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First, this paper studies the derivation process of the plain Bayesian classification algorithm in big data technology, which is built based on statistics. Then to make up for the feature independence assumption of plain Bayes, the plain Bayesian classification algorithm based on feature weighting is proposed to be optimized mainly by the Laplace algorithm, which improves the classification accuracy to a certain extent. Finally, based on the connotation and characteristics of health culture in Shaanxi, the formation and development of health culture theory in Shaanxi are clarified, and policy suggestions are proposed for the development problems of health culture in Shaanxi and the development level of cultural industry in Shaanxi province. The analysis of the health culture industry in Shaanxi is based on the vegetative Bayesian classification algorithm. The results show that the cultural service industry in Shaanxi Province achieved an output value of 41.309 billion yuan, accounting for 63.9% of the added value of the cultural industry in the province. The cultural manufacturing industry in Shaanxi accounts for a large gap with the national level, with a difference of 19.3 percentage points. This study combines big data technology and the advantages of Shaanxi’s healthy cultural resources to provide reasonable countermeasure suggestions to promote the transformation of Shaanxi from a large cultural province to a strong cultural province.

Cancer tumor modeling is crucial for understanding tumor dynamics, treatment strategies, and the effects of therapies on progression. While extensive research exists on fractional cancer models, innovation is limited in incorporating fuzzy-fractional calculus into cancer diffusion models. This paper introduces a fuzzy-fractional diffusion cancer model solved using the He-Laplace algorithm in the Liouville-Caputo sense. A novel hybrid algorithm, combining homotopies, perturbation techniques, and Laplace transforms, is developed to solve this complex model. Our method employs triangular fuzzy numbers to capture uncertainty, enabling analysis of cancer diffusion across lower and upper bounds and extending beyond conventional crisp models, opening up an entirely new domain. This model explores two different scenarios for the killing rate of cancer cells, namely time-dependent killing rate, and space dependent killing rate. Numerical solutions are provided for both lower and upper bounds, with results varying across different fractional orders and residual errors calculated to validate the method’s authenticity and applicability. 2D and 3D visualizations demonstrate the model’s complexity, and solutions are analyzed in a fuzzy environment. Contour diagrams further enhance the accuracy of capturing diffusion models in the fuzzy-fractional context. The results demonstrate the method’s efficiency and accuracy, providing valuable insights into cancer tumor dynamics. It effectively models tumor heterogeneity, improving understanding, prediction, and treatment optimization. Future work could involve applying real-life data to compare the simulation’s accuracy in reflecting real-world tumor dynamics. This study emphasizes the method’s effectiveness for solving complex models in scientific and biological fields.

Cancer encompasses various diseases characterized by the uncontrolled growth of abnormal cells, which can invade healthy tissues and spread throughout the body, making it the second leading cause of death worldwide. This study presents a fractional cancer treatment model with immunotherapy to enhance understanding of cancer’s mathematical framework and behavior. The model comprises fractional differential equations analyzed using the Caputo-fractional derivative, aiming to control cancer growth while considering cell population metrics. A framework integrating various homotopies and Laplace transforms is developed to explore cancer’s complexities. Simultaneous solution profiles for effector immune cells and tumor cells illustrate their mutual influence. The model examines parameters such as the death rate of immune cells, natural tumor growth rate, rate of immune cells killing fractional tumor cells and numerous others graphically for clarity. The fractional parameter is visually represented through 2D, 3D, and contour plots. This comprehensive analysis validates the proposed approach, suggesting its applicability to other complex cancer treatment models for better decision-making in cancer treatment.

Edges are a basic and fundamental feature in image processing that is used directly or indirectly in huge number of applications. Inspired by the expansion of image resolution and processing power, dilated-convolution techniques appeared. Dilated convolutions have impressive results in machine learning, so naturally we discuss the idea of dilating the standard filters from several edge-detection algorithms. In this work, we investigated the research hypothesis that use dilated filters, rather than the extended or classical ones, and obtained better edge map results. To demonstrate this hypothesis, we compared the results of the edge-detection algorithms using the proposed dilation filters with original filters or custom variants. Experimental results confirm our statement that the dilation of filters have a positive impact for edge-detection algorithms from simple to rather complex algorithms.

The propagation and spread of computer viruses is a significant threat that greatly affects network security. By closely examining the diffusion patterns of viruses in wireless sensor networks (WSNs), the future can be predicted, and preventive measures can be taken to avoid network damage. This manuscript presents modeling the transmission characteristics of computer viruses in WSNs within a fuzzy-fractional framework. The fractional derivative is taken in Caputo sense throughout the manuscript. Also, triangular fuzzy numbers (TFNs) are utilized to incorporate uncertainties in the virus model. This approach is aligned with real scenarios because mathematical model of virus outbreak in WSNs contains uncertain patterns. A semi-numerical scheme is proposed for the solution and analysis purposes. This approach includes multiple homotopies along with perturbation process and Laplace transform to derive series-form solutions for different wireless nodes. The obtained solutions offer a clear understanding of how proposed methodology addresses virus propagation at lower and upper bounds. Moreover, detailed error analysis is conducted to validate the obtained results in fuzzy and non-fuzzy contexts, demonstrating the ability of proposed algorithm to capture the complexities of the network problem. Additionally, a comprehensive graphical analysis is performed to investigate the behavior of wireless nodes within the fuzzy-fractional framework. The fractional parameter is particularly examined under various constraints and assumptions and presented as 2D, 3D plots and gradient contour diagrams. This investigation confirms the effectiveness of hybrid approach in handling uncertainties related to the unpredictable in WSNs, and deepening our understanding of ongoing challenges related to virus transmission. This approach also applicable to other complex models encounter in different fields.

Color plays an indispensable role in the formation of movie style, and hue, as an important part of color, plays a pivotal role in the study of the quality of movie pictures. The study is based on the basic theory of the color and color space of the movie picture, equalizing the histogram of the movie picture, and then combining the HistoGAN network and Laplace algorithm of computer vision algorithms to realize the enhancement of the hue of the movie picture, and then adjusting and improving the quality of the movie picture automatically. Taking 10 comedy movies by Wes Anderson as an example, the movie tones are measured and counted. According to the results, the movie screen tones adjusted have a strong ability to convey image details and have better contrast and clarity enhancement effects while maintaining image fidelity. As the year progresses, the brightness of the adjacent period in Wes Anderson’s comedy movies becomes more frequent and larger after the movie screen hue is adjusted. The overall of his movies is the color matching law of warm tones with larger saturation with cooler tones with smaller saturation, and the hue adjustment gives the movie screen a more advanced sense of beauty.

When photoelectric measuring equipment is used to track satellites, the extraction of the short-term or long-term target often fails because the target is weak, clouds block the target, and/or the sun’s angle is too small, resulting in the loss of the tracking target. In this study, an improved Laplacian satellite tracking method based on the Kalman filter is proposed. Firstly, the improved Laplacian algorithm was used for the initial fitting of the equation of motion of a small amount of measurement data. Judgment of the validity and Kalman filtering was carried out on the current frame’s measurement data to calculate the optimal estimate of the current frame’s orbit data, and the accurate equation of motion was iteratively fitted to obtain high-precision data for predicting the satellite’s orbit frame by frame. Numerical tracking of the equipment was carried out. This method was experimentally validated on an actual optical measurement device. The test results showed that this method can make up for the frequent loss of short-term targets. Under the condition that the maximum deviation is less than 3″, the length of extrapolated data can be up to 30 s and the length of the measurement data was less than 30 s. This method may improve the stability of tracking equipment as well as the accuracy and integrity of the measurement data.

In this study, the Fokker-Planck model, which describes the time-evolution of probability density functions, is reformulated within a fuzzy-fractional structure to incorporate uncertainties. Triangular fuzzy numbers are employed to represent uncertainty by incorporating fuzzy parameter in the initial conditions. After fuzzification, He-Laplace framework is applied to derive approximate analytical solutions. To evaluate the efficiency and reliability of the proposed methodology, residual errors are computed for both upper and lower bound solutions. The numerical results are further analyzed numerically through comparative tables, and visually as 2D, 3D and contour plots. The results demonstrate that the observed errors remain negligible, supporting the efficacy of proposed methodology and validity of obtained solutions. The proposed framework provides an efficient tool for analyzing fuzzy–fractional Fokker–Planck models and can be extended to other nonlinear fuzzy fractional systems.

The quality of Friction Stir Welded joint depends on the input parameters like tool rotational speed, tool traverse speed (mm/min), tool tilt angle, and an axial plunge force. If there is any variation in these input parameters then there will be a chance of formation of various surface defects such as groovy edges, flash formation, and non-homogeneous mixing of alloys. The main objective of the present work is to use machine learning algorithms such as Deep Convolutional Neural Network (DCNN) and Laplace transformation algorithm to detect these surface defects present on the Friction Stir Welded joint. The results showed that the used algorithms can easily detect such surface defects with good accuracy.

Cancer is a complex and heterogeneous condition marked by the unchecked growth and dissemination of abnormal cells, posing significant challenges in detection, treatment, and patient care. As one of the leading global causes of death, a deep understanding of its underlying biological mechanisms is essential for advancing therapeutic strategies and improving clinical outcomes. Mathematical modeling serves as a crucial tool in capturing the multifaceted dynamics of cancer initiation, progression, and response to interventions. By simulating critical aspects of cancer within a controlled computational framework, mathematical models enable scientists to explore innovative treatment strategies, investigate the disease’s underlying biological dynamics, and identify novel therapeutic targets. This study presents a fuzzy-fractional differential model of tumor-immune interaction, incorporating tumor cells, immune effector cells, and the concentration of chemotherapy agents in the bloodstream, modeled using Caputo-type time-fractional derivatives. To better capture the uncertainty associated with patient-specific factors—particularly psychological impacts such as depression—triangular fuzzy numbers are integrated into the initial conditions, thereby enhancing the model’s realism and predictive capability. The current model is addressed using the proposed modified He–Laplace–Carson algorithm for solution and analysis by creating multiple homotopies related to the perturbation method. The model’s solution trajectories for chemotherapy levels, immune effector cells, and tumor cell populations are examined to evaluate the bidirectional interaction between immune response and tumor growth. Additionally, the simulation provides insight into the dynamic behavior of chemotherapy concentration over the duration of treatment, offering a clearer understanding of its therapeutic progression. An extensive graphical analysis is conducted by varying a range of parameters, including effect of depression, death rate of immune cells due to malignant cells attachment, maximum growth rate factors, and fuzzy parameters introduced in the cancer system. It was observed that as the fractional parameter increased, all profiles rose, with effector cells showing a more notably faster growth than tumor cells. Furthermore, all fuzzy and non-fuzzy parameters generally showed a strong positive influence on effector cells, with tumor cell growth remaining comparatively subdued. The fractional parameter is analyzed under diverse conditions using 2D/3D visualizations and contour gradients, confirming the method’s reliability in handling uncertainty and highlighting its adaptability to broader fuzzy-fractional systems. Such applications have the capability to significantly enhance the understanding of ongoing challenges faced in oncology.