With the proliferation of interconnection networks in mission-critical systems ranging from cloud computing infrastructures to large-scale data centers, the escalating structural complexity has intensified network vulnerability to malicious attacks and cyber warfare incidents. This article establishes a theoretical framework for evaluating network self-diagnostic capability through a novelh-extrar-component diagnosability metric, denoted as$\widehat{ec}_{r}^{h}(G)$, which quantifies a network’s resilience under compound fault patterns. The proposed metric requires that after removing specific nodes, the remaining subgraph is required to preserve at leastrconnected components where every component maintains a node count exceedingh. Through rigorous combinatorial analysis, we derive closed-form expressions for star networks$S_{n}$,$\widehat{ec}_{2}^{1}(S_{n}) = 4n - 9$and$\widehat{ec}_{3}^{1}(S_{n}) = 6n - 15$when$n \ge 6$, establishing the tight diagnosability bounds for this fundamental network topology. To enable practical implementation, we design a Trial System-based Fault Diagnosis Algorithm (TSFD) that features adaptive syndrome verification and parallel fault localization mechanisms. Extensive simulations demonstrate the accuracy of 98.99% fault detection with linear-time complexity$O(Nd)$inn-dimensional star networks. This work advances network reliability theory by introducing a multi-feature diagnosability measure for system-level diagnosis and developing an efficient diagnosis algorithm validated through large-scale network emulation.

Essential proteins are a crucial component of living organisms, and their absence will lead to cell death or reproductive arrest. Discovering these proteins can propel advancements in synthetic biology and facilitate the development of novel antibiotics and therapies for various diseases. However, current computational methods suffer from two major drawbacks that hinder their discovery rate: one is the significant noise in protein-protein interaction (PPI) data, and the other is the inadequate consideration of feature relationships. To enhance identification capabilities, this study proposes a novel essential protein prediction method, Feature Synergy Method (FSM), which leverages a features synergy model and GO pure centrality. The FSM is described as follows:Firstly, based on the principle of co-expression, gene expression data are integrated with the original PPI network to construct a pure PPI network (PPIN). Subsequently, GO annotation data are employed to calculate GO_sim weights for the interactions within the original PPI network, forming a GS_PIN. The PPIN and GS_PIN are then fused to establish the GS_PPIN, which helps mitigate the impact of noise in PPI data. Secondly, a new centrality measure, GO pure centrality (GPC), is designed based on this GO similarity-weighted pure PPI network. Thirdly, an evolutionary conservation score (ECS) is extracted from subcellular localization and orthologous proteins data. Fourthly, after analyzing the relationship between GPC and ECS, a novel fusion model, the features synergy model, is developed to integrate GPC and ECS, ultimately leading to the proposal of the new essential protein prediction method, FSM. To validate the performance of FSM, six computational methods (PeC, WDC, ION, NCCO, E_POC, and JDC) and six centrality measures (NC, IC, EC, SC, CC, and DC) were evaluated on three distinct yeast datasets. The results demonstrate that FSM achieves a higher essential protein identification rate. Similarly, GPC identifies more essential proteins compared to the six centrality-based approaches (NC, IC, EC, SC, CC, and DC).

Essential proteins are fundamental to the reproduction and survival of cells, and if they are killed, the cells will stop reproducing or die. Many computational methods of identifying essential proteins are proposed which fuse a large number of features from multi-omics data. Some of them extract features from subcellular localization data by subjectively selecting certain subcellular locations. Meanwhile, there is still room to improve the identification rate of essential proteins. In this paper, a new deep learning framework for identifying essential proteins based on Vision Transformer is proposed, named EPViT. Firstly, topological features are extracted from the protein-protein interaction network. Secondly, a feature matrix is designed from the subcellular localization information without subjective factor. Then, the two classes of features are fused into a new feature matrix by outer product operation. Finally, the new feature matrix is input into the Vision Transformer model to discover essential proteins. The results show that EPViT has the highest recognition rate among the comparison experiments on yeast data.

As critical reliability metrics for multiprocessor systems, connectivity and diagnosability respectively determine network robustness against node failures and the capability to accurately identify faulty units. This article presents a comprehensive reliability analysis of bubble-sort networks (Bn), a class of Cayley graphs that implement adjacent-node swap operations, offering inherent advantages for distributed sorting systems. First, we investigate theh-extrar-component connectivity and diagnosability ofBnunder the Preparata-Metze-Chien (PMC) diagnostic model through rigorous topological analysis. Then, we characterize theg-good-neighborr-component connectivity and diagnosability ofBnunder the PMC model by establishing tight bounds through fault pattern analysis. In addition, we develop a three-round fault identification algorithm, TRFI-PMC, that achieves robust diagnostic performance in simulated experiments. Specifically, for the networkB8with 40320 nodes, the algorithm maintains superior performance (fault density achieving 25%) across five metrics: accuracy (98.81%), true negative rate (97.81%), false positive rate (2.18%), true positive rate (99.3%), and precision (98.98%). The theoretical results establish fundamental reliability limits forBnarchitectures, while the practical algorithm provides an efficient fault diagnosis solution forn-dimensional bubble-sort network.

With the scale of multiprocessor systems constantly increasing, the large number of interconnected processors (or nodes) makes faulty nodes inevitable. The fault diagnosis of multiprocessor systems therefore is a key technique for the system’s robustness. In this paper, we first propose a novel diagnostic metric, the$h$-extra$r$-component diagnosability, denoted$ECD^{h}_{r}(G)$, which characterizes one special pattern of faults. We derive some theoretical results for the ECD of hypercube, denoted$ECD^{h}_{r}(Q_{n})$, under the PMC model. Diagnostic algorithms is proposed and implemented to detect faulty nodes that will disconnect hypercube$Q_{n}$into$r$components each containing at least$h+1$nodes. We also test the ECD-PMC algorithm to the hypercube network with different number of faulty processors satisfying the$h$-extra$r$-component condition. Extensive simulation results show that our proposed method achieves very good performance in terms of ACCR, TPR, FPR, and TNR.

The proliferation of interconnection networks has intensified the demand for robust fault diagnosis methodologies. Although existing research focuses predominantly on single-condition diagnosability metrics, these approaches often fail to capture hybrid failure scenarios in large-scale networks. To provide a more comprehensive and realistic resilience assessment, this article introduces a new diagnosability metric termed the$g$-good-neighbor$r$-component diagnosability, denoted by$D_{g,r}(G)$. This metric imposes two stringent constraints on the network after removing a faulty node set$F$: i) the residual network must contain at least$r$connected components, and ii) every fault-free node must retain at least$g$fault-free neighbors. We focus on the hypercube ($Q_{n}$), a prevalent interconnection architecture renowned for its high symmetry, scalability, and fault tolerance. Under the PMC and MM* diagnostic models, we establish the exact value$D_{2,2}(Q_{n}) = 8n - 21$for$n \geq 24$. Leveraging the distinct characteristics of the PMC and MM* models, we propose two scalable fault localization algorithms tailored for hypercube architectures. Simulation experiments on$Q_{n}$networks demonstrate that the proposed framework achieves approximately 100% true positive rate (TPR) when faulty nodes constitute$\leq 20\%$of the network, maintaining TPR$> 98.7\%$even as fault densities approach 50% .

MOTIVATION: Cancer as a public health problem is driven by genomic variations in "cancer driver" genes. The identification of driver genes is critical for the discovery of key biomarkers and the development of personalized therapy. RESULTS: We propose a prediction method MNMO: a multi-layer network model based on multi-omics data. MNMO firstly constructs a dynamically adjusted four-layer network composed of miRNAs and three kinds of genes with different features. Then three kinds of scores, i.e. control capacity, mutation score, and network score, are devised and calculated by harmonic mean to produce the integrated gene score. Experiments were performed on three kinds of real cancer data to compare the identification performance of method MNMO with that of six state-of-the-art ones. The results indicate that method MNMO presents the best identification performance under most circumstances. The genes prioritized by method MNMO not only have a better match to the benchmark ones than those identified by the other methods, but also are all associated with the development and progression of cancers. In addition, some extended versions of method MNMO can further achieve better performance on most evaluation metrics for some specific datasets. They may be more conducive to identifying tissue-specific genes, which has been verified through a number of experiments. AVAILABILITY AND IMPLEMENTATION: The source code and the R package "MNMO" are available at https://github.com/Zheng-D/MNMO. The dataset and code are archived at https://doi.org/10.5281/zenodo.14969986.

Correct identification of cancer driver genes plays a significant role in cancer research. The advancement of graph neural network (GNN) research has led to the emergence of many high-performance cancer driver gene prediction methods. However, GNN-based methods frequently overlook the importance of capturing global information. Additionally, as GNN layers increase, the feature representation of genes begins to become overly smooth. These problems hinder the effectiveness of GNN-based identification methods. In this study, we introduce TGCN, a method integrating Transformer and graph convolutional network (GCN), aiming to address these issues and improve cancer driver gene identification. First, we composed multivariate feature matrices of genes from multi-omics data and multi-dimensional gene association networks. Second, we constructed a Transformer module to enrich gene feature representations. Finally, we utilized Chebyshev GCN to yield the identification results. The experimental results demonstrate that TGCN outperforms representative methods in identifying driver genes for both pan-cancer and single-type cancers.

Essential proteins play an essential role in cell survival and replication. Currently, more and more computational methods are developed to identify essential proteins, which overcome the time-consuming, costly and inefficient shortcomings with biological experimental methods. In order to improve the recognition rate, some new methods by fusing multiple features are developed, but they seldom consider the connection among features. After analyzing a large number of methods based on multi-feature fusion, a phenomenon among features is found, called weak consensus, then a weak consensus model to fuse these features is proposed in this paper. After analyzing the relationship between a protein and its neighbors in protein-protein interaction networks, a new centrality, namely neighborhood aggregation centrality(NAC) is developed in this paper. Then, a Max-Min strategy is used to integrate NAC with Pearson correlation coefficient and Jaccard similarity coefficient based on gene expression data to obtain local importance score. In addition, orthologous feature score is used to measure proteins conservation. Finally, by using the weak consensus model to fuse orthologous feature score with local importance score, a new method WOL is proposed in this paper. Then experiments are performed on S.cerevisiae data. The results show that compared with WDC, PeC, ION, JDC, NCCO and E_POC, WOL has a higher recognition rate.

The identification of cell types by clustering single-cell RNA sequencing (scRNA-seq) data is a fundamental step in the downstream analysis of single-cell data. However, great challenges remain owing to the inherent characteristics of scRNA-seq data, including high dimensionality, high noise, and high sparsity. In this study, we propose a proximity enhanced graph convolutional sparse subspace clustering method scPEGSSC for scRNA-seq data. Method scPEGSSC generates the similarity matrix with the self-expression matrix (SEM) learned from a graph autoencoder, and enhances it further through its square. Experiments were performed on thirteen real biological datasets. The experimental results indicate compared with eleven state-of-the-art single-cell clustering methods, method scPEGSSC have attained superior performance across most datasets.

Identifying cancer driver genes can accelerate the discovery of drug targets and the development of cancer therapies. Recent research methods improve the accuracy of identifying cancer driver genes by using deep learning framework. However, due to ignore the connection among learned features, they usually have weak feature representations that limits further improvement in the accuracy of identifying cancer driver genes. In this work, we propose a graph neural network framework combining graph convolutional network, Transformer with cross-attention, and multi-layer perceptron classifier, called GTCM, to improve the accuracy of identifying cancer driver genes. Specifically, GTCM first uses graph convolutional network to learn gene feature representations from three different gene association networks. Second, to enhance the feature representations of cancer driver genes, GTCM adopts Transformer with cross-attention to dynamically learn the connections between different feature sets. Finally, GTCM predicts cancer driver genes using multi-layer perceptron classifier. Ablation experiments prove that Transformer with cross-attention effectively improves the feature representations learned from graph convolutional network and further improves the identification rate. Compared with existing representative methods, GTCM exhibits excellent performance in terms of area under the receiver operating characteristic curves and area under precision-recall curves.

With the application and rapid development of high-performance computing and cloud computing technology, the scale of the interconnection network has appeared to grow exponentially. Network attacks have become increasingly sophisticated and stealthy. To reach a high reliable network system, widespread attention has been paid to fault diagnosis. In this article, we put forward a reliable and adaptive self-diagnosis strategy, the$h$-extra$r$-component conditional diagnosability, denoted by$ct_{r}^{h}(G)$. Then, we provide a theoretical derivation to characterize the$h$-extra$r$-component conditional diagnosability of bubble sort networks$B_{n}$under the PMC model. Furthermore, we develop a fast and adaptive fault self-diagnosis algorithm FAFD-PMC to detect all faulty units. Extensive experiments are implemented and applied to synthetic networks and real networks in terms of accuracy (ACCR), true negative rate, false positive rate, recall, and precision, which demonstrates the ACCR/efficiency of our algorithm.

Abstract Multiprocessor systems play a significant role in big data era. As the probability of presence of processor failures in a multiprocessor system raises with the increase of the system scale, the effect of processor failure is worthy of quantifying. The subsystem reliability of a multiprocessor system is the probability that a fault-free subsystem of certain size still operate with the rise of individual faults. In this work, we employ the probabilistic fault model and the Principle of Inclusion-Exclusion (PIE) to establish the approximation and upper bound on the subsystem reliability of the cactus-based networks through decomposition into $(n-1)$-dimensional subsystems by fixing one position-pair. Numerical simulations show that the upper bound derived in this way is close to the approximation of the accurate subsystem reliability.

Cancer is a complex genomic mutation disease, and identifying cancer driver genes promotes the development of targeted drugs and personalized therapies. The current computational method takes less consideration of the relationship among features and the effect of noise in protein-protein interaction(PPI) data, resulting in a low recognition rate. In this paper, we propose a cancer driver genes identification method based on dynamic incentive model, DIM. This method firstly constructs a hypergraph to reduce the impact of false positive data in PPI. Then, the importance of genes in each hyperedge in hypergraph is considered from three perspectives, network and functional score(NFS) is proposed. By analyzing the relation among features, the dynamic incentive model is proposed to fuse NFS, the differential expression score of mRNA and the differential expression score of miRNA. DIM is compared with some classical methods on breast cancer, lung cancer, prostate cancer, and pan-cancer datasets. The results show that DIM has the best performance on statistical evaluation indicators, functional consistency and the partial area under the ROC curve, and has good cross-cancer capability.

Essential proteins play an essential role in cell survival and replication. Currently, more and more computational methods are developed to identify essential proteins, which overcome the time-consuming, costly and inefficient shortcomings with biological experimental methods. In order to improve the recognition rate, some new methods by fusing multiple features are developed, but they seldom consider the connection among features. After analyzing a large number of methods based on multi-feature fusion, a weak consensus model to fuse features is proposed in this paper. Then, this paper uses the weak consensus model to fuse protein-protein interaction network, gene expression data, and orthologous data, thus proposing a new method, WOL. Then experiments are performed on one S.cerevisiae dataset. The results show that compared with WDC, PeC, ION, JDC, NCCO and E_POC, WOL has a higher recognition rate.

BACKGROUND: Although gene expression data play significant roles in biological and medical studies, their applications are hampered due to the difficulty and high expenses of gathering them through biological experiments. It is an urgent problem to generate high quality gene expression data with computational methods. WGAN-GP, a generative adversarial network-based method, has been successfully applied in augmenting gene expression data. However, mode collapse or over-fitting may take place for small training samples due to just one discriminator is adopted in the method. RESULTS: In this study, an improved data augmentation approach MDWGAN-GP, a generative adversarial network model with multiple discriminators, is proposed. In addition, a novel method is devised for enriching training samples based on linear graph convolutional network. Extensive experiments were implemented on real biological data. CONCLUSIONS: The experimental results have demonstrated that compared with other state-of-the-art methods, the MDWGAN-GP method can produce higher quality generated gene expression data in most cases.

Abstract Diagnosability is an important metric to fault tolerance and reliability for multiprocessor systems. However, plenty of research on fault diagnosability focuses on node failure. In practical scenario, not only node failures take place but also link malfunctions may arise. In this work, we investigate the diagnosability of general regular networks with failing nodes as well as missing malfunctional links. Let $S$ be a set of the missing links and broken-down nodes. We first prove that the diagnosability of the survival graph $G\setminus S$ persists $\delta (G\setminus S)$ under the PMC model (Preparata, F.P., Metze, G. and Chien, R.T. (1967) On the connection assignment problem of diagnosable systems. IEEE Trans. Electron. Comput., EC-16, 848–854) for a $t$-regular and $t$-connected triangle-free network $G$ subject to $|S|\leq t-1$ and $|V(G)|\geq 3t-2$ ($t\geq 3$). Furthermore, we determine the diagnosability of $G\setminus S$ for some kinds of extensively explored $t$-regular networks with triangles subject to $|S|\leq t-1$ ($t\geq 3$).

Abstract In this paper, we propose a new digragh model for system level fault diagnosis, which is called the $(f_1,f_{2})$-bounded Preparata–Metze–Chien (PMC) model (shortly, $(f_1,f_{2})$-BPMC). The $(f_1,f_{2})$-BPMC model projects a system such that the number of faulty processors that test faulty processors with the test results $0$ does not exceed $f_{2}$$(f_2\leq f_{1})$ provided that the upper bound on the number of faulty processors is $f_{1}$. This novel testing model compromisingly generalizes PMC model (Preparata, F.P., Metze, G. and Chien R.T. (1967) On the connection assignment problem of diagnosable systems. IEEE Tran. Electron. Comput.,EC-16, 848–854) and Barsi–Grandoni–Maestrini model (Barsi, F., Grandoni, F. and Maestrini, P. (1976) A theory of diagnosability of digital systems. IEEE Trans. Comput.C-25, 585–593). Then we present some characterizations for one-step diagnosibility under the $(f_1,f_{2})$-bounded PMC model, and determine the diagnosabilities of some special regular networks. Meanwhile, we establish the characterizations of $f_1/(n-1)$-diagnosability and three configurations of $f_1/(n-1)$-diagnosable system under the $(f_1,f_{2})$-BPMC model.

Fault tolerance plays an important role in the interconnection networks, where permanent and intermittent faults are two kinds of fault situations. Permanent fault diagnosabilities of regular networks have been proposed widely while the intermittent fault diagnosabilities are also noteworthy. In this paper, we give a sufficient and necessary condition for k-regular k-connected graph Gn to be ti-diagnosable without repair in intermittent fault pattern. Detailly, we show that the intermittent fault diagnosability of Gn under the PMC model is k−⌈g−12⌉−2⁠, where g is the maximum number of common neighbors for any two distinct vertices. As applications, intermittent fault diagnosabilities of many famous networks are explored.

As a critical parameter in evaluating the reliability of a multiprocessor system when processors malfunction, the \boldmath h-extra connectivity (h-EC) of a multiprocessor system modeled by a graph G, denoted by κo(h)(G), is an h-extra vertex-cut with minimum cardinality. Both of the h-extra conditional diagnosability (h-ECD) and the t/h-diagnosability of the multiprocessor system are vital to tolerate and diagnose faulty processors. These two parameters rely on the resolving of hEC. For the multiprocessor system based on star graph Sn, we show that the 5-EC κo(5)(Sn) of Sn(n ≥ 5) is 6n - 18. As a by-product, we present a novel proof of κo(2)(Sn) = 3n - 7 (resp., κo(4)(Sn) = 5n - 14) by relaxing the restriction n ≥ 10 (resp., n ≥ 7) to n ≥ 5 (resp., n ≥ 5). Furthermore, we determine that the h-ECD of Sn(n ≥ 5) under the preparata, metze, and chien (PMC) model is (h + 1)n - 2h - 1 for 1 ≤ h ≤ 3 and (h + 1)n - 3h + 2 for 4 ≤ h ≤ 5. In addition, we show that Snis [(h + 1)n - 4h + 2]/h-diagnosable for 4 ≤ h ≤ 5, which extends the result that Snis [(h + 1)n - 3h - 1]/h-diagnosable for 1 ≤ h ≤ 3 by [Zhou et al. “The t/k-diagnosability of star graph networks,” IEEE Trans. Comput., vol. 64, no. 2, pp. 547-555, Feb. 2015].