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The solution of fractional-order systems has been a complex problem for our research. Traditional methods like the predictor-corrector method and other solution steps are complicated and cumbersome to derive, which makes it more difficult for our solution efficiency. The development of machine learning and nonlinear dynamics has provided us with new ideas to solve some complex problems. Therefore, this study considers how to improve the accuracy and efficiency of the solution based on traditional methods. Finally, we propose an efficient and accurate nonlinear auto-regressive neural network for the fractional order dynamic system prediction model (FODS-NAR). First, we demonstrate by example that the FODS-NAR algorithm can predict the solution of a stochastic fractional order system. Second, we compare the FODS-NAR algorithm with the famous and good reservoir computing (RC) algorithms. We find that FODS-NAR gives more accurate predictions than the traditional RC algorithm with the same system parameters, and the residuals of the FODS-NAR algorithm are closer to 0. Consequently, we conclude that the FODS-NAR algorithm is a method with higher accuracy and prediction results closer to the state of fractional-order stochastic systems. In addition, we analyze the effects of the number of neurons and the order of delays in the FODS-NAR algorithm on the prediction results and derive a range of their optimal values.

Prediction of Lotka-Volterra equations has always been a complex problem due to their dynamic properties. In this paper, we present an algorithm for predicting the Lotka-Volterra equation and investigate the prediction for both the original system and the system driven by noise. This demonstrates that deep learning can be applied in dynamics of population. This is the first study that uses deep learning algorithms to predict Lotka-Volterra equations. Several numerical examples are presented to illustrate the performances of the proposed algorithm, including Predator nonlinear breeding and prey competition systems, one prey and two predator competition systems, and their respective systems. All the results suggest that the proposed algorithm is feasible and effective for predicting Lotka-Volterra equations. Furthermore, the influence of the optimizer on the algorithm is discussed in detail. These results indicate that the performance of the machine learning technique can be improved by constructing the neural networks appropriately.

The health of rolling bearing is of great importance for the normal operation of rotating machinery. The fault diagnosis process can be roughly summarized as signal processing, feature extraction, and fault classification. In this paper, a novel feature extraction and fault diagnosis method with fractional order back-propagation neural network is put forward. The new sine cosine algorithm optimized variational mode decomposition is performed on vibration signals, and the fault feature vectors are selected and built by singular value decomposition. Inspired by the fractional order calculus, a fractional order back-propagation neural network is employed to realize fault classification. The capability of the developed fault diagnosis algorithm is comprehensively evaluated via benchmark bearing data. The experimental results demonstrate that the designed method substantially extracts bearing defect features, increases classification accuracy and efficiency, and also outperforms existing algorithms. [ABSTRACT FROM AUTHOR]

In order to evaluate the water quality changes of Dahai Lake in Inner Mongolia, the water quality monitoring data of Dahai Lake from 2008 to 2021 were used as an example, and the improved Nemero pollution index method and the principal component analysis method were used to evaluate the water quality changes of Dahai Lake. The results show that the two evaluation methods of Daihai Lake evaluation of water quality change trend results are basically the same, are able to fully reflect the comprehensive level of water quality pollution, but each evaluation method has disadvantages, the improved Nemero pollution index method can not reflect the contribution of each pollutant, the principal component analysis method can not evaluate the water quality category. Therefore, the combination of two methods, the improved Nemero pollution index method and the principal component analysis method, can complement and support each other's evaluation conclusions, and the evaluation results are more accurate and objective, and can reflect the changes in the water quality of Daihai Lake in a comprehensive manner.

In recent years, there has been a growing awareness of the potential health benefits of the natural environment for human well-being. Given the fast-paced nature of contemporary lifestyles, research into the use of virtual environments as a means to provide various seasonal landscapes has gained increasing importance. Objective: The aim of this study is to investigate the impact of different sensory modes on the preferences and therapeutic effects of virtual autumn landscapes on university campuses. Methods: In this study, 320 participants, with an average age of 21.11 years (±1.21 years), were exposed to virtual environments featuring autumn color landscapes and bare tree landscapes using visual, auditory, and combined conditions. A control group was included for comparison. Differences in participants' physiological indicators (EEG, heart rate) and psychological measures (POMS, PANAS, SVS, ROS) were analyzed, with the use of the Holm correction (P < 0.05). Results: (1) Autumn virtual landscapes with color had a superior therapeutic effect. (2) There were significant differences in the therapeutic effects of different sensory modes within the same season's landscape categories, suggesting that incorporating additional sensory dimensions may enhance therapeutic outcomes. Conclusion: Based on the study's findings, we recommend that when designing therapeutic environments, attention should be given to seasonal variations and the integration of various sensory modes to optimize therapeutic results. [ABSTRACT FROM AUTHOR]

Cigarette smoking is known to induce serious lung diseases, but there is not an effective method to solve this problem. The present study investigated vitamin D3 on over-expression of CXCR3 and CXCL10 in mice induced by cigarette smoking. A pulmonary airway model was designed, and morphological assessment of emphysema, IL-4, IFN-γ and CXCL10 concentration in bronchoalveolar lavage fluids, expression of CXCR3 and CXCL10 were detected. Emphysema of the mice only exposed to cigarette smoke was significant, and concentration of IL-4, IFN-γ and CXCL10 was also increased. In addition, CXCR3 and CXCL10 were over-expressed. The degree of emphysema, concentration of IL-4, IFN-γ and CXCL10, and expression of CXCR3 and CXCL10 in mice administrated with low dose vitamin D3 were similar to the normally treated mice. Low dose of vitamin D3 can effectively protect the lung from the damage induced by cigarette smoke.

Moisture plays a pivotal role in the establishment of vegetation in sandy areas, underscoring the need to comprehend the water utilization strategies employed by established trees for the judicious use of water resources. Despite this significance, there exists a research gap concerning the water uptake patterns and consumption disparities between the dominant trees, namely the dry willow (Salix matsudana) and small-leafed poplar (Populus simonii), in the Mu Us sandy region. Consequently, our study sought to investigate the water utilization patterns and transpiration water consumption of these two plants. This was achieved through the analysis of hydrogen and oxygen isotope compositions in xylem water, soil water, and groundwater, coupled with the assessment of stem flow rates of tree trunks. The findings reveal that both Salix matsudana and Populus simonii exhibited variations in soil water content with soil depth, characterized by an initial increase followed by a subsequent decrease. During the months of July, August, and September, both species demonstrated the ability to absorb water from multiple sources concurrently. Specifically, Salix matsudana and Populus simonii predominantly utilized middle and shallow soil water sources in July and September, respectively. However, in August, both species primarily relied on shallow soil water for absorption. Over the period from July to September, the sap flow rate of Salix matsudana surpassed that of Populus simonii by 1888.2 mL·h−1 to 2499.04 mL·h−1, representing a 1.5 to 2.2 times increase. This underscores the necessity for Salix matsudana to draw water from middle and deep soil layers to compensate for shallow water deficits. In summary, schemes for the establishment of vegetation in sandy areas should consider the dynamic nature of water uptake and evapotranspiration, emphasizing the importance of regulating these processes for efficient water conservation and utilization. [ABSTRACT FROM AUTHOR]