Ganoderma lucidum spore powder was used as raw material,  ethanol  with a volume fraction of  70%  as extractant.  We adopted a combination of enzymatic  hydrolysis and ultrasound assisted extraction method,  set different liquid-solid ratios,  ultrasound time,  enzymatic hydrolysis time,  and enzyme dosage  as  four factors for a one-way test and designed a response surface experiment to  determine the optimal extraction method and its influencing factors. The   Ganoderma triterpene were separated and purified by using macroporous resin chromatography. By optimizing the  separation and purification process, the optimal elution resin,   eluent volume fraction,  flow rate of the upper sample solution and the mass ratio of the upper sample solution were determined. The compositional differences of the total  Ganoderma triterpenes were analysed by high performance liquid chromatography (HPLC). Though the pre-experimental analysis, the results show that the enzyme + ultrasound assisted extraction is more efficient compared to the single extraction method. Ethanol is used as an extractant to extract triterpenoids from Ganoderma lucidum can enhance the purity of triterpenoids. Under optimal conditions, the  rapid and accurate determination of the triterpene content can be achieved, providing a theoretical basis for the separation and purification of Ganoderma triterpenes.

We considered a  class of tumor-immune model, discussed the existence  conditions  of their equilibrium points, and used characteristic equations to analyze the local kinetic stability of each equilibrium point,  proving that the model underwent Hopf bifurcation under the corresponding conditions. By calculating the first Lyapunov coefficient, it can be concluded that if the coefficient is not zero, the model undergoes Hopf bifurcation,  the bifurcation is supercritical if the coefficient is less than zero, and the bifurcation is subcritical if the coefficient is greater than zero. Finally, numerical simulations are used to validate the theoretical analysis results.

Aiming at the complexity and diversity of current network intrusion, the traditional model was insufficient to extract traffic characteristics, and had low accuracy, we proposed an intrusion detection method based on CR-BiGRU hybrid model improved by merging residual network. Firstly, the dataset was normalized and one-hot encoding treatment in the model. Secondly, the convolutional neural network based on the residual network was used to extract the spatial features. Finally,   the bidirectional gated neural network was used to extract the temporal features,  complete the training of the model and realize the intrusion detection of the abnormal network. In order to illustrate the applicability of the model, comparative analysis experiments were conducted based on NSL-KDD and UNSW-NB15 datasets. The results show that the accuracy of the method based on the above datasets is 99.40% and 83.79% respectively, which is obviously superior to the classical network intrusion detection algorithm, and can effectively improve the accuracy of network intrusion detection, so as to  better ensure the  communication security of network data.

We studied  the antioxidant active components and mechanism of  dandelion based on  high performance liquid chromatograph (HPLC) method and network pharmacology method.   The effective components of Chinese herbal medicine dandelion were extracted by  organic reagents,  such as petroleum ether,  ethyl acetate,  dichloromethane and n-butanol,  and their antioxidant effects were studied. Multiple online databases of network pharmacology were used to obtain  common targets of dandelion antioxidant construct PPI network,  and conduct GO enrichment analysis and KEGG signal pathway enrichment analysis. The results show that the  extracts of each phase of dandelion have a certain scavenging ability to hydroxy radical (.OH),  superoxide anion radical (O^2-.) and 1,1-diphenyl-2-picrylhydrazyl radical (DPPH.),  the ethyl acetate phase extract of dandelion and the dichloromethane phase extract of dandelion have better scavenging effects,  and the main antioxidant active components are isorhamnetin and oleanolic acid. There are 137 dandelion antioxidant targets screened from the online database. The common targets are mainly concentrated on membrane rafts,  which are resistant to the response of cells to inorganic substances,  nitrogen compounds,  and nutrient levels oxidation. The common targets are closely related to cancer signal pathway,  NF-kappa B signal pathway,  and PPAR signal pathway. 

Aiming at the problem that the traditional causality extraction in natural language processing was mainly based  on  pattern matching methods
 or machine learning algorithms, and accuracy of the results was low, and only explicit causality with causal cue words could be extracted, we proposed an algorithm BERT-GCN using large-scale pretraining model combined with graph convolutional neural network. Firstly,  we used BERT （bidirectional encoder representation from transformers） to encode the corpus and generate word vectors. Secondly,  we put the generated word vectors into the graph convolutional neural network for training. Finally, we put them into the Softmax layer to complete the extraction of causality. The experimental results show that  the model obtains good results on the SEDR-CE dataset, and the effect of implicit causality is also good.

Aiming at the  characteristics of  subtle, uneven, imperceptible inter-class differences between classes and real-world data distribution in  fine-grained image classification, we proposed a fine-grained image classification model based on attention mechanism. Firstly, the preliminary feature extraction of the image was carried out  by introducing the fusion of a two-way channel attention and residual network. Secondly,  the multi-head self-attention mechanism was applied to extract fine-grained relationships between  deep feature data. Thirdly, the training of loss function measurement system was designed by combining cross entropy loss and center loss. The experimental results show that the test accuracy of the model on two standard datasets 102 Category Flower and CUB200-2011 is  94.42% and 89.43%, respectively. Compared with other mainstream classification models, the classification effect is better.

Mesenchymal stem cell exosomes (MSC-Exos) are a class of nanoscale vesicles with great potential in experimental research  and clinical applications. They contain a variety of biomolecules,  including miRNA,  mRNA,  proteins and lipids,  and have the function of  mediating  cell signaling and participating in regulation of receptor cells. Based on the important role of  MSC-Exos, we review the significant effects of  MSC-Exos in promoting tissue repair,  immune regulation and neuroprotection from the research progress and clinical applications,   especially in the treatment of autoimmune diseases,  neurodegenerative diseases,  cardiovascular diseases and tumors. We analyze a series of unsolved problems and application popularization challenges in its clinical application,  including elucidation of mechanism of action,  separation,  extraction and purification technology,  formulation of standardized production rules,  determination of dosage and administration route,  enhancement of stability,  and reduction of immunogenicity. This provides a basis for addressing these limitations to achieve widespread clinical application of MSC-Exos.

We discuss  the existence of positive 2π-periodic solutions of the second-order ordinary differential equation with nonlinear derivative term by using positive operator perturbation method and fixed point index theory in cones. Under certain inequality conditions of the 
nonlinear term f(t,x,y), we obtain the existence of positive 2π-periodic solutions of the equation.

Aiming at the problems of the limitation of obtaining global features in image recognition and the difficulty in improving recognition accuracy, we proposed  an image recognition method based on the lightweight model of random augmentation Swin-Tiny Transformer.  The method combined the random data augmentation based enhancement (RDABE) algorithm to enhance image features in the preprocessing stage, and adopted the Transformer’s self-attention mechanism to obtain more comprehensive 
high-level visual semantic information. By optimizing the Swin-Tiny Transformer model and fine-tuning the parameters on a maize disease dataset, the applicability of the algorithm was verified on maize diseases in the agricultural field, and more accurate disease detection was achieved. The experimental results show that the lightweight Swin-Tiny+RDABE model based on stochastic 
enhancement has an accuracy of 93.586 7% for maize disease image recognition. The experimental results compared with the excellent performance lightweight Transformer and convolutional neural network (CNN) series models with consistent parameter weights show that  the accuracy of the improved model is higher than that of the  Swin-Tiny Transformer, Deit3_Small, Vit Small, 
Mobilenet_V3_Small, ShufflenetV2 and Efficientnet_B1_Pruned models by 1.187 7% to 4.988 1%, and can converge rapidly.

 The studies of reactions involving water radical cations and their cluster ion ((H₂O)⁺_n)  can  better understand the mechanisms of certain natural processes,  such as proton transfer in aqueous solutions,  the formation of hydrogen bonds,  the destruction of bio-molecules such as DNA,  and the discovery of novel gas phase reactions and products. In addition,  the potential of water radical cations in  radio-biology have broad application prospects and its use as a primary reactive ion have attracted much attention for efficient selective  chemical ionization as well as improving the analytical sensitivity. At present, there are many studies on the bonding properties and  structure  of protonated water clusters and hydrated electrons, but there are few studies on the isolation and physicochemical properties of (H₂O)⁺_n due to  their ultra-high reaction activity and extremely short lifetime. Since significant progress has been made in the  technology  of mass spectroscopy,  molecular spectrometry  and high-precision  theoretical calculation of quantum chemistry, we review the current knowledge of    (H₂O)⁺_n, including  the formation  methods  and generation mechanisms,  structural theoretical simulation and experimental verification,   chemical property analysis,  and their application research.

We discussed a class of Schnakenberg models with homogeneous Neumann boundary conditions in view of the periodic oscillation phenomenon in biochemical reactions. By using the  methods of Hopf bifurcating theory, center manifold theory, normal form method and perturbation theory, we gave  the existence, stability and Turing instability of the Hopf bifurcating periodic solutions of the reaction-diffusion Schnakenberg system.

The purpose of mobile Internet information accessibility (MIIA) was to ensure that mobile application content was equally accessible, convenient, and barrier-free for all users, including those with visual impairments.  We systematically review the latest research progress in the field of mobile Internet information accessibility, focusing on the analysis and summary of research achievements in  semantic representation and understanding of mobile GUI, accessibility detection and layout repair. The analysis shows that from traditional heuristic rule methods to deep learning-driven automated tools, related technologies have gradually improved detection accuracy and adaptability, while also revealing challenges in addressing complex dynamic interactions and diverse user needs. We have provided an outlook on  future research directions.  MIIA technologies have significantly improved  the digital experience for visually impaired users, but they still need continuous innovation and optimization  to achieve a truly inclusive digital society.

We constructed a three-stage representation learning model by combining convolutional neural network and transformer encoder with meta-learning as the core idea. In order to express the interaction between  entities and task relations in the reference set,  we used convolutional neural network to obtain relation-meta, applied the transformer encoder to enhance the entity representation in query set, and  designed a processor for calculating matching score of incomplete triples to  solve the problem of few-shot knowledge graph completion, i.e., the phenomenon that the large-scale knowledge graph was sparse, and the number of entity pairs corresponding to the long-tail relations with low frequency was large. The experimental results on the NELL-One and Wiki-One datasets show that the proposed model performs well  in predicting head and tail entities corresponding to long-tail relations in large-scale knowledge graphs, and can achieve efficient feature representation generation and missing entity completion for entities and relations in knowledge graphs.

Firstly, we established a class of SEI₁I₂QR infectious disease models that included  transmission mode of asymptomatic infected individuals. Secondly, by using the next generation matrix method, we calculated the basic reproduction number of the model, performed the dynamic analysis of the model, and gave the threshold conditions for the extinction and outbreak of infectious disease. Finally, combined with  epidemic data, the sensitivity of the model parameters were analyzed through numerical simulations.

Aiming at the problems of high input dimensionality and long training time in traditional game intelligent  algorithm models, we  proposed a novel deep reinforcement learning game intelligent  guidance algorithm that integrated state information transformation and reward function shaping techniques. Firstly, using  the interface provided by the Unity engine to directly read game backend  information effectively compressed  the dimensionality of the state space and reduced the amount of input data. Secondly, by finely designing  the reward mechanism, the convergence process of the model was accelerated. Finally, we conducted comparative experiments between the proposed algorithm model and existing methods  from both subjective qualitative and objective quantitative perspectives. The experimental results show that this algorithm not only significantly improves the training efficiency of the model,  but also markedly enhances the performance of the  agent.

With the development of deep learning technology,  the number of parameters in automatic speech recognition task  models was becoming  increasingly  large, which gradually increased  the computing overhead, storage requirements and power consumption of the models, and it was difficult to deploy on resource-constrained devices. Therefore, it was of great  value to compress the automatic speech recognition models based on deep learning to reduce the size of the modes while maintaining the original performance as much as possible. Aiming at the above problems,  a comprehensive survey was conducted on  the main works in this field in recent years, which was summarized as several methods, including knowledge distillation, model quantization, low-rank decomposition, network pruning, parameter sharing and combination models, and  conducted a systematic review  to  provide alternative solutions for the deployment of models on resource-constrained devices.

We consider a variant of the classic problem of  the traveling salesman problem (TSP) in combinatorial optimization problem: 
 the close enough traveling salesman problem (CETSP).  Firstly, we comprehensively introduce the history, solving methods, and algorithms for both TSP and CETSP, including exact algorithms (such as branch and bound method, linear programming) and heuristic algorithms (such as particle swarm optimization, greedy algorithms, etc.). The TSP requires finding the shortest path to visit each city  once and return to the starting point given a list of cities and distances. CETSP is a generalization of TSP, allowing the visiting point for each target to be chosen from within a specified neighborhood, rather than  exact location. It is  suitable for practical applications that can  tolerate errors, such as logistics distribution, intelligent transportation, and wireless sensor networks, etc. CETSP has higher flexibility and adaptability, which can significantly reduce computational resources and time consumption, particularly for large-scale problems with greater advantages. Secondly, we introduce  the potential  of CETSP in practical applications, especially in logistics, industrial manufacturing, traffic planning, information and communication, offering effective solutions for improving efficiency, reducing costs, and promoting intelligent decision-making. Finally, we have identified some future research directions for CETSP.

Aiming at the problem of effectively protecting user privacy data,  we proposed a privacy-preserving logistic regression training scheme based on two-party secure computation  to complete the  joint modeling work of multiple data parties.  Firstly, the scheme  optimized the  generation process of the multiplicative triplet to reduce the time required in  the offline phase. Secondly, we replaced  the activation functions that were difficult to calculate in secure multi-party computation with approximate functions. 
Finally, we vectorized the proposed protocols  and accelerated the local matrix computation by using  CUDA (compute unified device architecture).  The experimental results of using different datasets to test the privacy-preserving logistic regression  performance in both local and wide area networks show that the scheme can enable the model to converge in a  short time and  increase the possibility of solving privacy-preserving machine learning related problems in real world.

The author considered a class of delayed predator-prey model with fear effect. Firstly, by using the characteristic equation and Lyapunov-LaSalle invariance principle, the global asymptotic stability of the boundary equilibrium was proved when R(τ)≤1. Secondly, by using the Hopf bifurcation theory of delay differential equation, the author discussed the stability of the coexistence equilibrium point and the existence of the global Hopf bifurcation when R(τ)>1, and obtained the results that fear effect and delay affected the stability of the system. Finally, the correctness of the theoretical results was verified by numerical simulations.

Aiming at the shortcomings of existing methods in the image segmentation performance of small and medium-sized organs in the abdomen, we proposed  a network model based on local and global parallel coding  for multi-organ image segmentation in the abdomen. Firstly, a local coding branch was designed to extract multi-scale feature information. Secondly, the global feature coding branch adopted the  block Transformer, which not only captured the global long distance dependency information but also reduced the computation amount through the combination of intra-block Transformer and inter-block Transformer. Thirdly, a feature fusion module was designed to fuse the context information from two coding branches. Finally, the decoding module was designed to realize the interaction between global information and local context information, so as to better compensate for the information 
loss in the decoding stage. Experiments were conducted on the Synapse multi-organ CT dataset, compared with the current nine advanced methods, the average Dice similarity  coefficient  (DSC) and Hausdorff distance (HD) indicators achieve the best performance, with 83.10% and 17.80 mm, respectively.

Aiming at  the blurring problem of remote sensing images, we designed an image restoration algorithm based on non-subsampled shearlet  transformation and sparse prior. Firstly, the image recovery model was created by setting the sparse a priori condition of remote sensing image under non-subsampled shearlet decomposition of the high-frequency image. Secondly, the model was solved by using the alternating direction multiplier method. Thirdly, the high-frequency image was restricted by the soft thresholding method, and the guided filtering was conducted in the low-frequency image to maintain the detailed information of the image as much as possible. Finally, the high-frequency image and the low-frequency image were reconstructed, the  
 reconstructed image was subjected to deep denoising by  using  convolutional neural networks, ultimately restoring a clear image. The deblurring algorithm was compared with H-PNP, GSR, and L2TV algorithms through experiments. The experimental results show that the algorithm can effectively remove  blurring and noise in remote sensing images, preserve the edge details of the image, and  the objective evaluation indexes are higher than the other three comparative experimental algorithms.

Firstly, based on the Black-Scholes stock price model,  the neural stochastic differential equation (NSDE) model was established by parameterizing the asset return rate and volatility as a drift network and a diffusion network, respectively. Secondly, in the empirical analysis, the underlying asset as a single stock option was used as the research object, and real stock data was used for  the network training  and testing. The experimental results show that the NSDE model can overcome the defects of the constant assumption of the Black-Scholes model. Finally, for the case where the price of the underlying asset of the option was unobservable, we  proposed that the price of any target option and the price of a known option could be constrained within the Wasserstein distance of their risk-neutral equivalent martingale measure, and theoretically  proved the method.

Aiming at the problems of overfitting and low classification accuracy in brain tumor magnetic resonance image classification, we proposed a brain tumor classification method based on an improved EfficientNetV2 network. The method  introduced the coordinate attention mechanism in the EfficientNetV2 network, which simultaneously obtained the feature information of brain tumor from both vertical and horizontal directions and accurately identified the lesion features of brain tumor. It helped the model to locate and identify the lesion area information more comprehensively and accurately, and effectively suppressed the influence of background information on the detection results, so that the model had higher classification accuracy. The problem of low classification accuracy caused by  insufficient acquisition of feature information was solved. In order to further improve the classification accuracy, the Hard-Swish activation function was introduced, which could not only improve the computational speed of the brain tumor classification network model, but also effectively improve the classification accuracy. Meanwhile, the improved model was equipped with Dropout layer and normalization layer, which could better suppress the occurrence of overfitting, accelerate the convergence speed of the model, improve the robustness of the model, and significantly improve the classification accuracy. The experimental results show that the improved model obtains classification accuracy of 98.4% in the validation set, and the effectiveness of the improved model in brain tumor classification task is verified by comparison experiments and ablation experiments.

Aiming at  the problems of blurred details, large computer resource occupation, and slow image processing for the existing image deblurring algorithms, we proposd a lightweight image blind deblurring network. Firstly, the main framework of the network used a multi-scale architecture to input images of different resolutions into the network, and gradually optimized the datails through cyclic processing.  Secondly, the asymmetric structure was designed to enhance the feature extraction ability of the encoder and the feature fusion ability of decoder. In the encoder, the mixed multi-scale convolutional layer and residual pyramid module were proposed to enhance feature extraction and  reduce the number of network parameters. In the decoder stage, deep semantics were introduced  by using jump linkage, and the multi-scale joint structure  loss function was proposed for optimization. Finally, we used two evaluation indicators to compare the performance of the method with the other classical methods on two widely used 
 GoPro and Kohler datasets. The experimental results show that the effect of the network  is better than that of the traditional methods and other classical deep learning mehtods. It not only improves the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM), but also shortens the processing time.

Aiming at the problem that the connected temporal classification model needed to have output independence assumption, and there was strong dependence on language model and long training period, we proposed  a speech recognition method based on connected temporal classification model. Firstly, based on the framework of traditional acoustic model, spectrogram feature extraction network based on attention mechanism was trained by using prior knowledge, which effectively improved the discrimination and robustness of speech features. Secondly, the spectrogram feature extraction network was spliced in the 
front of the connected temporal  classification model, and the number of layers of the recurrent neural network in the model was reduced for retraining. The test analysis results show that the improved model shortens the training time, and effectively improves the  accuracy of speech recognition.

With the rapid depletion of fossil fuels and increasing pollution,  the development and utilization  of clean energy are becoming increasingly important. Photocatalytic technology that  converts solar energy into clean hydrogen energy  is  an effective solution. It is necessary to solve the contradiction between  the bandgap of photocatalysts and the intensity of sunlight  due to limitations in water splitting electrode potential. Therefore,  it is highly significant to develop and utilize photocatalysts with visible light  response capability. We review  the development and principles of photocatalysts,  discuss their immense potential for advancement, and introduce the most  common photocatalysts and  current research progress.

We considered the coexistence solution problem of a class of Lotka-Volterra competitive systems with nonlinear cross-diffusion under homogeneous Dirichlet boundary conditions. Firstly, the stability of trivial solutions and semi-trivial solutions of the problem was analyzed by using spectral theory of linear operators. Secondly,  sufficient conditions for the existence of coexistence solutions of the problem were given by using the fixed point index theory on positive cone.

Aiming at the problem of  static resource allocation of the Storm platform, we proposed a distributed adaptive elastic resource allocation strategy,  which could  optimally meet the resource requirements of applications. Based on this strategy, combined with the resource allocation mechanism, application programming interface and user interface parameters of Storm, an elastic resource allocation component deployed in Storm was implemented to support adaptive and dynamic adjustment of application resources. The experimental results show that on the real stream data set, compared with the middle-value dynamic resource allocation strategy and the static resource allocation strategy of Storm, this distributed optimal strategy has advantages in throughput, loss rate and resource utilization. Meanwhile, this adaptive elastic resource allocation component can well interact with the Storm system, providing a reference solution for the development of other elastic resource scheduling components.

Aiming at the problem of  the navigational challenges for visually impaired users on diverse webpages, we proposed a method for automatically identifying navigation bars to improve  webpage accessibility. Firstly, by designing heuristic rules, elements within the navigation bars were  autonomously extracted based on the ordered element arrangement within the navigation bar, as well as rules such as hyperlinks and succinct textual content within sub-elements. Secondly, a decision tree binary classification algorithm was used to categorize elements with pronounced feature disparities in the navigation bars. Finally, the identified navigation bar elements were subject to the injection of Landmark attributes. In experimental evaluations of  100 websites, the method successfully identified  92.6% of navigation bar elements, and the infusion of Landmark attributes significantly improves website accessibility, thereby ameliorating the user experience for visually impaired individuals.

By applying mathematics induction and combinatorial analysis, we gave D(2)-vertex-distinguishing total colorings of cactus graphs G_T with maximum degree of 3, and then obtained χ_2vt(G_T)≤6. The result shows that D(β)-VDTC conjecture holds for cactus graphs with maximum degree of 3.

Aiming at the problems of the complicated underwater image imaging environment resulted in the subsequent image analysis often being affected by color bias and other factors, we proposed a deep convolutional neural network image restoration method based on multi-scale features and triple attention multimodal fusion. Firstly, the deep convolutional neural network introduced the image multi-scale transformation feature on the basis of extracting the image spatial feature. Secondly, by using channel attention, supervised attention and non-local attention, the scale correlation and feature correlation of image features were mined. Finally, by designing a multimodal feature fusion mechanism, the above two types of features could be effectively fused. The proposed method was tested on the open underwater image test set and compared with the current mainstream methods. The results show that this method is superior to the comparison method in quantitative comparison such as peak signal-to-noise ratio and structural similarity, as well as qualitative comparison such as color and details.

By using the Schauder fixed point theorem and topological degree theory, the author studies the existence of positive solutions of Neumann boundary value problems for second order ordinary differential systems with variable coefficients, where f,g: [0,1]×R→R are continuous functions, and f(x,0)<0, g(x,0)<0; a,b∈C([0,1],[0,∞)) are not always 0 on any subinterval of [0,1]. The result shows that under suitable conditions, there exists λ₀>0 such that the problem has at least one positive solution for 0<λ<λ₀.

Based on the properties of the matrix structure, we used the block matrix techniques to give the specific form for the Moore-Penrose generalized inverse of the adjacency matrix of caterpillar trees with any number of vertices and any diameter length, which provided theoretical support for further study of the algebraic properties of caterpillar trees.

Aiming at the problem of insufficient feature extraction resulting in low classification accuracy of the traditional encrypted traffic classification model, we  proposd an encrypted traffic classification model based on an improved convolutional neural network combined with Transformer by using deep learning techniques.  In order to improve the classification accuracy, firstly, we cut and filled the dataset,  and completed standardization processing. Secondly, the multi-head attention mechanism in the Transformer network model was used to capture long-distance feature dependencies, and the convolutional neural network was used to extract local features. Finally, the Inception module was added to achieve multi-dimensional feature extraction and feature fusion, and the model training and encrypted traffic classification were completed. The experimental verification was conducted on the 
ISCX VPN-non-VPN 2016 public dataset, the experimental results show that the classification accuracy of the proposed  model reaches 98.5%, with the precision rate, recall rate and F₁ value  all exceeding  98.2%, which show better classification effect compared with other models.

By using T-weak continuous operator method and classical Galerkin technique, we discussed the initial boundary value problem of a class of incompressible magneto-micropolar fluid equations in a two-dimensional bounded smooth region, and obtained the existence and uniqueness theorems of the global weak solutions for the problem,   further improving the regularity of the weak solutions.

Aiming at the high-dimensional “big p small n” problem where the number of genes in biomics data (denoted as p) was far more than the number of samples (denoted as n), we proposd a graph attention network GATOr with local and global attention mechanisms. Firstly, the model used Pearson correlation coefficient to calculate the correlation between features on the omic data, and constructed a single sample network of the omic data. Secondly, we proposed a graph attention network which combined local and global attention mechanisms to learn graph-based omics feature representation from a single-sample network, thereby transforming the high-dimensional characteristics of the omics data into low-dimensional representations. The experimental results show that compared with other traditional classification algorithms, GATOr achieves better performance in classification task accuracy and other indexes.

By using the maximum likelihood estimation method, we considered the parameter estimation of a class of nonlinear stochastic differential equations driven by Lévy process. Firstly, the unbiasedness, the asymptotic consistency and the asymptotic normality of the estimator as T→∞ were discussed under time-continuous observations. Secondly, the continuous martingale part was approximated by a threshold method, and the unbiasedness and asymptotic normality of the estimator as n→∞ were obtained under the condition of high-frequency discrete observations and finite activity. Finally, the unbiasedness and asymptotic normality of estimator were verified by numerical simulation results.

Aiming at the problems of non-uniform experimental platforms and heterogeneous datasets faced in the field of vulnerability dete
ction, we  studied  the application of word vector models in C/C++ function vulnerability detection. Five word vector models were used for the knowledge representation of the abstract syntax tree structure generated by the source code, and six neural network models were used for vulnerability detection. The experimental results show that function-level code has shallow semantic relationships and tight connections within code blocks.

We used the Faedo-Galerkin method to investigate the three-dimensional magnetofluid equations with nonlinear damping terms and  delay terms on a bounded domain  and solved the problem of well-posedness of the solutions. Firstly, the existence of strong solutions was proven when α≥16/5. Secondly, the uniqueness of strong solutions was proven by using the Gagliardo-Niernberg inequality.

Inspired by attention mechanism and transductive learning method, we proposed a node classification algorithm based on weighted meta-learning. Firstly, Euclidean distance was used to calculate the difference of data distribution between subtasks in meta-learning. Secondly, adjacency matrices of subgraph was used  to calculate and capture structural difference of data points  between subtasks. Finally, the captured information above between subtasks were converted into weights  to weight the process of updating the  meta-learner in the meta-training procedure, and  an optimized meta-learning model was constructed to solve the problem that the loss of all meta-training subtasks in meta-training procedure of classical meta-learning algorithms was equal-weight to update the parameters of meta-learners. The experimental results of this algorithm on Citeseer and Cora datasets are superior to other classical algorithms, which demonstrates the effectiveness of the algorithm on few-shot node classification task.