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The Perron–Frobenius eigenvalue (PFE) is widely used as measurement of the number of loops in networks, but what exactly the relationship between the PFE and the number of loops in networks is has not been researched yet, is it strictly monotonically increasing? And what are the relationships between the PFE and other measurements of loops in networks? Such as the average loop degree of nodes, and the distribution of loop ranks. We make researches on these questions based on samples of ER random network, NW small-world network and BA scale-free network, and the results confirm that, both the number of loops in network and the average loop degree of nodes of all samples do increase with the increase of the PFE in general trend, but neither of them are strictly monotonically increasing, so the PFE is capable to be used as a rough estimative measurement of the number of loops in networks and the average loop degree of nodes. Furthermore, we find that a majority of the loop ranks of all samples obey Weibull distribution, of which the scale parameter A and the shape parameter B have approximate power-law relationships with the PFE of the samples.

We build a complex networks model of combat System-of-Systems (SoS) based on empirical data from a real war-game, this model is a combination of command & control (C2) subnetwork, sensors subnetwork, influencers subnetwork and logistical support subnetwork, each subnetwork has idiographic components and statistical characteristics. The C2 subnetwork is the core of whole combat SoS, it has a hierarchical structure with no modularity, of which robustness is strong enough to maintain normal operation after any two nodes is destroyed; the sensors subnetwork and influencers subnetwork are like sense organ and limbs of whole combat SoS, they are both flat modular networks of which degree distribution obey GEV distribution and power-law distribution respectively. The communication network is the combination of all subnetworks, it is an assortative Small-World network with core–periphery structure, the Intelligence & Communication Stations/Command Center integrated with C2 nodes in the first three level act as the hub nodes in communication network, and all the fourth-level C2 nodes, sensors, influencers and logistical support nodes have communication capability, they act as the periphery nodes in communication network, its degree distribution obeys exponential distribution in the beginning, Gaussian distribution in the middle, and power-law distribution in the end, and its path length obeys GEV distribution. The betweenness centrality distribution, closeness centrality distribution and eigenvector centrality are also been analyzed to measure the vulnerability of nodes.

Purpose: This study analyzes the effect, long-term survival rate, and complications about preserving the left colonic artery (LCAP) in rectal cancer surgery. Methods: Relevant articles were systematically retrieved from multiple electronic databases, for example, EMBASE, BioMed Central, PubMed, Web of Science, and Cochrane. The time for retrieving was from the establishment of the database to December 31, 2018. Evaluated endpoints were effect of LCAP on the curative effect of rectal neoplasms, such as operation time, the amount of bleeding during the operation, root lymph nodes positive number, and the related complications (anastomotic leakage, etc.), postoperative urinary retention, 5-year survival rate, and recurrence differences in rates. Results: Totally 12 studies were included in this review. The meta-analysis showed that LCAP has less operation time and lower anastomotic leakage incidence. Intraoperative bleeding, root lymph nodes, and other complications did not show any significant difference. Conclusions: LCAP in radical rectal cancer surgery ensures both the radical resection of the tumor and the safety of the operation. So it can provide a new approach to the management of blood vessels and lymph nodes.

To solve the problem of existing consensus algorithms converging to the same equilibrium point, a new consensus algorithm for unmanned aerial vehicle formation is proposed. By constructing virtual relative position errors, this algorithm's equilibrium point isn't determined by initial states and it can make all members approaching to ideal positions as well as consistent velocity. Based on algebraic graph theory, the topological conditions and parameter conditions required by algorithm convergence are derived. Simulation results verify the validity of this algorithm which is suitable for general design of unmanned aerial vehicle formation system.

The weapon-target assignment (WTA) problem, known as an NP-complete problem, aims at seeking a proper assignment of weapons to targets. The biobjective WTA (BOWTA) optimization model which maximizes the expected damage of the enemy and minimizes the cost of missiles is designed in this paper. A modified Pareto ant colony optimization (MPACO) algorithm is used to solve the BOWTA problem. In order to avoid defects in traditional optimization algorithms and obtain a set of Pareto solutions efficiently, MPACO algorithm based on new designed operators is proposed, including a dynamic heuristic information calculation approach, an improved movement probability rule, a dynamic evaporation rate strategy, a global updating rule of pheromone, and a boundary symmetric mutation strategy. In order to simulate real air combat, the pilot operation factor is introduced into the BOWTA model. Finally, we apply the MPACO algorithm and other algorithms to the model and compare the data. Simulation results show that the proposed algorithm is successfully applied in the field of WTA which improves the performance of the traditional P-ACO algorithm effectively and produces better solutions than the two well-known multiobjective optimization algorithms NSGA-II and SPEA-II.

Multiobjective weapon-target assignment is a type of NP-complete problem, and the reasonable assignment of weapons is beneficial to attack and defense. In order to simulate a real battlefield environment, we introduce a new objective—the value of fighter combat on the basis of the original two-objective model. The new three-objective model includes maximizing the expected damage of the enemy, minimizing the cost of missiles, and maximizing the value of fighter combat. To solve the problem with complex constraints, an improved nondominated sorting algorithm III is proposed in this paper. In the proposed algorithm, a series of reference points with good performances in convergence and distribution are continuously generated according to the current population to guide the evolution; otherwise, useless reference points are eliminated. Moreover, an online operator selection mechanism is incorporated into the NSGA-III framework to autonomously select the most suitable operator while solving the problem. Finally, the proposed algorithm is applied to a typical instance and compared with other algorithms to verify its feasibility and effectiveness. Simulation results show that the proposed algorithm is successfully applied to the multiobjective weapon-target assignment problem, which effectively improves the performance of the traditional NSGA-III and can produce better solutions than the two multiobjective optimization algorithms NSGA-II and MPACO.

For solving the problem of difficulty to select formation with uncertain information of target equipment in air combat condition, a method for formation optimization based on commanders' subjective recognition is proposed. First, combat power of lighter is calculated, which is the basis of evaluation for combat power of target via commanders' subjective recognition. Then the air combat formation is optimized by employing prospect theory and comprehensive fuzzy evaluation. Finally, an application example is set to illustrate the validity and usability of the method proposed.

In view of the difficult detection of infrared dim point target from complex backgrounds, a multiscale homogeneous feature (MHF) based multispectral image fusion detection method is proposed in this paper. Inspired by the local contrast measure (LCM), we extract two local statistical features from the perspective of the homogeneity of gray difference distribution to characterize local structure of the infrared point target. Based on these two local features, we obtain the MHF map that can effectively highlight the potential point targets and suppress the backgrounds simultaneously. For the pixel-size electronic noise (PSEN) and some similar local structures to the point target, the multispectral image fusion detection is a positive way to alleviate these interferences and promote the robustness of the dim point target detection. Experimental results on six real scenarios and synthetic scenarios demonstrate that the proposed method not only works more stably for different target sizes and brightness, but also can achieve superior detection performance compared with the state-of-art detection methods.