At present， most accelerated Magnetic Resonance Imaging （MRI） reconstruction algorithms reconstruct undersampled amplitude images and use real-value convolution for feature extraction， without considering that the MRI data itself is complex， which limits the feature extraction ability of MRI complex data. In order to improve the feature extraction ability of single slice MRI complex data， and thus reconstruct single slice MRI images with clearer details， a Complex Convolution Dual-Domain Cascade Network （ComConDuDoCNet） was proposed. The original undersampled MRI data was used as input， and Residual Feature Aggregation （RFA） blocks were used to alternately extract the dual domain features of the MRI data， ultimately reconstructing the Magnetic Resonance （MR） images with clear texture details. Complex convolution was used as a feature extractor for each RFA block. Different domains were cascaded through Fourier transform or inverse transform， and data consistency layer was added to achieve data fidelity. A large number of experiments were conducted on publicly available knee joint dataset. The comparison results with the Dual-task Dual-domain Network （DDNet） under three different sampling masks with a sampling rate of 20% show that： under the two-dimensional Gaussian sampling mask， the proposed algorithm decreases Normalized Root Mean Square Error （NRMSE） by 13.6%， increases Peak Signal-to-Noise Ratio （PSNR） by 4.3%， and increases Structural SIMilarity （SSIM） by 0.8%； under the Poisson sampling mask， the proposed algorithm decreases NRMSE by 11.0%， increases PSNR by 3.5%， and increases SSIM by 0.1%； under the radial sampling mask， the proposed algorithm decreases NRMSE by 12.3%， increases PSNR by 3.8%， and increases SSIM by 0.2%. The experimental results show that ComConDuDoCNet， combined with complex convolution and dual-domain learning， can reconstruct MR images with clearer details and more realistic visual effects.

Concerning the problem that destruction of nodes or edges in coal transportation road network for emergencies has caused problems in blockage of coal transportation road networks, based on complex network theory, the network models constructed by original method and dual method were established, and their reliability were simulated by Matlab software. Firstly, basic characteristics of two networks were compared and analyzed, and then relative changes of network efficiency were proposed to identify key road segments in network. Based on this, a network reliability evaluation model was established, and three reliability evaluation indexes including network efficiency, maximum connected subgraph relative size and network dispersion were proposed to simulate network reliability under two destruction modes:random destruction and deliberate destruction. The experimental result shows that in deliberate destruction mode, when 10% of nodes fail, three reliability index values are 10%, 20%, and 20, respectively, while the index values in random destruction mode still maintain at a high level. Therefore, the coal transportation network is robust to random destruction and vulnerable to deliberate destruction. The protection of important nodes in network should be strengthened.

There are several problems that the System Dynamics (SD) model cannot express both random delay and conditional transitions between different states, and the Stochastic Petri-Net (SPN) itself still has the defect of insufficient computing ability. In order to solve the problems, firstly, the SPN was expanded and the Stochastic Function Petri-Net (SFPN) model was proposed. Secondly, combining SFPN with SD, the SFPN-SD model was put forward. Because the transits in SFPN could be used to accurately describe random delay, therefore, the first problems in SD model was solved. Because the conditions arcs in SFPN could be used to express the conditional transferring among places, as a result, the second problem in SD was solved. Finally, some state variables and state transition equations were appended in places and transitions of SPN, while these state variables and state transition equations were the different interpretations of level, auxiliary and rate variables as well as level and rate equations in SD model. The state transition equations could realize complicated computations, and thus the problem of insufficient computing ability in SPN was solved. The SFPN-SD model inherited all the features of the SD model, at the same time, all the features of SPN were incorporated into the SFPN-SD model. Compared with the SD model, the proposed SFPN-SD model has such advantages that system states and the meaning of their types as well as the process of state evolution become more clear. And the system's dynamic changes are driven by events in SFPN-SD, which it can describe autonomous dynamic stochastic evolution of complex system more realistically. The case studies show that, compared with the SD model, the proposed SFPN-SD model has stronger, more comprehensive abilities such as relevancy analysis description and simulation of complex system.

To get all the accurate solutions to Nonlinear Systems of Equations (NSE), the algorithm with global convergence was constructed for solving NSE based on the characteristics of Cellular Automata (CA). In the algorithm, the theoretical search space of NSE was divided into the discrete space, the discrete space was defined as the cellular space; each point in the discrete space was a cell in the cellular space, and each cell was a trial solution of NSE; a cellular state consisted of position and increment of position. The cellular space was divided into many nonempty subsets, and states evolution of all cells from one nonempty subset to another realized the search of the cellular space on the theoretical search space. During evolution process of all cells, each cells transition probability from one position to any another position could be simply calculated; each state of cells during evolution corresponded to a state of a finite Markov chain. The stability condition of a reducible stochastic matrix was used to prove the global convergence of the algorithm. The case study shows that the algorithm is efficient.

In view of that the traditional decision tree algorithm that cannot solve the mass data mining and the multi-value bias problem of ID3 algorithm, the paper designed and realized a parallel decision tree classification algorithm based on the MapReduce framework. This algorithm adopted attribute similarity as the choice standard to avoid the multi-value bias problem of ID3 algorithm, and used the MapReduce model to solve the mass data mining problems. According to the experiments on the Hadoop cluster set up by ordinary PCs, the decision tree algorithm based on MapReduce can deal with massive data classification. What's more, the algorithm has good expansibility while ensuring the classification accuracy and can get close to linear speedup rate.

In order to solve the problem that the domain partition of Zaike variable precision rough set can not overlap, an expansion was made on the domain of Zaike variable precision rough set based on multi-set, a multiple variable precision rough set model was put forward, and its corresponding definitions, theorems and properties were fully described, which included definitions of multiple domain and multiple variable precision approximate sets, proofs of their properties, and relations between multiple Zaike variable precision rough set and multiple variable precision rough set. These definitions, theorems and properties have not only differences but also relations between multiple variable precision rough set and Zaike variable precision rough set. Multiple variable precision rough set can fully describe overlap among knowledge particles, difference of significance among objects and polymorphism of objects, and can conveniently find associated knowledge from data saved in a relation database, having one-to-many and many-to-many dependency, and thought to have no relations.