Censoring mechanisms are widely used in various life tests, such as medicine, engineering, biology, etc., as they save (overall) test time and cost. In this context, we consider the problem of estimating the unknown xgamma parameter and some survival characteristics, such as reliability and failure rate functions in the presence of adaptive type-II progressive hybrid censored data. For this purpose, the maximum likelihood and Bayesian inferential approaches are used. Using the observed Fisher information under s-normal approximation, different asymptotic confidence intervals for any function of the unknown parameter were constructed. Using the gamma flexible prior, Bayes estimators against the squared-error loss were developed. Two procedures of Bayesian approximations—Lindley’s approximation and Metropolis–Hastings algorithm—were used to carry out the Bayes estimates and to construct the associated credible intervals. An extensive simulation study was implemented to compare the performance of the different methods. To validate the proposed methodologies of inference—two practical studies using datasets that form engineering and chemical fields are discussed. Full article

Objective: 1. Interpretation of the variations of solute medicine amount in blood vessels and TAF concentration with respect to the flow rates of injected drugs into liver and heart. 2. Description of the alteration of tumor cell density versus the time and radius variations. Methodology: Step 1. Compartmental analysis is adopted for the concentration of chemotaxis caused by injected substances $L$ and $H$ based on the assumption: two different medicines $I_1$ and $I_2$ are injected into heart and liver to recover the functions of each organ, respectively, without any side effects. Step 2. A partial differential equation is derived for the growth of TAF considering the diffusion of TAF and the rate of decay of TAF according to the disturbance of medicine $M$ in blood vessels. Step 3. A partial differential equation is derived for the motion of tumor cells in the lights of random motility and chemotaxis in response to TAF gradients. Step 4. Exact solutions are obtained for the concentration of chemotaxis caused by injected substances $L$ and $H$ under the assumption that the loss of mass is proportional to mass itself. Step 5. Exact solution is obtained for the partial differential equation describing the growth of TAF using the separation of variables. Step 6. A finite volume approach is executed to search approximated solutions due to the complexity of the partial differential equation describing the motion of tumor cells. Results: 1. The concentration of medicine ($M$) decreases as the ratio of flow rate from heart into vessel to flow rate from liver into heart ($\frac{k_1}{k_2})$ increases. 2. TAF concentration increases with the growth of the value of ratio $\frac{k_1}{k_2}$ and TAF shows the smallest concentration when the flow rate of each injected medicine is similar. 3. Tumor cells react highly sensitive as soon as medicine supplies and tumor cell’s density is decreased drastically at the moment of medicine injection. 4. Tumor cell density decreases exponentially at an early stage and the density decrease is developed in a fluctuating manner along the radius. Conclusions: 1. The presented mathematical approach has the potential for the profound analysis of the variations of solute medicine amount in blood vessels, TAF concentration, and the alteration of tumor cell density according to the functional recoveries of liver and heart. 2. The mathematical approach may be applicable in the investigation of tumor cell’s behavior on the basis of complex interaction among five represented organs: kidney, liver, heart, spleen, and lung. A mathematical approach is developed to describe the variation of a solid tumor cell density in response to drug supply. The investigation is progressed based on the assumption that two different medicines, $I_1$ and $I_2,$ are injected into heart and liver with flow rates $k_1$ and $k_2$ to recover the functions of each organ, respectively. A medicine function system for the reactions of tumor angiogenic factors (TAF) to medicine injection is obtained using a compartmental analysis. The mathematical governing equations for tumor cells motion are derived taking into account random motility and chemotaxis in response to TAF gradients and a finite volume method with time-changing is adopted to obtain numerical solutions due to the complexity of the governing equations. The variation of the flow rates $k_1$ and $k_2$ exerts profound influences on the concentration of medicine, and similar flow rate of $k_1$ and $k_2$ produces the greatest amount of medicine in blood vessels and suppresses strong inhibition in TAF movement. Tumor cells react very sensitively to drug injection and the tumor cell density decreases to less than 20% at an early stage of administration. However, the density of tumor cell diminishes slowly after the early stage of sudden change and the duration for complete therapy of tumor cells requires a long time. Full article

As a special class of non-negative matrix factorization, symmetric non-negative matrix factorization (SymNMF) has been widely used in the machine learning field to mine the hidden non-linear structure of data. Due to the non-negative constraint and non-convexity of SymNMF, the efficiency of existing methods is generally unsatisfactory. To tackle this issue, we propose a two-phase algorithm to solve the SymNMF problem efficiently. In the first phase, we drop the non-negative constraint of SymNMF and propose a new model with penalty terms, in order to control the negative component of the factor. Unlike previous methods, the factor sequence in this phase is not required to be non-negative, allowing fast unconstrained optimization algorithms, such as the conjugate gradient method, to be used. In the second phase, we revisit the SymNMF problem, taking the non-negative part of the solution in the first phase as the initial point. To achieve faster convergence, we propose an interpolation projected gradient (IPG) method for SymNMF, which is much more efficient than the classical projected gradient method. Our two-phase algorithm is easy to implement, with convergence guaranteed for both phases. Numerical experiments show that our algorithm performs better than others on synthetic data and unsupervised clustering tasks. Full article

For non-linear systems (NLSs), the state estimation problem is an essential and important problem. This paper deals with the nonlinear state estimation problems in nonlinear and non-Gaussian systems. Recently, the Bayesian filter designer based on the Bayesian principle has been widely applied to the state estimation problem in NLSs. However, we assume that the state estimation models are nonlinear and non-Gaussian, applying traditional, typical nonlinear filtering methods, and there is no precise result for the system state estimation problem. Therefore, the larger the estimation error, the lower the estimation accuracy. To perfect the imperfections, a projection filtering method (PFM) based on the Bayesian estimation approach is applied to estimate the state. First, this paper constructs its projection symmetric interval to select the basis function. Second, the prior probability density of NLSs can be projected into the basis function space, and the prior probability density solution can be solved by using the Fokker–Planck Equation (FPE). According to the Bayes formula, the proposed estimator utilizes the basis function in projected space to iteratively calculate the posterior probability density; thus, it avoids calculating the partial differential equation. By taking two illustrative examples, it is also compared with the traditional UKF and PF algorithm, and the numerical experiment results show the feasibility and effectiveness of the novel nonlinear state estimation filter algorithm. Full article

We introduce some research results on a type of third-order boundary value problem for positive iterative solutions. The existence of solutions to these problems was proved using the monotone iterative technique. As an examination of the proposed method, an example to illustrate the effectiveness of our results was presented. Full article

Under the existing single sample condition, the fatigue detection method of an automobile driver has some problems, such as an improper camera calibration method, image denoising beyond the controllable range, low fatigue detection accuracy, and unsatisfactory effect. A fatigue detection method for drivers based on face recognition under a single sample condition is proposed. Firstly, the camera is calibrated by Zhang Zhengyou’s calibration method. The optimal camera parameters were calculated by linear simulation analysis, and the image was nonlinear refined by the maximum likelihood method. Then, the corrected image effect is enhanced, and the scale parameter gap in the MSRCR image enhancement method is adjusted to the minimum. The detection efficiency is improved by a symmetric algorithm. Finally, the texture mapping technology is used to enhance the authenticity of the enhanced image, and the face image recognition is carried out. The constraint conditions of fatigue detection are established, and the fatigue detection of car drivers under the condition of a single sample is completed. Experimental results show that the proposed method has a good overall detection effect: the fatigue detection accuracy is 20% higher than that of the traditional method, and the average detection time is over 30%. Compared with the traditional fatigue detection methods, this method has obvious advantages, can effectively extract more useful information from the image, and has strong applicability. Full article

Although hepatitis B is widespread, it is hard to cure. This paper presents a new and more accurate model for the diagnosis and treatment of hepatitis B. Based on previous research, the diagnosis and treatment modes were combined into one. By adding more influencing factors and risk factors, the overall diagnosis and treatment model will be further expanded, and a richer and more detailed overall diagnosis and treatment model will be constructed. Reverse logic gates are used in the model to improve the accuracy of the treatment planning. The new unified model is more accurate in subdividing diagnosis results, and it is more flexible and accurate in providing dynamic treatment plans. The prediction process and the static diagnosis process of the model are symmetric, and the related sub-graph is symmetric in structure. In addition, an algorithm for predicting the response probability of treatment scheme is developed, so as to predict the subsequent treatment effects of the current treatment scheme, such as the probability of drug resistance. The results show that this method is more accurate than other available systems, and it has encouraging diagnostic accuracy and effectiveness, which provides a promising help for doctors in diagnosing hepatitis B. Full article

The convergence of the digital economy and real economy is an irreversible trend. This article uses the adjusted Logistic coevolution Model as the main tool to study the interaction factors in the convergence concentrating on conducting the empirical research by using four dimensions data from 2005 to 2019 in China to calculate the intrinsic growth rate, the maximum environmental capacity, the coevolution factors and other key indicators. The study could further simulate and predict the coevolution of the digital economy and real economy under various modes, in attempt to explore an objective reference and theoretical basis for the convergence in China, which could help to fill the research gap to some extent. Full article

Risk and security are two symmetric descriptions of the uncertainty of the same system. If the risk early warning is carried out in time, the security capability of the system can be improved. A safety early warning model based on fuzzy c-means clustering (FCM) and back-propagation neural network was established, and a genetic algorithm was introduced to optimize the connection weight and other properties of the neural network, so as to construct the safety early warning system of coal mining face. The system was applied in a coal face in Shandong, China, with 46 groups of data as samples. Firstly, the original data were clustered by FCM, the input space was fuzzy divided, and the samples were clustered into three categories. Then, the clustered data was used as the input of the neural network for training and prediction. The back-propagation neural network and genetic algorithm optimization neural network were trained and verified many times. The results show that the early warning model can realize the prediction and early warning of the safety condition of the working face, and the performance of the neural network model optimized by genetic algorithm is better than the traditional back-propagation artificial neural network model, with higher prediction accuracy and convergence speed. The established early warning model and method can provide reference and basis for the prediction, early warning and risk management of coal mine production safety, so as to discover the hidden danger of working face accident as soon as possible, eliminate the hidden danger in time and reduce the accident probability to the maximum extent. Full article

In view of the lack of image enhancement processing in the traditional methods in image preprocessing, which leads to a long detection time for internal cracks in the image and poor visual effects, an intelligent detection method for internal cracks in aircraft landing gear images under multimedia processing is proposed. A spatial index structure is established based on the multimedia database, and the aircraft landing gear images in the structure are enhanced and denoised. Image segmentation is performed according to the preprocessing results, the crack foreground and the road surface background in the image are separated, and the threshold value of each image is calculated. The threshold segmentation result is used to distinguish which pixels are the areas where the cracks may exist and which pixels belong to the image background, and the judgment result realizes crack detection. The experimental results show that the crack detection time of the proposed method is shorter, the visual effect of the detection results is better, and the average of the expert score reaches 93.6 points, which verifies the effectiveness of the proposed method from both the subjective and objective aspects. Full article

The current study aims to design an integrated numerical computing-based scheme by applying the Levenberg–Marquardt backpropagation (LMB) neural network to solve the nonlinear susceptible (S), infected (I) and recovered (R) (SIR) system of differential equations, representing the spreading of infection along with its treatment. The solutions of both the categories of spreading infection and its treatment are presented by taking six different cases of SIR models using the designed LMB neural network. A reference dataset of the designed LMB neural network is established with the Adam numerical scheme for each case of the spreading infection and its treatment. The approximate outcomes of the SIR system based on the spreading infection and its treatment are presented in the training, authentication and testing procedures to adapt the neural network by reducing the mean square error (MSE) function using the LMB. Studies based on the proportional performance and inquiries based on correlation, error histograms, regression and MSE results establish the efficiency, correctness and effectiveness of the proposed LMB neural network scheme. Full article

In this article, we begin by introducing two classes of lacunary fractional spline functions by using the Liouville–Caputo fractional Taylor expansion. We then introduce a new higher-order lacunary fractional spline method. We not only derive the existence and uniqueness of the method, but we also provide the error bounds for approximating the unique positive solution. As applications of our fundamental findings, we offer some Liouville–Caputo fractional differential equations (FDEs) to illustrate the practicability and effectiveness of the proposed method. Several recent developments on the the theory and applications of FDEs in (for example) real-life situations are also indicated. Full article

The ocean occupies more than two-thirds of the earth’s area, providing a lot of oxygen and materials for human survival and development. However, with human activities, a large number of sewage, plastic bags, and other wastes are discharged into the ocean, and the problem of marine water pollution has become a hot topic in the world. In order to extract the characteristics of marine water pollution, this study proposed K-means clustering technology based on cosine distance and discrimination to study the polluted water. In this study, the polygonal area method combined with six parameters of water quality is used to analyze the marine water body anomalies, so as to realize the rapid and real-time monitoring of marine water body anomalies. At the same time, the cosine distance method and discrimination are used to classify marine water pollutants, so as to improve the classification accuracy. The results show that the detection rate of water quality anomalies is more than 88.2%, and the overall classification accuracy of water pollution is 96.3%, which proves the effectiveness of the method. It is hoped that this study can provide timely and effective data support for the detection of marine water bodies. Full article

As one of the common methods to construct classifiers, naïve Bayes has become one of the most popular classification methods because of its solid theoretical basis, strong prior knowledge learning characteristics, unique knowledge expression forms, and high classification accuracy. This classification method has a symmetry phenomenon in the process of data classification. Although the naïve Bayes classifier has high classification performance in single-label classification problems, it is worth studying whether the multilabel classification problem is still valid. In this paper, with the naïve Bayes classifier as the basic research object, in view of the naïve Bayes classification algorithm’s shortage of conditional independence assumptions and label class selection strategies, the characteristics of weighted naïve Bayes is given a better label classifier algorithm framework; the introduction of cultural algorithms to search for and determine the optimal weights is proposed as the weighted naïve Bayes multilabel classification algorithm. Experimental results show that the algorithm proposed in this paper is superior to other algorithms in classification performance. Full article

Helicopter tail rotors adopt a segmented driveline connected by flexible couplings, and dry friction dampers to suppress resonance. Modeling for this system can provide a basic foundation for parameter analysis. In this work, the lateral-torsional vibration equation of the shaft with continuous internal damping is established. The static and dynamic effects caused by flexible diaphragm couplings subject to parallel and angular misalignment is derived. A novel dual rub-impact model between the shaft and dry friction damper with multiple stages is proposed. Finally, a model of a helicopter tail rotor driveline incorporating all the above elements is formulated. Numerical simulations are carried out by an improved Adams–Bashforth method following the design flowchart. The dynamics of multiple vibration suppression, and the static and dynamic misalignment are analyzed to illustrate the accuracy and characteristics of the model. The coeffect of the rub impact and the misalignment on shafts and dampers are presented through the results of simulation and experiment. It provides an accurate and comprehensive mathematical model for the helicopter driveline. Response characteristics of multiple damping stages, static and dynamic misalignment, and their interaction are revealed. Full article

Inspired by the large number of applications for symmetric nonlinear equations, an improved full waveform inversion algorithm is proposed in this paper in order to quantitatively measure the bone density and realize the early diagnosis of osteoporosis. The isotropic elastic wave equation is used to simulate ultrasonic propagation between bone and soft tissue, and the Gauss–Newton algorithm based on symmetric nonlinear equations is applied to solve the optimal solution in the inversion. In addition, the authors use several strategies including the frequency-grid multiscale method, the envelope inversion and the new joint velocity–density inversion to improve the result of conventional full-waveform inversion method. The effects of various inversion settings are also tested to find a balanced way of keeping good accuracy and high computational efficiency. Numerical inversion experiments showed that the improved full waveform inversion (FWI) method proposed in this paper shows superior inversion results as it can detect small velocity–density changes in bones, and the relative error of the numerical model is within 10%. This method can also avoid interference from small amounts of noise and satisfy the high precision requirements for quantitative ultrasound measurements of bone. Full article

The flow and heat transfer characteristics of a film jet inclined to different supersonic situations with a varying Mach number of the main flow were numerically investigated. In supersonic situations, complicated waves are generated by the obstacle of the film jet. In this work, extra pressure is exerted onto the film jet, causing better film attachment to the wall. The strengthening of attachment decreases mixing between the main flow and film jet, causing better film cooling. We observed multi-interfacial layered structures caused by the film jet under the complicated effect of shock waves. At the interfaces of the film jet and shock waves, additional pressure is exerted on the film towards the wall. The pressure increases as the Mach number of the main flow increases and contributes to the increased adhesion of the gas film, which causes the cooling enhancement under a supersonic condition. In the vicinity of the film hole exit, a local low pressure region is formed under the influence of the supersonic main flow. An aerodynamic convergent–divergent state was formed in the film hole, devastating the state of supersonic congestion of the film hole and further enhancing the film cooling effect. Full article

An intrusion behavior recognition method based on deep learning is proposed in this paper in order to improve the recognition accuracy of raster perimeter intrusion behavior. The Mach–Zehnder fiber optic interferometer was used to collect the external vibration signal sensing unit, capture the external vibration signal, use the cross-correlation characteristic method to obtain the minimum frame length of the fiber vibration signal, and preprocess the intrusion signal according to the signal strength. The intrusion signals were superimposed and several sections of signals were intercepted by fixed window length; the spectrum information is obtained by Fourier transform of the intercepted stationary signals. The convolution neural network was introduced into the pattern recognition of the intrusion signals in the optical fiber perimeter defense zone, and the different characteristics of the intrusion signals were extracted, so as to realize the accurate identification of different intrusion signals. Experimental results showed that this method was highly sensitive to intrusion events, could effectively reduce the false alarm rate of intrusion signals, and could improve the accuracy and efficiency of intrusion signal recognition. Full article

With the rapid development of the P2P (peer-to-peer) online lending industry, which is facing significant credit risk, personal credit evaluation is an important method to reduce credit risk. Based on the various indexes of personal credit risk evaluation of domestic and foreign commercial banks, and according to the characteristics of P2P online lending, this paper analyzes the factors that affect the credit risk of P2P online borrowers, introduces the unique risk factors in the field of Internet information, and constructs an index system of personal credit risk evaluation of P2P online lending, which combines qualitative and quantitative indexes, including six major indexes and 21 small indexes. It then quantifies each index and defines the judgment standard of the evaluation results. Using analytic hierarchy process (AHP), expert scoring method, and fuzzy comprehensive evaluation method, this paper establishes a personal credit risk evaluation model of P2P online lending based on AHP method. The public information of two borrowers on the “PaiPai Lending” platform are selected for experimental verification. The results show that the improved personal credit risk evaluation model has better applicability and can evaluate the borrower’s credit status more scientifically, accurately, and comprehensively; thus, it is an effective method of personal credit risk evaluation of P2P online lending. Full article

The precision of current research on fault recognition of marine bearing remains to be improved. Therefore, a recognition method of crack-rubbing coupling fault of bearing under high water pressure based on polar symmetry mode decomposition is proposed in this article. The structure of marine bearing was analyzed, and the system was divided into several subsystems. Then, the nonlinearity relationship among the subsystems was confirmed. One subsystem was used to represent other subsystems, which was imported into the kinetic equation to obtain the equation after dimensionality reduction. According to the results of dimensionality reduction, the features of signal were measured from time domain, energy, and entropy. Meanwhile, the interior features of signal were extracted. Based on the feature extraction, the classifier of probabilistic neural network was introduced. The signal was recognized, and the recognition results were output via the training of signal sample data. Experimental results show that the method has better dimensionality reduction effect and high recognition precision. The method is practical. Full article

In order to enhance the real-time and retrieval performance of road traffic data filling, a real-time data filling and automatic retrieval algorithm based on the deep-learning method is proposed. In image detection, the depth representation is extracted according to the detection target area of a general object. The local invariant feature is extracted to describe local attributes in the region, and it is fused with depth representation to complete the real-time data filling of road traffic. According to the results of the database enhancement, the retrieval results of the deep representation level are reordered. In the index stage, unsupervised feature updating is realized by neighborhood information to improve the performance of a feature retrieval. The experimental results show that the proposed method has high recall and precision, a short retrieval time and a low running cost. Full article

Owing to the importance of coalbed methane (CBM) as a source of energy, it is necessary to predict its future production. However, the production process of CBM is the result of the interaction of many factors, making it difficult to perform accurate simulations through mathematical models. We must therefore rely on the historical data of CBM production to understand its inherent features and predict its future performance. The objective of this paper is to establish a deep learning prediction method for coalbed methane production without considering complex geological factors. In this paper, we propose a multivariate long short-term memory neural network (M-LSTM NN) model to predict CBM production. We tested the performance of this model using the production data of CBM wells in the Panhe Demonstration Area in the Qinshui Basin of China. The production of different CBM wells has similar characteristics in time. We can use the symmetric similarity of the data to transfer the model to the production forecasting of different CBM wells. Our results demonstrate that the M-LSTM NN model, utilizing the historical yield data of CBM as well as other auxiliary information such as casing pressures, water production levels, and bottom hole temperatures (including the highest and lowest temperatures), can predict CBM production successfully while obtaining a mean absolute percentage error (MAPE) of 0.91%. This is an improvement when compared with the traditional LSTM NN model, which has an MAPE of 1.14%. In addition to this, we conducted multi-step predictions at a daily and monthly scale and obtained similar results. It should be noted that with an increase in time lag, the prediction performance became less accurate. At the daily level, the MAPE value increased from 0.24% to 2.09% over 10 successive days. The predictions on the monthly scale also saw an increase in the MAPE value from 2.68% to 5.95% over three months. This tendency suggests that long-term forecasts are more difficult than short-term ones, and more historical data are required to produce more accurate results. Full article

Divisibility networks of natural numbers present a scale-free distribution as many other process in real life due to human interventions. This was quite unexpected since it is hard to find patterns concerning anything related with prime numbers. However, it is by now unclear if this behavior can also be found in other networks of mathematical nature. Even more, it was yet unknown if such patterns are present in other divisibility networks. We study networks of rational numbers in the unit interval where the edges are defined via the divisibility relation. Since we are dealing with infinite sets, we need to define an increasing covering of subnetworks. This requires an order of the numbers different from the canonical one. Therefore, we propose the construction of four different orders of the rational numbers in the unit interval inspired in Cantor’s diagonal argument. We motivate why these orders are chosen and we compare the topologies of the corresponding divisibility networks showing that all of them have a free-scale distribution. We also discuss which of the four networks should be more suitable for these analyses. Full article