Search

Zhu et al. [Theoret. Comput. Sci. 758 (2019) 1--8] introduced the $h$-edge tolerable diagnosability to measure the fault diagnosis capability of a multiprocessor system with faulty links. This kind of diagnosability is a generalization of the concept of traditional diagnosability. A graph is called a maximally connected graph if its minimum degree equals its vertex connectivity. It is well-known that many irregular networks are maximally connected graphs and the $h$-edge tolerable diagnosabilities of these networks are unknown, which is our motivation for research. In this paper, we obtain the lower bound of the $h$-edge tolerable diagnosability of a $t$-connected graph and establish the $h$-edge tolerable diagnosability of a maximally connected graph under the PMC model and the MM$^*$ model, which extends some results in [IEEE Trans. Comput. 23 (1974) 86--88], [IEEE Trans. Comput. 53 (2004) 1582--1590] and [Theoret. Comput. Sci. 796 (2019) 147--153]., 20 pages, 6 figures. arXiv admin note: text overlap with arXiv:1904.07020

Introduction: segmentation of 3d shapes is a fundamental problem in computer graphics and computer-aided design. It has received much plays attention in recent years. The analysis and research methods of 3d mesh models have established reliable mathematical foundations in graphics and geometric modeling. Compared with color and texture, shape features describe the shape information of objects from geometric structure features. And it an important role in a wide range of applications, including mesh parameterization, skeleton extraction, resolution modeling, shape retrieval, character recognitio,, robot navigation, and many others. Methods: The interactive selection surface of models is mainly used for shape segmentation. The common method is boundary-based selection, which requires user input some stokes near the edge of the selected or segmented region. Chen et al.introduced an approach to join the specified points form the boundaries for region segmentation on the surface. Funkhouser et al. improve the Dijkstra algorithm to find segmentation boundary contour. The graph cut algorithm use the distance between the surface and its convex hull as the growing criteria to decompose a shape into meaningful components. The watershed algorithm, widely used for image segmentation, is a region-growing algorithm with multiple seed points. Wu and Levine use simulated electrical charge distributions over the mesh to deal with the 3D part segmentation problem. Other methods using a watershed algorithm for surface decomposition. Results: We implemented our algorithm in C++ and Open MP and conducted the experiments on a PC with a 3.07 GHz Intel(R) Core(TM) i7 CPU and 6 GB memory. Our method can get a similar region under different interaction vertices in specific regions. Figure 6a and Figure 6b are the calculation results of tolerance region selection of this algorithm in a certain region of kitten model at two different interaction points, from which we can see the obtained regions are similar from different vertices in this region. Figure 6c and figure 6d are two different interactive points in the same region, and the region selection results are obtained by Region growing technique. Discussion: In this paper, we proposed a novel magic wand selection tool to interactive select surface of 3D model. The feature vector is constructed by extracting the HKS feature descriptor and means curvature of 3D model surface, which allows users to input the feature tolerance value for region selection and improves the self-interaction of users. Many experiments show that our algorithm has obvious advantages in speed and effectiveness. The interactive generation of region boundary is very useful for many applications including model segmentation. Conclusion: In consideration of a couple of requirements including user-friendliness and effectiveness in model region selection, we propose a novel magic wand selection tool to interactive selection surface of 3D models. First, we pre-compute the heat kernel feature and mean curvature of the surface, and then form the eigenvector of the model. Then we provide two ways for region selection. One is to select the region according to the feature of tolerance value. The other is to select the region that aligns with stroke automatically. Finally, we use the geometry optimization approach to improve the performance of the computing region con-tours. Extensive experimental results show that our algorithm is efficient and effective.

Introduction: Shape segmentation is a fundamental problem of computer graphics and geometric modeling. Although the existence segmentation algorithms of shapes have been widely studied in mathematics community, little progress has been made on how to compute them on polygonal surfaces interactively using geodesic loops. Method: We compute the geodesic distance fields with improved Fast March Method (FMM) proposed by Xin and Wang. We propose a new algorithm to compute geodesic loops over a triangulate surface and a new interactive shape segmentation manner on triangulate surface. Result: The average computation time on 50K vertices model is less than 0.08s. Discussion: In the future, we will use an accurate geodesic algorithm and parallel computing techniques to improve our algorithm to obtain better smooth geodesic loop. Conclusion: A large number of experimental results show that the algorithm proposed in this paper can effectively achieve high precision geodesic loop paths, and our method can also be used to interactive shape segmentation in real time.

The unbalanced assignment problem (UAP) aims to distribute a set of jobs to some workers. The cost of the jobs is different when they are distributed to different workers. The goal is: (1) minimizing the total cost of arranging jobs to workers; (2) making the distribution of jobs as even as possible among all the workers. We transform the UAP into a min-cost network flow problem with squared terms, and apply the belief propagation (BP) algorithm to deal with it. We prove that, when the min-cost network flow problem has a unique optimal solution, the BP algorithm converges to the optimal solution within [Formula: see text] iterations, where [Formula: see text] represents the number of vertices of the flow network, [Formula: see text] is the difference between value of the optimal solution and the second optimal solution and [Formula: see text] is the maximum value of the terms of the objective function. Next, we prove that BP converges to the optimal solution in [Formula: see text] operations, where [Formula: see text] represents the number of edges and [Formula: see text] is the tight upper bound of the slope of the terms of the objective function.

We calculate the neutral current jet production semi-inclusive deeply inelastic scattering process in this paper. Neutral current implies that interactions can be mediated by the photon, $Z^0$-boson and their interference. The initial electron is assumed to be polarized and then scattered off by a target particle with spin-1/2. Calculations are carried out up to twist-3 level in the quantum chromodynamics parton model by applying the collinear expansion formalism where multiple gluon scattering is taken into account and gauge links are obtained automatically. After obtaining the differential cross section, we introduce the definition of the intrinsic asymmetry. This quantity reveals the asymmetry in the distribution of the quark intrinsic transverse momentum. We find that these asymmetries can be expressed in terms of the transverse momentum dependent parton distribution functions and the electroweak couplings. As a result, our calculations provide a set of new quantities for analyzing the parton distribution functions and the electroweak couplings. It is helpful to understand the hadronic weak interactions and strong interactions in the deeply inelastic scattering process simultaneously., Comment: arXiv admin note: text overlap with arXiv:2004.01359

In recent years, the incidence of myopia has increased at an alarming rate among children and adolescents in China. The exploration of an effective prevention and control method for myopia is in urgent need. With the development of information technology in the past decade, artificial intelligence with the Internet of Things technology (AIoT) is characterized by strong computing power, advanced algorithm, continuous monitoring, and accurate prediction of long-term progression. Therefore, big data and artificial intelligence technology have the potential to be applied to data mining of myopia etiology and prediction of myopia occurrence and development. More recently, there has been a growing recognition that myopia study involving AIoT needs to undergo a rigorous evaluation to demonstrate robust results.

BACKGROUND Retinal vein occlusion (RVO) is the second common cause of blindness following diabetic retinopathy. Patients with RVO often develop macular edema and neovascular glaucoma, which may damage the visual function irreversibly. RVO includes macular retinal vein occlusion, central retinal vein occlusion, and branch retinal vein occlusion. OBJECTIVE Providing patients with an accurate diagnosis, followed by timely and effective treatment is very important for the prognosis of visual function. Therefore, in this paper, we use the Swin Transformer model with a label smoothing method to identify fundus images. METHODS First, 483 and 161 fundus images were used as the training set and the validation set, respectively, to train and regulate the model, whose accuracy reached 98.1%. Additional 161 fundus images were used as the test set to evaluate the model's performance. Next, the area under the receiver operating curve corresponding to macular retinal vein occlusion, central retinal vein occlusion, and branch retinal vein occlusion were obtained using the Swin Transformer model. Finally, we compared the results using the model trained by the deep convolutional neural network. RESULTS The values obtained using the Swin Transformer model for macular retinal vein occlusion, central retinal vein occlusion, and branch retinal vein occlusion were 0.9987, 0.9981, and 0.9974, respectively. The comparison results with other models indicated that the Swin Transformer model performed the best. The results of the study demonstrated that our method can automatically diagnose RVO and determine the type through fundus images, which has the potency to help in the early diagnosis of patients with RVO. CONCLUSIONS Our model can automatically diagnose RVO through fundus images, and its diagnostic accuracy is higher than that of MobileNetV2 and ResNet18. In addition, it can process data sets automatically and efficiently without manual assistance. We can not only diagnose RVO, but also accurately judge its specific type, which has an important clinical significance in real life.

A quantity of particular experimental interest is the forward-backward asymmetry in the angular distribution of positively and negatively charged fermions produced in Z0 decays. Measurements of this asymmetry can enable independent determinations of the neutral-current couplings of these fermions, i.e., the Z0 boson couplings for left- and right-handed fermions, respectively. Due to the quark confinement, however, it is difficult to determine the electroweak interactions of quarks, especially for light quarks. In the hadron production electron positron annihilation process, the parton model with factorization theorem gives a reliable approximate description. Quantities are thus expressed in terms of fragmentation functions in the annihilation process. In this paper, we consider the vector meson production in the inclusive electron positron annihilation process and calculate the forward-backward asymmetry in the hadronic level. Calculations are carried out by applying the collinear expansion in the parton model at leading order twist-4. We note here this process provides not only a tool for analyzing the hadronic weak interactions but also an opportunity for understanding the parton model of the strong interaction. In other words, the results can be used to test the electroweak and strong interactions simultaneously.

Accurate and quantitative investigation of the physical structure and fractal geometry of coal has important theoretical and practical significance for coal bed methane (CBM) development and the prevention of dynamic disasters such as coal and gas outbursts. This study investigates the pore structure and fractal characteristics of soft and hard coals using nitrogen and carbon dioxide (N2/CO2) adsorption. Coal samples from Pingdingshan Mine in Henan province of China were collected and pulverized to the required size (0.20–0.25 mm). N2/CO2 adsorption tests were performed to evaluate the specific surface area (SSA), pore size distribution (PSD), and pore volume (PV) using Braunuer-Emmett-Teller (BET), Barrett-Joyner-Halenda (BJH), and Density Functional Theory (DFT). The pore structure was characterized based on the theory of fractal dimensions. The results unveiled that the strength of coal has a significant influence on pore structure and fractal dimensions. There are significant differences in SSA and PV between both coals. The BJH-PV and BET-SSA obtained by N2-adsorption for soft coal are 0.029–0.032 cm3/g and 3.523–4.783 m2/g. While the values of PV and SSA obtained by CO2-adsorption are 0.037–0.039 cm3/g and 106.016–111.870 m2/g. Soft coal shows greater SSA and PV than hard coal, which is consistent with the adsorption capacity ($${V}_{\mathrm{L}}$$ V L ). The fractal dimensions of soft and hard coal are respectively different. The Ding coal exhibits larger D1 and smaller D2, and the reverse for the Wu coal seam is observed. The greater the value of D1 (complexity of pore surface) of soft coal is, the larger the pore surface roughness and gas adsorption capacity is. The results enable us to conclude that the characterization of pores and fractal dimensions of soft and hard coals is different, tending to different adsorption/desorption characteristics. In this regard, the results provide a reference for formulating corresponding coal and gas outburst prevention and control measures.

The problem of finding the maximum independent sets (or maximum cliques) of a given graph is fundamental in graph theory and is also one of the most important in terms of the application of graph theory. Let $A(n,d,w)$ be the size of the maximum independent set of $Q_{n}^{(d-1,w)}$, which is the induced subgraph of points of weight $w$ of the $d-1^{th}$-power of $n$-dimensional hypercubes. In order to further understand and study the dependent set of $Q_{n}^{(d-1,w)}$, we explore its clique number and the structure of the maximum clique. This paper obtains the clique number and the structure of the maximum clique of $Q_{n}^{(d-1,w)}$ for $5\leq d\leq 6$. Moreover, the characterizations for $A(n,d,w)=2$ and $3$ are also given.

Atomically dispersed oxide-on-metal inverse nanocatalysts provide a blueprint to amplify the strong oxide-metal interactions for heterocatalysis but remain a grand challenge in fabrication. Here we report a 2D inverse nanocatalyst, RuOx -on-Pd nanosheets, by in situ creating atomically dispersed RuOx /Pd interfaces densely on ultrathin Pd nanosheets via a one-pot synthesis. The product displays unexpected performance toward the oxygen reduction reaction (ORR) in alkaline medium, which represents 8.0- and 22.4-fold enhancement in mass activity compared to the state-of-the-art Pt/C and Pd/C catalysts, respectively, showcasing an excellent Pt-alternative cathode electrocatalyst for fuel cells and metal-air batteries. Density functional theory calculations validate that the RuOx /Pd interface can accumulate partial charge from the 2D Pd host and subtly change the adsorption configuration of O2 to facilitate the O-O bond cleavage. Meanwhile, the d-band center of Pd nanosubstrates is effectively downshifted, realizing weakened oxygen binding strength.

The angiography and color fundus images are of great assistance for the localization of central serous chorioretinopathy (CSCR) lesions. However, it brings much inconvenience to ophthalmologists because of these two modalities working independently in guiding laser surgery. Hence, a novel fundus image fusion method in non-subsampled contourlet transform (NSCT) domain, aiming to integrate the multi-modal CSCR information, is proposed. Specifically, the source images are initially decomposed into high-frequency and low-frequency components based on NSCT. Then, an improved deep learning-based method is employed for the fusion of low-frequency components, which helps to alleviate the tedious process of manually designing fusion rules and enhance the smoothness of the fused images. The fusion of high-frequency components based on pulse-coupled neural network (PCNN) is closely followed to facilitate the integration of detailed information. Finally, the fused images can be obtained by applying an inverse transform on the above fusion components. Qualitative and quantitative experiments demonstrate the proposed scheme is superior to the baseline methods of multi-scale transform (MST) in most cases, which not only implies its potential in multi-modal fundus image fusion, but also expands the research direction of MST-based fusion methods.

The fractional matching preclusion number of a graph is the minimum number of edges whose deletion results in the remaining graph that has no fractional perfect matchings. For many networks, their optimal fractional matching preclusion sets are precisely those edges incident with a single vertex. The probability that all failures concentrate around a vertex is often small. To overcome the shortcoming, we consider the concept of conditional fractional matching preclusion, in which isolated vertices are not permitted in fault networks. We establish the conditional fractional matching preclusion numbers and all possible minimum conditional fractional matching preclusion sets for n -dimensional torus networks with n ≥ 3 .

This study aimed to screen anaplasia-related genes that influence the progression of retinoblastoma (RB) and to identify immune cells associated with the poor prognosis.Differentially expressed genes (DEGs) between retina and RB samples were acquired from gene expression omnibus (GEO) database. Candidate hub genes were screened by taking intersections among the co-expressed genes, the hub nodes, and DEGs of the validation set. The hub genes were identified by receiver operating characteristic (ROC) and quantitative real-time PCR (qPCR). Immune infiltration levels of RB tissues were estimated using single-sample gene set enrichment analysis (ssGSEA). The functions of RB cells were detected by CCK8, EDU and flow cytometry assays.665 DEGs involved in the genesis and progression of RB were acquired from GEO database. 29 candidate hub genes were screened by examining 43 co-expressed genes and 63 hub nodes. 9 hub genes (CHEK1, EXO1, FANCI, GTSE1, MELK, MKI67, NCAPH, PRC1, and UBE2T) strongly related to the anaplastic grades were validated by ROC curve analysis (AUC0.8). Based on the ssGSEA scores, the immune infiltration levels of Th2 cells were positively associated with anaplastic grade. qPCR assay showed that 9 hub genes were upregulated in RB cells, and UBE2T expressed remarkably high. CCK 8, EDU, and flow cytometry assays revealed that UBE2T silencing inhibited the proliferation of RB cells and incited apoptosis.The increased infiltration of Th2 cells and upregulated expression of 9 hub genes predict a poor prognosis of RB. UBE2T can be a therapeutic target for RB treatment.

Hepatocellular carcinoma (HCC) is one of the dominating tumors causing death due to lack of timely discovery and valid treatment. Abnormal increase of Rac GTPase activating protein 1 (RACGAP1) has been verified to be an oncogene in plenty tumors. The profound mechanism of RACGAP1 was rarely reported in HCC. In this study, we explored the function and mechanism of RACGAP1 in HCC through multiple analysis and experiments. RACGAP1 expression was up-regulated in HCC samples and the high expression of RACGAP1 was an independent prognostic risk factor for HCC patients. Meanwhile, RACGAP1 promoted developments of HCC both in vitro and in vivo. We verified that RACGAP1 promoted proliferation of HCC via PI3K/AKT/CDK2 and PI3K/AKT/GSK3β/Cyclin D1 signaling pathway. RACGAP1 accelerated the invasion and metastasis of HCC via phosphorylation of GSK3β and nuclear translocation of β-catenin. Furthermore, by luciferase reporter assay and Chromatin immunoprecipitation (ChIP) assay, we confirmed Recombinant GA Binding Protein Transcription Factor Alpha (GABPA) regulated the transcription of RACGAP1. All these findings revealed that RACGAP1 promotes the progression of HCC through a novel mechanism, which might be a new therapeutic target for HCC patients.

Silver nanoparticles (AgNPs) in surface water are highly toxic to humans and difficult to remove due to their adsorption to humic acid (HA). In this study, laminarin (LA) was used as a coagulant aid in a coagulation-ultrafiltration (C-UF) system to improve AgNPs-HA removal efficiency. C-UF efficiency, membrane flux, and flocs properties were investigated to explore the AgNPs-HA removal mechanism and membrane fouling. Results showed that when poly aluminum chloride (PAC) was dosed with LA, AgNPs-HA removal was 10–15% higher than when using PAC alone. The C-UF system using only PAC improved the AgNPs-HA removal efficiency through increased coagulation but resulted in membrane fouling. LA application helped mitigate membrane fouling, and the highest normalized permeate flux and smallest resistance values (0.573 and 2.180 × 1010 m−1, respectively) were achieved when 0.1 mg/L of LA was applied with 5 mg/L of PAC. The alleviating mechanism was related to flocs with large sizes and small fractal dimension (Df) values, generating a cake layer with porous morphology. This cake layer was easily removed by flushing and backwashing, which resulted in minimal resistance and fouling of the UF membrane.

Purpose: Clonal architecture is fundamental for the understanding of cancer biology and therapy; however, multiregional sampling in advanced-stage cancers is not always applicable. This prospective clinical trial was to investigate whether paired tissue and circulating tumor DNA (ctDNA) could describe the clonal architecture of advanced non–small cell lung cancer (NSCLC) and its association with clinical outcome (NCT03059641). Patients and Methods: Paired tumor and plasma ctDNA samples were sequenced by target-capture deep sequencing of 1,021 genes. Clonal dominance analysis was performed on the basis of PyClone. Results: Overall, 300 treatment-naïve patients with stage IIIB–IV NSCLC were recruited from 14 centers. Of the 94 patients with available ctDNA data for EGFR clonal architecture analysis, 72 (76.6%) showed EGFR as the dominant clone. The median progression-free survival was longer for these patients than for the 22 patients whose EGFR was nondominant clone [11 vs. 10 months; HR, 0.46; 95% confidence interval (CI), 0.24–0.88; P = 0.02]. The difference was more significant if both tissue and ctDNA defined EGFR as dominant clone (n = 43) versus those not (n = 8; 11 vs. 6 months; HR, 0.13; 95% CI, 0.04–0.50; P = 0.003). Moreover, multivariate Cox proportional HR analysis demonstrated EGFR clonal architecture as an independent prognostic indicator of the efficacy of EGFR-tyrosine kinase inhibitors (TKIs). Conclusions: Paired tissue and ctDNA could be analyzed for clonal architecture in advanced cancer. EGFR mutations do not always make up a dominant clone in advanced NSCLC, which was associated with the efficacy of EGFR-TKIs in NSCLC.

Edge fault-tolerance of interconnection network is of significant important to the design and maintenance of multiprocessor systems. A connected graph G is maximally edge-connected (maximally-λ for short) if its edge-connectivity attains its minimum degree. G is super edge-connected (super-λ for short) if every minimum edge-cut isolates one vertex. The edge fault-tolerance of the maximally-λ (resp. super-λ) graph G with respect to the maximally-λ (resp. super-λ) property, denoted by m λ ( G ) (resp. S λ ( G ) ), is the maximum integer m for which G − S is still maximally-λ (resp. super-λ) for any edge subset S with | S | ≤ m . In this paper, we give upper and lower bounds on m λ ( G ) . Furthermore, we completely determine the exact values of m λ ( G ) and S λ ( G ) for vertex transitive graphs.

Meibomian glands dysfunction (MGD) is the main cause of dry eyes. Biological parameters of meibomian gland (MG) such as height, tortuosity and the degree of atrophy are closely related to its function. However, Thus, an effective quantitative diagnostic tool is needed for clinical diagnosis. Automatic quantification of MGs' morphological features could be a challenging task and play an important role in MGD diagnosis and classification. Our main objective is to develop an artificial intelligence (AI) system for evaluating MGs' morphology and explore the relationship between the morphological parameters and functions. We proposed a novel MGs extraction method based on convolutional neural network (CNN) with enhanced mini U-Net. A prospective study was conducted, 120 subjects were included and taken meibography. The training and validation sets encompassed 60 subjects; and the test set consisted of other 60 subjects with comprehensive examinations for ocular surface disease index questionnaire (OSDI), tear meniscus height (TMH), tear break-up time (TBUT), corneal fluorescein staining (CFS), lid margin score, and meibum expressibility score. The algorithm effectively extracted MGs from meibography even with this small training sample. As a result, while the intersection over union (IoU) achieved 0.9077, the repeatability was 100%. The processing time for each image was 100ms. Using this method, the investigators identified a significant and linear correlation between MG morphology and clinical parameters. This study provided a new method for quantification of MGs' morphological features obtained by meibography, which has advantages in reducing analysis time, improving diagnostic efficiency, and assisting ophthalmologists with limited clinical expertise.

In this study, a completely autotrophic nitrogen-removal over nitrite (CANON) process was started in a membrane bioreactor at ambient temperature, to which a static magnetic field (SMF) at a 20 ​mT intensity was applied to evaluate the enhancement of the CANON process by SMF. The results indicated that the SMF was capable of enhancing the nitrogen removal rate and shortening the start-up period of the CANON process. After running for about 8 months, the average nitrogen removal rate of the CANON process with SMF exposure was 324.8 ​± ​64.8 gN/m3/d, which was 30.4% higher than that of the control. Moreover, the SMF has the potential to protect the CANON process from being inhibited by low temperatures. Importantly, the SMF induced the synthesis and secretion of the extracellular polymeric substance (EPS) of the activated sludge and simultaneously reduced the zeta potential. This was conducive to the aggregation of the sludge material and the formation of an oxygen gradient in the sludge flocs, which promoted the coexistence of ammonium-oxidizing bacteria (AOB) and anaerobic ammonium-oxidizing bacteria (AnAOB). The high-throughput 16S rRNA gene sequence analysis confirmed that the abundances of the Nitrosomonas and Candidatus Brocadia genera, respectively the main AOB and AnAOB, were enhanced by SMF exposure.

In order to achieve an efficient collection of wave energy and stable power output, a two-float oscillating flapping-wing wave energy converter is proposed. Based on the hydraulic conversion system of the multi-chamber cylinder, a hydraulic conversion and merging system of the multi-chamber cylinder is created. The composition and working principle of the system, as well as the parameters of the acquisition mechanism, hydraulic conversion and merging system, are determined. AQWA is used to simulate the flapping-wing angular displacement response, and AMESim is used to build the simulation model of the acquisition mechanism, the hydraulic conversion and merging of multi-chamber cylinders, and the power conversion and energy storage system. The research results show that the system can work stably under level 3 and 4 sea conditions, and the input power of the battery is stable at about 46.5kW and 56.5kW, respectively. The rationality and feasibility of the two-float oscillating flapping-wing wave energy converter are verified by simulation.

The diagnosability is one of the most important measures of the reliability of networks. Consider the setting where there are large-scale failures that disconnect the network and result in many components. Then, the diagnosability is closely related to the number of components. In this paper, we define and study the $\boldsymbol{g}$-component diagnosability of network $\boldsymbol{G}$, which is denoted by $\boldsymbol{ct_g(G)}$ and has not been addressed before. $\boldsymbol{ct_g(G)}$ is the maximum number of nodes in the faulty node set $\boldsymbol{F}$ of $\boldsymbol{G}$ such that $\boldsymbol{G-F}$ has at least $\boldsymbol{g}$ components and diagnosis model can identify all nodes in $\boldsymbol{F}$. Under PMC and MM$^*$ diagnosis models, we show that, in the hypercube $\boldsymbol{Q_n\ (n\geq 7)}$, $\boldsymbol{ct_{g+1}(Q_n)=-(1/2)g^2+(n-3/2)g+n}$ when $\boldsymbol{g\leq n-1}$. Moreover, we determine the $\boldsymbol{(n+1)}$-component diagnosability $\boldsymbol{ct_{n+1}(Q_n)=n^2/2+n/2-2}$ for $\boldsymbol{n\geq 7}$.