Nonlinear Relationship Model Research Articles

OPTIMIZING REAL-TIME DYNAMIC PRICING STRATEGIES IN RETAIL AND E-COMMERCE USING MACHINE LEARNING MODELS

This study investigates the application of machine learning models for real-time dynamic pricing strategies in the retail and e-commerce sectors. We employed three prominent supervised machine learning models—Linear Regression, Random Forest, and Gradient Boosting Machines (GBM)—to predict optimal prices using a dataset sourced from Kaggle. The models were trained and evaluated with a 70:30 train-test split, while hyperparameter tuning was performed using grid search and cross-validation. The results indicate that the Gradient Boosting Machines (GBM) model consistently outperformed the other models, achieving the lowest Mean Absolute Error (MAE) and Root Mean Square Error (RMSE), and demonstrating a higher R-squared (R²) value. The comparative analysis highlights GBM's ability to capture complex interactions in dynamic pricing data, making it a robust choice for accurate price forecasting. The Random Forest model also delivered satisfactory results, balancing accuracy and computational efficiency, whereas the Linear Regression model showed higher prediction errors due to its limitations in modeling non-linear relationships. Real-time testing in a simulated environment confirmed the models' adaptability and responsiveness in a dynamic marketplace. These findings provide actionable insights for retail and e-commerce businesses, emphasizing the importance of model selection, hyperparameter optimization, and system integration to implement efficient dynamic pricing strategies. Future work should explore more extensive datasets and real-world applications to address seasonal variations, regional preferences, and consumer behavior, ensuring a more comprehensive and practical deployment of machine learning-driven dynamic pricing models.

Predictive modeling and anomaly detection in large-scale web portals through the CAWAL framework

This study presents an approach that uses session and page view data collected through the CAWAL framework, enriched through specialized processes, for advanced predictive modeling and anomaly detection in web usage mining (WUM) applications. Traditional WUM methods often rely on web server logs, which limit data diversity and quality. Integrating application logs with web analytics, the CAWAL framework creates comprehensive session and page view datasets, providing a more detailed view of user interactions and effectively addressing these limitations. This integration enhances data diversity and quality while eliminating the preprocessing stage required in conventional WUM, leading to greater process efficiency. The enriched datasets, created by cross-integrating session and page view data, were applied to advanced machine learning models, such as Gradient Boosting and Random Forest, which are known for their effectiveness in capturing complex patterns and modeling non-linear relationships. These models achieved over 92% accuracy in predicting user behavior and significantly improved anomaly detection capabilities. The results show that this approach offers detailed insights into user behavior and system performance metrics, making it a reliable solution for improving large-scale web portals’ efficiency, reliability, and scalability.

Tropical Cyclone Intensity Prediction Using BP-RNN From GPS-Derived Precipitable Water Vapor and Surface Meteorological Data

Abstract Tropical cyclones frequently threaten tropical coastal areas, making accurate prediction vital. While cyclone track forecasting has improved, predicting cyclone intensity remains challenging. This study uses precipitable water vapor (PWV) and other surface meteorological data to predict wind intensity during tropical cyclone Seroja in southern Indonesia. Data from two GPS stations, CKUP and CRTE, near the cyclone’s path, were analyzed. We employed neural network (NN) algorithms to model nonlinear relationships between variables, utilizing backpropagation to minimize error. The NN was fed with time series data across various hour window sizes (0h, 6h, 9h, and 12h), under the assumption that current parameters influence future conditions. Independent variables included PWV, ZTD, partial pressure of water vapor, temperature, and air pressure, with additional attributes implemented in multiple scenarios. Two years of data (2019-2020) were used to train the model, and wind velocities were estimated during cyclone Seroja. At CKUP, scenario 1 with a 9h window size achieved a probability of detection (POD) of 89% and a critical success index (CSI) of 84%. At CRTE, scenario 4 with a 6h window size achieved a POD of 73% and a CSI of 55%. The root mean square error for predicted wind speed was 1.32 m/s at CKUP and 2.08 m/s at CRTE. This study demonstrates the potential of integrating GPS and meteorological data to enhance cyclone intensity prediction, especially in cyclone-prone regions like Indonesia, offering a valuable contribution to local and global disaster preparedness.

Application of Machine Learning Models in Social Sciences: Managing Nonlinear Relationships

The increasing complexity of social science data and phenomena necessitates using advanced analytical techniques to capture nonlinear relationships that traditional linear models often overlook. This chapter explores the application of machine learning (ML) models in social science research, focusing on their ability to manage nonlinear interactions in multidimensional datasets. Nonlinear relationships are central to understanding social behaviors, socioeconomic factors, and psychological processes. Machine learning models, including decision trees, neural networks, random forests, and support vector machines, provide a flexible framework for capturing these intricate patterns. The chapter begins by examining the limitations of linear models and introduces essential machine learning techniques suited for nonlinear modeling. A discussion follows on how these models automatically detect interactions and threshold effects, offering superior predictive power and robustness against noise compared to traditional methods. The chapter also covers the practical challenges of model evaluation, validation, and handling imbalanced data, emphasizing cross-validation and performance metrics tailored to the nuances of social science datasets. Practical recommendations are offered to researchers, highlighting the balance between predictive accuracy and model interpretability, ethical considerations, and best practices for communicating results to diverse stakeholders. This chapter demonstrates that while machine learning models provide robust solutions for modeling nonlinear relationships, their successful application in social sciences requires careful attention to data quality, model selection, validation, and ethical considerations. Machine learning holds transformative potential for understanding complex social phenomena and informing data-driven psychology, sociology, and political science policy-making.

Unlocking biological complexity: the role of machine learning in integrative multi-omics.

The increasing complexity of biological systems demands advanced analytical approaches to decode the underlying mechanisms of health and disease. Integrative multi-omics approaches use multi-layered datasets such as genomic, transcriptomic, proteomic, and metabolomic data to understand biological processes much more comprehensively compared to the single-omics analysis and to provide a comprehensive view of cellular and molecular processes. However, these integrative approaches have their own computational and analytical challenges due to the large volume and nature of multi-omics data. Machine learning has emerged as a powerful tool to help and resolve these challenges. It offers sophisticated algorithms that can identify and discover hidden patterns and provide insights into complex biological networks. By integrating machine learning in multi-omics, we can enhance our understanding of drug discovery, disease, pathway, and network analysis. Machine learning and ensemble methods allow researchers to model nonlinear relationships and manage high-dimensional data, improving the precision of predictions. This approach paves the way for personalized medicine by identifying unique molecular signatures for individual patients, which can provide valuable insights into treatment planning and support more effective treatment. As machine learning continues to evolve, its role in multi-omics analysis will be pivotal in advancing our ability to interpret biological complexity and translate findings into clinical applications.

Development of New Electricity System Marginal Price Forecasting Models Using Statistical and Artificial Intelligence Methods

The System Marginal Price (SMP) is the cost of the last unit of electricity supplied to the grid, reflecting the supply–demand equilibrium and serving as a key indicator of market conditions. Accurate SMP forecasting is essential for ensuring market stability and economic efficiency. This study addresses the challenges of SMP prediction in Turkey by proposing a comprehensive forecasting framework that integrates machine learning, deep learning, and statistical models. Advanced feature selection techniques, such as Minimum Redundancy Maximum Relevance (mRMR) and Maximum Likelihood Feature Selector (MLFS), are employed to refine model inputs. The framework incorporates time series methods like Multilayer Perceptron (MLP), Long Short-Term Memory (LSTM), Bidirectional LSTM (Bi-LSTM), and Convolutional LSTM (ConvLSTM) to capture complex temporal patterns, alongside models such as Support Vector Machine (SVM), Extreme Gradient Boosting (XGBoost), and Extreme Learning Machine (ELM) for modeling non-linear relationships. Model performance was evaluated using the Mean Absolute Percentage Error (MAPE) across regular weekdays, weekends, and public holidays. XGBoost combined with MLFS consistently achieved the lowest MAPE values, demonstrating exceptional accuracy and robustness. Among all of the models, XGBoost combined with MLFS consistently achieved the lowest MAPE values, demonstrating superior accuracy and robustness. The results highlight the inadequacy of traditional models like ARIMA and SARIMA in capturing non-linear and highly volatile patterns, reinforcing the necessity of using advanced techniques for effective SMP forecasting. Overall, this study presents a novel and comprehensive approach tailored for complex electricity markets, significantly enhancing predictive reliability by incorporating economic indicators and sophisticated feature selection methods.

Remaining useful life prognostics of bearings based on convolution attention networks and enhanced transformer

Rolling bearings are critical components of industrial equipment, and predicting their remaining useful life (RUL) is a challenging task. This article proposes a new end-to-end model (MDSCT) to achieve efficient and accurate prediction of bearing RUL. MDSCT uses the raw vibration signals collected by sensors for prediction, without relying on a large amount of prior knowledge. The feature extraction backbone of this model is composed of an MDSC attention module that integrates multiple parallel depth-wise separable convolutions and an efficient attention mechanism, combined with a tansformer encoder (PPSformer) optimized using patch embedding and probesparse self attention techniques. They are respectively used to capture local subtle features and global dependent features in degraded signals. This article also proposes an improved adaptive activation function AdaptH_Swish to enhance the model's ability to model nonlinear relationships. To comprehensively verify the comprehensive performance of the model, this paper conducted detailed ablation and comparative experiments using two standard datasets, PHM2012 and XJTU-SY. The experimental results not only confirm the rationality and efficiency of the model structure design, but also demonstrate significant advantages in three evaluation indicators compared to various existing methods, fully demonstrating the high generalization and strong robustness of the MDSCT model in bearing RUL prediction tasks.

Proxy endpoints — bridging clinical trials and real world data

Objective:Disease severity scores, or endpoints, are routinely measured during Randomized Controlled Trials (RCTs) to closely monitor the effect of treatment. In real-world clinical practice, although a larger set of patients is observed, the specific RCT endpoints are often not captured, which makes it hard to utilize real-world data (RWD) to evaluate drug efficacy in larger populations. Methods:To overcome this challenge, we developed an ensemble technique which learns proxy models of disease endpoints in RWD. Using a multi-stage learning framework applied to RCT data, we first identify features considered significant drivers of disease available within RWD. To create endpoint proxy models, we use Explainable Boosting Machines (EBMs) which allow for both end-user interpretability and modeling of non-linear relationships. Results:We demonstrate our approach on two diseases, rheumatoid arthritis (RA) and atopic dermatitis (AD). As we show, our combined feature selection and prediction method achieves good results for both disease areas, improving upon prior methods proposed for predictive disease severity scoring. Conclusion:Having disease severity over time for a patient is important to further disease understanding and management. Our results open the door to more use cases in the space of RA and AD such as treatment effect estimates or prognostic scoring on RWD. Our framework may be extended beyond RA and AD to other diseases where the severity score is not well measured in electronic health records.

Artificial Intelligence Advancements for Accurate Groundwater Level Modelling: An Updated Synthesis and Review

Artificial Intelligence (AI) methods, including Artificial Neural Networks (ANNs), Adaptive Neuro-Fuzzy Inference Systems (ANFISs), Support Vector Machines (SVMs), Deep Learning (DL), Genetic Programming (GP) and Hybrid Algorithms, have proven to be important tools for accurate groundwater level (GWL) modelling. Through an analysis of the results obtained in numerous articles published in high-impact journals during 2001–2023, this comprehensive review examines each method’s capabilities, their combinations, and critical considerations about selecting appropriate input parameters, using optimisation algorithms, and considering the natural physical conditions of the territories under investigation to improve the models’ accuracy. For example, ANN takes advantage of its ability to recognise complex patterns and non-linear relationships between input and output variables. In addition, ANFIS shows potential in processing diverse environmental data and offers higher accuracy than alternative methods such as ANN, SVM, and GP. SVM excels at efficiently modelling complex relationships and heterogeneous data. Meanwhile, DL methods, such as Long Short-Term Memory (LSTM) and Convolutional Neural Networks (CNNs), are crucial in improving prediction accuracy at different temporal and spatial scales. GP methods have also shown promise in modelling complex and nonlinear relationships in groundwater data, providing more accurate and reliable predictions when combined with optimisation techniques and uncertainty analysis. Therefore, integrating these methods and optimisation techniques (Hybrid Algorithms), tailored to specific hydrological and hydrogeological conditions, can significantly increase the predictive capability of GWL models and improve the planning and management of water resources. These findings emphasise the importance of thoroughly understanding (a priori) the functionalities and capabilities of each potentially beneficial AI-based methodology, along with the knowledge of the physical characteristics of the territory under investigation, to optimise GWL predictive models.

Survey on Neural Networks in Networking: Applications and Advancements

The integration of neural networks into networking has paved the way for substantial advancements in network performance, security, and management. This survey delves into the diverse applications of neural networks within the networking domain, highlighting their impact on traffic prediction, anomaly detection, network optimization, and security enhancements. By leveraging the inherent capabilities of neural networks to model complex and non-linear relationships, significant improvements in efficiency and reliability can be achieved. This survey provides a thorough examination of current methodologies, key advancements, and practical implementations, offering insights into the future potential of neural networks in the field of networking.

Research on the evaluation model for the tactile feel of custom wardrobe furniture finishes

The decision-making process of consumers regarding custom wardrobe furniture transcends product functionality to include the sensory experience, notably the tactile aspect. This study focuses on the tactile experience to assist consumers in evaluating the tactile feel of custom wardrobe finishes, such as cognitive fuzziness during the experience, the challenge of clearly describing the connection between touch sensation and the physical attributes of the custom wardrobe, and reducing communication costs between users and designers. The research first clarifies the hierarchical cognitive structure of the tactile sensation of custom wardrobe finishes, then explores the logical relationships between levels through linear regression models. Subsequently, a nonlinear relationship model between the “Physical Attributes Layer” and the “Tactile Sensation Layer” is constructed using a Backpropagation Neural Network, and the connection between the “Tactile Sensation Layer” and the “Comprehensive Evaluation Layer” is mapped through a multiple linear regression equation. This comprehensive evaluation system for the tactile feel of custom wardrobe finishes provides designers with a tool to optimize the tactile characteristics of products, thereby shortening the design iteration cycle and improving design precision. It also helps users better express their emotional needs in terms of tactile sensations, enhancing the connection between tactile experience and emotion.

Interpretable and explainable hybrid model for daily streamflow prediction based on multi-factor drivers.

Streamflow time series data typically exhibit nonlinear and nonstationary characteristics that complicate precise estimation. Recently, multifactorial machine learning (ML) models have been developed to enhance the performance of streamflow predictions. However, the lack of interpretability within these ML models raises concerns about their inner workings and reliability. This paper introduces an innovative hybrid architecture, the TCN-LSTM-Multihead-Attention model, which combines two layers of temporal convolutional networks (TCN) followed by one layer of long short-term memory (LSTM) units, integrated with a Multihead-Attention mechanism for predicting streamflow with streamflow causation-driven prediction samples (RCDP), employing local and global interpretability studies through Shapley values and partial dependency analysis. The find_peaks method was used to identify peak flow events in the test dataset, validating the model's generality and uncovering the physical causative patterns of streamflow. The results show that (1) compared to the LSTM model with the same hyperparameter settings, the proposed TCN-LSTM-Multihead-Attention hybrid model increased the R2 by 52.9%, 2.5%, 43.1%, and 10.7% respectively at four stations in the test set predictions using RCDP samples. Moreover, comparing the prediction results of the hybrid model under different samples in Hengshan station, the R2 for RCDP increased by 5.06% and 1.22% compared to streamflow autoregressive prediction samples (RAP) and meteorological-soil volumetric water content coupled autoregressive prediction samples (MCSAP) respectively. (2) Historical streamflow data from the preceding 3days predominantly influences predictions due to strong autocorrelation, with flow quantity (Q) typically emerging as the most significant feature alongside precipitation (P), surface soil moisture (SSM), and adjacent station flow data. (3) During periods of low and normal flow, historical data remains the most crucial factor; however, during flood periods, the roles of upstream inflow and precipitation become significantly more pronounced. This model facilitates the identification and quantification of various hydrodynamic impacts on flow predictions, including upstream flood propagation, precipitation, and soil moisture conditions. It also elucidates the model's nonlinear relationships and threshold responses, thereby enhancing the interpretability and reliability of streamflow predictions.

Integrating Machine Learning Techniques for Real Estate Analysis

Machine learning can be applied to prediction models. The study delved into house price prediction, an area of significance to both individual participants and policymakers within and beyond the real estate market. The advanced predictive model is a tool that informs quality decision-making. This study synthesizes and builds on existing research to implement and enhance house price prediction methods, assessing the performance of Convolutional Neural Networks (CNNs), Decision Trees, and K-Nearest Neighbors (KNN) which is of focus on Most Correlated Features (KNN-MCF). Although these techniques have been developed and refined over the years, they still face challenges such as overfitting, noises existing in the dataset, and the complexity of modeling both linear and non-linear relationships. By integrating the resources, the study aims to provide objective guides for addressing the common challenges and predicting house prices, illustrating the appropriate analytical methods to apply based on characteristics of a database, extra space for improvements, and critical concerns of their practical applications. Ultimately, the research strives to bridge the gap between theoretical models and real-world applications to develop practical tools for reliable house price prediction.

DHM-Net: Deep Hypergraph Modeling for Robust Feature Matching.

We present a novel deep hypergraph modeling architecture (called DHM-Net) for feature matching in this paper. Our network focuses on learning reliable correspondences between two sets of initial feature points by establishing a dynamic hypergraph structure that models group-wise relationships and assigns weights to each node. Compared to existing feature matching methods that only consider pair-wise relationships via a simple graph, our dynamic hypergraph is capable of modeling nonlinear higher-order group-wise relationships among correspondences in an interaction capturing and attention representation learning fashion. Specifically, we propose a novel Deep Hypergraph Modeling block, which initializes an overall hypergraph by utilizing neighbor information, and then adopts node-to-hyperedge and hyperedge-to-node strategies to propagate interaction information among correspondences while assigning weights based on hypergraph attention. In addition, we propose a Differentiation Correspondence-Aware Attention mechanism to optimize the hypergraph for promoting representation learning. The proposed mechanism is able to effectively locate the exact position of the object of importance via the correspondence aware encoding and simple feature gating mechanism to distinguish candidates of inliers. In short, we learn such a dynamic hypergraph format that embeds deep group-wise interactions to explicitly infer categories of correspondences. To demonstrate the effectiveness of DHM-Net, we perform extensive experiments on both real-world outdoor and indoor datasets. Particularly, experimental results show that DHM-Net surpasses the state-of-the-art method by a sizable margin. Our approach obtains an 11.65% improvement under error threshold of 5° for relative pose estimation task on YFCC100M dataset. Code will be released at https://github.com/CSX777/DHM-Net.

Advancing Computational Fluid Dynamics through Machine Learning: A Review of Data-Driven Innovations and Applications

This review explores Machine Learning (ML) integration with Computational Fluid Dynamics (CFD) to enhance simulation accuracy and efficiency. CFD has long been the standard for fluid flow analysis, but its computational cost and limitations in handling complex flows have spurred interest in data-driven approaches. With its ability to model nonlinear relationships, machine learning offers a promising solution. The review covers vital methodologies, including data acquisition from CFD simulations, feature extraction, and the selection of ML models such as neural networks and supervised learning algorithms. Furthermore, it examines the application of ML in accelerating CFD simulations and improving turbulence modeling. While promising, challenges remain, particularly in ensuring ML models respect the underlying physical laws governing fluid dynamics. The review concludes by discussing future research directions, particularly in physics-informed machine learning, which seeks to integrate physical constraints into the ML process. This combination of data-driven and physics-based approaches can transform CFD applications across industries.

A Novel Two-Stage Framework for Mid-Term Electric Load Forecasting

Electric utilities and planners rely heavily on accurate mid-term load projections to effectively schedule maintenance, coordinate load dispatch, and manage fuel reserves. Current approaches that attempt to forecast electric load for multiple horizons in a single stage, however, often result in inaccurate forecasts due to the lack of information for predicting the data at the farthest horizon and propagation of large errors. To address this issue, this paper presents a two-step mechanism for forecasting electric load that utilizes the benefits of both Backpropagation Neural Networks (BPNNs) and Radial Basis Function Neural Networks (RBFNNs). The first stage utilizes a pool of BPNNs to make partial predictions. BPNNs are used as they are well known for their capability of fast and accurate predictions. In the second stage, RBFNNs are used to make complete forecasts. RBFNNs are known for their ability to model non-linear relationships in the data which is crucial in this stage of the forecast process. Additionally, this paper also proposes a unique method for generating additional training samples by incorporating stacking noise, which adds more variability to the data, increasing the generalization capability of the models, resulting in better forecasting performance. The performance of the proposed framework has been investigated with simulation studies and has been validated on actual load data of Madhya Pradesh Power Transmission System, India. The performance comparison with the existing methods in terms of both accuracy and reliability shows that the proposed forecasting framework provides more accurate results.

Greedy knot selection algorithm for restricted cubic spline regression.

Non-linear regression modeling is common in epidemiology for prediction purposes or estimating relationships between predictor and response variables. Restricted cubic spline (RCS) regression is one such method, for example, highly relevant to Cox proportional hazard regression model analysis. RCS regression uses third-order polynomials joined at knot points to model non-linear relationships. The standard approach is to place knots by a regular sequence of quantiles between the outer boundaries. A regression curve can easily be fitted to the sample using a relatively high number of knots. The problem is then overfitting, where a regression model has a good fit to the given sample but does not generalize well to other samples. A low knot count is thus preferred. However, the standard knot selection process can lead to underperformance in the sparser regions of the predictor variable, especially when using a low number of knots. It can also lead to overfitting in the denser regions. We present a simple greedy search algorithm using a backward method for knot selection that shows reduced prediction error and Bayesian information criterion scores compared to the standard knot selection process in simulation experiments. We have implemented the algorithm as part of an open-source R-package, knutar.

Quantifying the effects of neutron dose, dose protraction, age and sex on mouse survival using parametric regression and machine learning on a 21,000-mouse data set

The biological effects of densely-ionizing radiations such as neutrons and heavy ions encountered in space travel, nuclear incidents, and cancer radiotherapy, significantly differ from those of sparsely-ionizing photons and necessitate a comprehensive understanding for improved protection measures. Data on lifespan studies of laboratory rodents exposed to fission neutrons, accumulated in the Janus archive, afford unique insights into the impact of densely ionizing radiation on mortality from cancers and various organ dysfunction. We extracted and analyzed data for 21,308 individual B6CF1 mice to investigate the effects of neutron dose, fractionation, protraction, age, and sex on mortality. As Cox regression encountered limitations owing to assumption violations, we turned to Random Survival Forests (RSF), a machine learning algorithm adept at modeling nonlinear relationships. RSF interpretation using Shapley Additive Explanations revealed a dose response for mortality risk that curved upwards at low doses < 20 cGy, became nearly-linear over 20–150 cGy, and saturated at high doses. The response was enhanced by fractionation/protraction of irradiation (exhibiting an inverse dose rate effect), and diminished by older age at exposure. Somewhat reduced mortality was predicted for males vs females. This research expands our knowledge on the long-term effects of densely ionizing radiations on mammal mortality.

Association of maternal age with adverse pregnancy outcomes: A prospective multicenter cohort study in China.

Although maternal age might affect pregnancy outcomes, it remains unclear whether this relationship is linear or curvilinear and if it differs between nulliparous and multiparous women. We aimed to characterize the relationship between maternal age and risks of pregnancy outcomes in a diverse sample of Chinese singleton pregnant women and to evaluate whether the relationship varied by parity. We based this prospective multicenter cohort study on data from 18 495 singleton pregnant women who participated in the University Hospital Advanced Age Pregnant Cohort Study, conducted in eight Chinese public hospitals from 2016 to 2021. We used restricted cubic splines to model nonlinear relationships between maternal age continuum and adverse outcomes, and performed multivariable log-binomial regression to estimate the adjusted relative risk (RR) and 95% confidence interval (CI). Among 18 495 singleton pregnant women (mean age 35.7, standard deviation (SD) = 4.2 years), maternal age was not related to postpartum hemorrhage or small for gestational age, but showed a positive, nonlinear relationship to gestational diabetes mellitus, hypertensive disorders of pregnancy, preeclampsia, placenta accreta spectrum, placenta previa, cesarean delivery, preterm birth, large for gestational age, macrosomia, and fetal congenital anomaly, with inflection points around 35.6-40.4 years. Compared to women younger than 35 years, older women had higher risks of adverse pregnancy outcomes, except for postpartum hemorrhage and small for gestational age. The risks of placenta accreta spectrum, placenta previa, large for gestational age, and macrosomia were highest for women aged 40-44 years, and risks of gestational diabetes mellitus, hypertensive disorders of pregnancy, preeclampsia, cesarean delivery, preterm birth and congenital anomaly were highest for those aged ≥45 years. Most risks were more pronounced in nulliparous than multiparous women (P for interaction <0.02). Delayed childbirth was related to increased risks of adverse pregnancy outcomes, especially for nulliparous women. Appropriate childbearing age, generally before 35 years, is recommended for optimising pregnancy outcomes.

Abnormal variation of P-wave velocity of red sandstone after cyclical thermal shock in water

Hot dry rock (HDR) has great development potential because of its advantages of clean, environmental protection and renewable. The study of physical and mechanical properties of HDR is one of the important links in the process of geothermal energy development. Previous studies have mainly focused on the granite thermal reservoir but research on the sandstone thermal reservoir, especially the physical properties of sandstone after multiple thermal shocks, is scarce. Therefore, in this study, cyclic thermal shock experiments of sandstone at different temperatures are carried out, and the variation law of P-wave velocity of sandstone after heat treatment is revealed. It is found that the P-wave velocity of red sandstone decreases with the increase of temperature and cycle times, especially when the temperature is higher than 400 °C, the maximum change rate of wave velocity reaches 52.6%. It is particularly noteworthy that the P- wave velocity of sandstone increases abnormally at about 600 °C. And this article puts forward three hypotheses to explain the wave velocity anomaly. In addition, the nonlinear relationship model among P-wave velocity, temperature and number of cycles is established for the first time, and the correlation coefficient R2 is more than 0.9. This study serves as a reference for the development and utilization of the sandstone geothermal reservoir.