution Network (GCN)-based network embedding methods have demonstrated great promise in link prediction due to their ability of capturing non-linear information of the network. To date, GCN-based network embedding algorithms utilize a Laplacian matrix in their convolution layers as the convolution matrix and the effect of the convolution matrix on algorithm performance has not been comprehensively characterized in the context of link prediction in biomedical networks. On the other hand, for a variety of biomedical link prediction tasks, traditional node similarity measures such as Common Neighbor, Ademic-Adar, and other have shown promising results, and hence there is a need to systematically evaluate the node similarity measures as convolution matrices in terms of their usability and potential to further the state-of-the-art.ResultsWe select 8 representative node similarity measures as convolution matrices within the single-layered GCN graph embedding method and conduct a systematic comparison on 3 important biomedical link prediction tasks: drug-disease association (DDA) prediction, drug–drug interaction (DDI) prediction, protein–protein interaction (PPI) prediction. Our experimental results demonstrate that the node similarity-based convolution matrices significantly improves GCN-based embedding algorithms and deserve more attention in the future biomedical link predictionAvailabilityOur method is implemented as a python library and is available at [email protected] informationSupplementary data are available at Bioinformatics online.