Prediction Residuals Research Articles

A Novel Deep Neural Network for Facial Beauty Improvement

<p>This study delves into how to combine deep learning and fuzzy logic reasoning to evaluate facial aesthetics and provide targeted makeup recommendations. To further optimize the prediction results, we adopted the BLS method to correct the prediction residuals generated by ResNet-50. Specifically, the predicted appearance score can be expressed as score = p + δ, where p is the predicted result and δ represents the predicted residual of the system. After determining the beauty rating, we further studied four different makeup combinations (x1, x2, x3, x4). Moreover, we introduced fuzzy logic reasoning, defined fuzzy sets and fuzzy relationships, and established membership matrices for each makeup combination. The results of these fuzzy logical reasoning allow us to set a value range of m, n for each makeup method. Based on these reasoning results, we have come up with makeup recommendations for different facial aesthetics. Performance our system with the data collected from internet (accuracy of the calculation = 93.26%), from one volunteer (accuracy of the calculation = 98.14%) and from the both with different makeup skills (accuracy of the calculation = 95.63%) demonstrated that the visual sensing problem is feasible and will be a novel direction for the related engineering applications.</p> <p> </p>

A gut aging clock using microbiome multi-view profiles is associated with health and frail risk

ABSTRACT Age-related changes in the microbiome have been reported in previous studies; however, direct evidence for their association with frailty is lacking. Here, we introduce biological age based on gut microbiota (gAge), an integrated prediction model that integrates gut microbiota data from different perspectives with potential background factors for aging assessment. Simulation results show that, compared with a single model, the ensemble model can not only significantly improve the prediction accuracy, but also make full use of the data in unpaired samples. From this, we identified markers associated with age development and grouped markers into accelerated aging and mitigated aging according to their effect on the prediction. Importantly, the application of gAge to an elderly cohort with different frailty levels confirmed that gAge and its predictive residuals are closely related to the individual’s health status and frailty stage, and age-related markers overlap significantly with disease and frailty characteristics. Furthermore, we applied the gAge prediction model to another independent cohort of the elderly population for aging assessment and found that gAge could effectively represent the aging population. Overall, our study explains the association between the gut microbiota and frailty, providing potential targets for the development of gut microbiota-based targeted intervention strategies for aging.

Machine learning empowered prediction of geolocation using groundwater quality variables over YSR district of India

Machine Learning (ML) has been used in the prediction of geolocation with improved accuracies in this work. The pre-processed data was subjected to prediction analytics using 22 machine learning algorithms over regression mode. It was observed that Extra Trees Regressor performed well with better accuracies in predicting latitude, longitude, and Haversine distance, respectively. Regression models like CatBoost, Extreme Gradient boosting, Light Gradient boosting machine, and Gradient boosting regressor were also tested. The R2 values were computed for each case, and we obtained 0.96 (Longitude), 0.98 (Latitude), and 0.96 (Haversine), respectively. The evaluation of models was done using metrics like MAE, MASE, RMSE, R2, RMSLE, and MAPE and R2 is considered most important than others. The effect of data point was calculated using Cooks’ distance, and the variable fluoride has a significant impact on the prediction accuracy of Longitude followed by RSC, Cl, SO4, SAR, NO3, NA, Ca, EC and pH variables. In the prediction of latitude, the SAR variable played a significant role, followed by Na and TH. According to the t-SNE manifold, three longitude values were quite different from the others. This work is supported by some of the manifests like Cooks’ distance outlier detection, feature importance plot, t-SNE manifold, prediction error plot, residuals plot, RFECV plot, and validation curve. This work is done to report that the challenge of predicting both latitude and longitude on a common ground is solved partially, if not completely, and machine learning tools can be used for this purpose. Haversine distance can be obtained from latitude and longitude and can be used in the prediction of geolocation.

Robustness investigation of cross-validation based quality measures for model assessment

In this paper the accuracy and robustness of quality measures for the assessment of machine learning models are investigated. The prediction quality of a machine learning model is evaluated model-independent based on a cross-validation approach, where the approximation error is estimated for unknown data. The presented measures quantify the amount of explained variation in the model prediction. The reliability of these measures is assessed by means of several numerical examples, where an additional data set for the verification of the estimated prediction error is available. Furthermore, the confidence bounds of the presented quality measures are estimated and local quality measures are derived from the prediction residuals obtained by the cross-validation approach.

Mapping Gross Domestic Product Distribution at 1 km Resolution across Thailand Using the Random Forest Area-to-Area Regression Kriging Model

Accurate spatial distribution of gridded gross domestic product (GDP) data is crucial for revealing regional disparities within administrative units, thus facilitating a deeper understanding of regional economic dynamics, industrial distribution, and urbanization trends. The existing GDP spatial models often rely on prediction residuals for model evaluation or utilize residual distribution to improve the final accuracy, frequently overlooking the modifiable areal unit problem within residual distribution. This paper introduces a hybrid downscaling model that combines random forest and area-to-area kriging to map gridded GDP. Employing Thailand as a case study, GDP distribution maps were generated at a 1 km spatial resolution for the year 2015 and compared with five alternative downscaling methods and an existing GDP product. The results demonstrate that the proposed approach yields higher accuracy and greater precision in detailing GDP distribution, as evidenced by the smallest mean absolute error and root mean squared error values, which stand at USD 256.458 and 699.348 ten million, respectively. Among the four different sets of auxiliary variables considered, one consistently exhibited a higher prediction accuracy. This particular set of auxiliary variables integrated classification-based variables, illustrating the advantages of incorporating such integrated variables into modeling while accounting for classification characteristics.

A state detection method of offshore wind turbines’ gearbox bearing based on the transformer and GRU

Through the analysis of data from the SCADA system of a wind turbine unit in a specific offshore wind farm located in Zhanjiang, it was observed that the most prevalent type of fault is bearing alarms on the gearbox’s generator side. Considering the growing need for intelligent offshore wind turbine maintenance, this study employed GRA on SCADA data collected over a significant duration from a representative wind turbine unit. Relevant features were extracted, with temperature serving as the target parameter. To address the challenge of long-term dependencies in long-term time series forecasting tasks, this study uniquely combined the GRU with the advanced Transformer neural network which incorporates attention mechanisms, to predict the temperature trend of the gearbox’s generator-side bearing. Based on the prediction residuals obtained during normal operation and their subsequent analysis, the study devised an effective anomaly detection process to identify early abnormal states of the gearbox’s generator-side bearing. Comparative performance evaluations were conducted, comparing the combined model with its individual component models, as well as the traditional LightGBM, in terms of temperature time series prediction and their application in anomaly detection. The results unequivocally demonstrate that the combined model outperforms both the individual models and LightGBM in terms of time series prediction accuracy and anomaly detection effectiveness, indicating an enhanced ability to handle long-term memory challenges. Furthermore, the combined model exhibits great potential of practical application for the early warning of gearbox bearing anomalies during actual wind turbine daily operation and maintenance, providing a valuable solution for the offshore wind turbine industry.

Neural Network Based Rate Control for Versatile Video Coding

In this work, we propose a neural network based rate control algorithm for Versatile Video Coding (VVC). The proposed method relies on the modeling of the Rate-Quantization (R-Q) and Distortion-Quantization (D-Q) relationships in a data driven manner based upon the characteristics of prediction residuals. In particular, a pre-analysis framework is adopted, in an effort to obtain the prediction residuals which govern the Rate-Distortion (R-D) behaviors. By inferring from the prediction residuals with deep neural networks, the Coding Tree Unit (CTU) level R-Q and D-Q model parameters are derived, which could efficiently guide the optimal bit allocation. Subsequently, the coding parameters, including Quantization Parameter (QP) and λ, at both frame and CTU levels, are obtained according to allocated bit-rates. We implement the proposed rate control algorithm on VVC Test Model (VTM-13.0). Experimental results exhibit that the proposed rate control algorithm achieves 0.77% BD-Rate savings under Low Delay B (LDB) configurations when compared to the default rate control algorithm used in VTM-13.0. For Random Access (RA) configurations, 1.77% BD-Rate savings can be observed. Furthermore, with better bit-rate estimation, more stable buffer status can be observed, further demonstrating the advantages of the proposed rate control method.

Wind Turbine Gearbox Condition Monitoring Using Hybrid Attentions and Spatio-Temporal BiConvLSTM Network

Gearbox fault deterioration can significantly impact the safety, reliability, and efficiency of wind turbines, resulting in substantial economic losses for wind farms. However, current condition monitoring methods face challenges in effectively mining the hidden spatio-temporal features within SCADA data and establishing reasonable weight allocations for model input variables. To tackle these issues, we proposed a novel condition monitoring method for wind turbine gearboxes called HBCE, which integrated a feature-time hybrid attention mechanism (HA), the bidirectional convolutional long short-term memory networks (BiConvLSTM), and an improved exponentially weighted moving-average (iEWMA). Specifically, utilizing historical health SCADA data acquired through the modified Thompson tau data-cleaning algorithm, a normal behavior model (HA-BiConvLSTM) of gearbox was constructed to effectively extract the spatio-temporal features and learn normal behavior patterns. An iEWMA-based outlier detection approach was employed to set dynamic adaptive thresholds, and real-time monitor the prediction residuals of HA-BiConvLSTM to identify the early faults of gearbox. The proposed HBCE method was validated through actual gearbox faults and compared with conventional spatio-temporal models (i.e., CNN-LSTM and CNN&LSTM). The results illustrated that the constructed HA-BiConvLSTM model achieved superior prediction precision in terms of RMSE, MAE, MAPE, and R2, and the proposed method HBCE can effectively and reliably identify early anomalies of a wind turbine gearbox in advance.

Specialist hybrid models with asymmetric training for malaria prevalence prediction.

Malaria is a common and serious disease that primarily affects developing countries and its spread is influenced by a variety of environmental and human behavioral factors; therefore, accurate prevalence prediction has been identified as a critical component of the Global Technical Strategy for Malaria from 2016 to 2030. While traditional differential equation models can perform basic forecasting, supervised machine learning algorithms provide more accurate predictions, as demonstrated by a recent study using an elastic net model (REMPS). Nevertheless, current short-term prediction systems do not achieve the required accuracy levels for routine clinical practice. To improve in this direction, stacked hybrid models have been proposed, in which the outputs of several machine learning models are aggregated by using a meta-learner predictive model. In this paper, we propose an alternative specialist hybrid approach that combines a linear predictive model that specializes in the linear component of the malaria prevalence signal and a recurrent neural network predictive model that specializes in the non-linear residuals of the linear prediction, trained with a novel asymmetric loss. Our findings show that the specialist hybrid approach outperforms the current state-of-the-art stacked models on an open-source dataset containing 22 years of malaria prevalence data from the city of Ibadan in southwest Nigeria. The specialist hybrid approach is a promising alternative to current prediction methods, as well as a tool to improve decision-making and resource allocation for malaria control in high-risk countries.

Observability-Constrained Resampling-Free Cubature Kalman Filter for GNSS/INS with Measurement Outliers

Integrating global navigation satellite systems (GNSSs) with inertial navigation systems (INSs) has been widely recognized as an ideal solution for autonomous vehicle navigation. However, GNSSs suffer from disturbances and signal blocking inevitably, making the performance of GNSS/INSs degraded in the occurrence of measurement outliers. It has been proven that the sigma points-based Kalman filter (KF) performs better than an extended KF in cases where large prior uncertainty is present in the state estimation of a GNSS/INS. By modifying the sigma points directly, the resampling-free sigma point update framework (SUF) propagates more information excepting Gaussian moments of prescribed accuracy, based on which the resampling-free cubature Kalman filter (RCKF) was developed in our previous work. In order to enhance the adaptivity and robustness of the RCKF, the resampling-free SUF depending on dynamic prediction residue should be improved by suppressing the time-varying measurement outlier. In this paper, a robust observability-constrained RCKF (ROCRCKF) is proposed based on adaptive measurement noise covariance estimation and outlier detection, where the occurrence of measurement outliers is modelled by the Bernoulli variable and estimated with the state simultaneously. Experiments based on car-mounted GNSS/INSs are performed to verify the effectiveness of the ROCRCKF, and result indicates that the proposed algorithm outperforms the RCKF in the presence of measurement outliers, where the heading error and average root mean square error of the position are reduced from 1.96° and 6.38 m to 0.27° and 5.95 m, respectively. The ROCRCKF is robust against the measurement outliers and time-varying model uncertainty, making it suitable for the real-time implementation of GNSS/INSs in GNSS-challenged environments.

Monitoring Statistical Properties of Kalman Filter Residuals in an Artificial Pancreas to Detect Overnight Pump Malfunctions Causing Insulin Suspension

Continuous Subcutaneous Insulin Infusion (CSII) pumps are essential components in a closed-loop insulin delivery system (the so-called artificial pancreas), a recent therapeutic option for type 1 diabetes management. The efficacy of glucose regulation obtained by such a system might be severely compromised if the pump fails, possibly putting the patient’s safety at risk. Therefore, reliable and timely detection of these malfunctions is of critical practical importance. For this reason, in this study we present a novel algorithm specifically designed to detect overnight pump malfunctions resulting in insulin suspension. This algorithm adopts a real-time model-based approach and builds upon our team’s previous work, which relied solely on the magnitude of prediction residuals. In contrast, our current contribution extends the fault detection strategy by incorporating a comprehensive analysis of various statistical properties associated with the residuals. These properties encompass not only the magnitude but also the sample mean, median, variance, power, and other statistics related to the whiteness of the residuals. The considered linear black-box patients’ models have been individualized by estimating the model parameters on seven days of each patient’s data. Subsequently, the model is used in a Kalman filter to generate the predicted glucose levels with their confidence intervals. The effectiveness of the new strategy is compared to the previously proposed approach on an in-silico dataset generated by the UVa/Padova Type 1 Diabetes simulator, which has been accepted by the US Food and Drug Administration as a substitute for animal testing prior to human clinical trials with an artificial pancreas. The best performing detection strategy is based on the sign-sum test and achieves a recall of 91.3%, while generating less than 1 false alarm every 10 days. This improves the performance of our previous contribution that exhibits a comparable number of false alarms, but an overall lower recall metric, equal to 82.7%. The proposed algorithm is designed to complement other dedicated modules within the system, aiming to detect malfunctions related to glucose sensors (such as missed samples and pressure-induced sensitivity losses) as well as human errors (including missed meal announcements). A robustness analysis has been conducted to examine the performance of the algorithm in the presence of these additional anomalies. The results of these analyses demonstrated that the proposed algorithm maintains its sensitivity to pump malfunctions while exhibiting only a marginal increase in false alarms.

The Predictive Validity of Individualised Load-Velocity Relationships for Predicting 1RM: A Systematic Review and Individual Participant Data Meta-analysis.

Load-velocity relationships are commonly used to estimate one-repetition maximums (1RMs). Proponents suggest these estimates can be obtained at high frequencies and assist with manipulating loads according to session-by-session fluctuations. Given their increasing popularity and development of associated technologies, a range of load-velocity approaches have been investigated. This systematic review and individual participant data (IPD) meta-analysis sought to quantify the predictive validity of individualised load-velocity relationships for the purposes of 1RM prediction. In September 2022, a search of MEDLINE, SPORTDiscus, Web of Science and Scopus was conducted for published research, with Google Scholar, CORE and British Ethos also searched for unpublished research. Studies were eligible if they were written in English, and directly compared a measured and predicted 1RM using load-velocity relationships in the squat, bench press, deadlift, clean or snatch. IPD were obtained through requests to primary authors and through digitisation of in-text plots (e.g. Bland-Altman plots). Risk of bias was assessed using the Prediction model Risk Of Bias ASsessment Tool (PROBAST) and the review conducted in accordance with PRISMA-IPD guidelines and an a priori protocol. Absolute and scaled standard error of the estimates (SEE/SEE%) were calculated for two-stage aggregate analyses, with bootstrapping performed for sampling variances. Estimates were pooled using three-level hierarchical models with robust 95% confidence intervals (CIs). One-stage analyses were conducted with random intercepts to account for systematic differences across studies and prediction residuals calculated in the absolute scale (kg) and as a percentage of the measured 1RM. Moderator analyses were conducted by including a priori defined categorical variables as fixed effects. One hundred and thirty-seven models from 26 studies were included with each identified as having low, unclear or high risk of bias. Twenty studies comprising 434 participants provided sufficient data for meta-analyses, with raw data obtained for 8 (32%) studies. Two-stage analyses identified moderate predictive validity [SEE% 9.8, 95% CI 7.4% to 12.2%, with moderator analyses demonstrating limited differences based on the number of loads (β2Loads:>2Loads = 0.006, 95% CI - 1.6 to 1.6%) or the use of individual or group data to determine 1RM velocity thresholds (βGroup:Individualised = - 0.4, 95% CI - 1.9 to 1.0%)]. One-stage analyses identified that predictions tended to be overestimations (4.5, 95% CI 1.5to 7.4kg), which expressed as a percentage of measured 1RM was equal to 3.7 (95% CI 0.5 to 6.9% 1RM). Moderator analyses were consistent with those conducted for two-stage analyses. Load-velocity relationships tend to overestimate 1RMs irrespective of the modelling approach selected. On the basis of the findings from this review, practitioners should incorporate direct assessment of 1RM wherever possible. However, load-velocity relationships may still prove useful for general monitoring purposes (e.g. assessing trends across a training cycle), by providing high-frequency estimates of 1RM when direct assessment may not be logistically feasible. Given limited differences in predictions across popular load-velocity approaches, it is recommended that practitioners opting to incorporate this practice select the modelling approach that best suits their practical requirements. https://osf.io/agpfm/ .

Math-data integrated prediction model for ship maneuvering motion

Highly accurate motion prediction is critical to facilitate safe navigation and autonomous control of a ship. In this paper, a math-data integrated prediction (MDIP) model of ship maneuvering motion is newly developed by combining with mathematical and data-driven modules. The math part is identified by employing variable-order hydrodynamic derivatives which are derived from Taylor expansion. Using extended Kalman filter, an optimal-order mathematical prediction model is obtained. The data-driven part dwells on prediction residuals which are approximated by a least square-support vector machine. Furthermore, integration mechanisms are devised to cohere mathematical and data-driven models as a whole, by deploying summation and neural network approximation, respectively. By comparisons, it is verified that not only order selection but also math-data integration can enhance ship motion prediction accuracy, for which various maneuvering tests are analyzed. The results demonstrate that the proposed MDIP model using math-data integration offers much stronger generalization, thereby paving a new path for ship maneuvering motion prediction.

Stochastic modeling with robust Kalman filter for real-time kinematic GPS single-frequency positioning

The centimeter-level positioning accuracy of real-time kinematic (RTK) depends on correctly resolving integer carrier-phase ambiguities. To improve the success rate of ambiguity resolution and obtain reliable positioning results, an enhanced Kalman filtering procedure has been developed. Based on a posteriori residuals of measurements and state predictions, the measurement noise variance–covariance matrix for double-differenced measurements is adaptively estimated, rather than approximated by an empirical function which uses satellite elevation angle as input. Since, in real-world situations, unexpected outliers and carrier-phase outages can degrade the filter performance, a stochastic model based on robust Kalman filtering is proposed, for which the double-differenced measurement noise variance–covariance matrix is computed empirically with a modified version of the IGG (Institute of Geodesy and Geophysics) III method in order to detect and identify outliers. The performance of the proposed method is assessed by two tests, one with simulated data and one with real data. In addition, the performance of F-ratio and W-ratio tests as proxies for the success of ambiguity fixing is investigated. Experimental results reveal that the proposed method can improve the reliability and robustness of relative kinematic positioning for simulation scenarios as well as in a real urban test.

Fault detection in wind turbine generators using a meta-learning-based convolutional neural network

Conventional fault detection methods for wind turbine (WT) generators often grapple with inadequate warning times and poor portability. These issues contribute to heightened safety risks and an increased false positive rate (FPR) and false negative rate (FNR). This study introduces a fault detection method for WT generators utilizing a 1D convolutional neural network (1DCNN) based on meta-learning principles. We incorporate the ”learning to learn” concept of model-agnostic meta-learning (MAML) into a 1DCNN, enabling effective fault detection. More specifically, the training data are transformed into numerous tasks through random sampling, and the model is trained task by task. The 1DCNN is utilized as the base learner, leveraging its superior feature extraction capability to discern task features. The first-order gradient of MAML is applied to ascertain the specific initialization parameters for each task, while the second-order gradient of MAML is used to understand the similarities and differences between all tasks’ initialization parameters. This approach equips the 1DCNN-MAML with the ability to adapt to new tasks and converge rapidly, thereby achieving swift regression prediction. We also employ the probability distribution fitting method to analyze the distribution of prediction residuals, thus setting the detection threshold. Based on this threshold, warnings can be issued for faults in WT generators. We used supervisory control and data acquisition (SCADA) data from the Liaoning wind farm in China to validate the robustness and portability of the proposed model. Experimental outcomes indicate that, compared with Reptile, FOMAML, LSTM-MAML, 1DCNN, and LSTM, our proposed method can detect faults earliest across different wind turbines and has the lowest FPR and FNR.

Physics-Guided Deep Learning for Improved Production Forecasting in Unconventional Reservoirs

Summary The complexity of physics-based modeling of fluid flow in hydraulically fractured unconventional reservoirs, together with the abundant data from repeated factory-style drilling and completion of these resources, has prompted the development and application of data-driven statistical models for predicting hydrocarbon production performance. More recently, machine learning algorithms have been widely studied in developing data-driven prediction models for unconventional reservoirs. These models often require a large amount of high-quality training data with sufficient range to avoid excessive extrapolation and produce reliable predictions. Unlike statistical models, physics-based models represent causal relations between input and output variables to provide predictions beyond available data. While a detailed physics-based description of fluid flow in unconventional reservoirs is not yet available, approximate physical flow functions have been proposed to capture the general production behavior of unconventional wells. These physical functions can be augmented with the available data to improve data-driven methods by constraining the models to adhere to the general production trends. In this paper, we develop a physics-constrained data-driven model by embedding physical flow functions into neural network models. Since the performance of the physics-constrained model depends on the relevance of the embedded physics, a sizeable residual prediction error is expected if the collected data do not sufficiently match the embedded model. The residual model typically represents errors in the description of inputs or any missing physical phenomenon. We compensate for such errors through residual learning, where an auxiliary neural network is designed to learn the complex relationship between the input parameters (such as formation and completion properties) and the expected prediction residuals. The new physics-guided deep learning (PGDL) model augments any physics-constrained prediction model with residual learning to increase its prediction accuracy. Several synthetic and actual field data sets, from the Bakken play, are used to demonstrate the performance of the PGDL model.

Gamma generalized linear model‐based control charts for high‐purity processes

AbstractStatistical process monitoring of high‐purity manufacturing processes becomes challenging if the defect rate depends on the fluctuations of a set of covariates (e.g., inspected weight, volume, temperature). This paper applies the generalized linear model framework to statistical process control for detecting contextual anomalies in high‐purity processes. Different types of predictive residuals (i.e., Pearson, deviance, and quantile) and recursive residuals are considered, and the performance of these schemes is compared via a simulation study.

Early identification of process deviation based on convolutional neural network

A novel process monitoring method based on convolutional neural network (CNN) is proposed and applied to detect faults in industrial process. By utilizing the CNN algorithm, cross-correlation and autocorrelation among variables are captured to establish a prediction model for each process variable to approximate the first-principle of physical/chemical relationships among different variables under normal operating conditions. When the process is operated under pre-set operating conditions, prediction residuals can be assumed as noise if a proper model is employed. Once process faults occur, the residuals will increase due to the changes of correlation among variables. A principal component analysis (PCA) model based on the residuals is established to realize process monitoring. By monitoring the changes in main feature of prediction residuals, the faults can be promptly detected. Case studies on a numerical nonlinear example and data from two industrial processes are presented to validate the performance of process monitoring based on CNN.

Elemental Abundances of Kepler Objects of Interest in APOGEE DR17

The elemental abundances of planet host stars can shed light on the conditions of planet forming environments. We test if individual abundances of 130 known/candidate planet hosts in APOGEE are statistically different from those of a reference doppelgänger sample. The reference set comprises objects selected with the same T eff, , [Fe/H], and [Mg/H] as each Kepler Object of Interest (KOI). We predict twelve individual abundances (X = C, N, O, Na, Al, Si, Ca, Ti, V, Cr, Mn, Ni) for the KOIs and their doppelgängers using a local linear model of these four parameters, training on ASPCAP abundance measurements for a sample of field stars with high-fidelity (signal-to-noise ratio > 200) APOGEE observations. We compare element prediction residuals (model–measurement) for the two samples and find them to be indistinguishable, given a high-quality sample selection. We report median intrinsic dispersions of ∼0.038 dex and ∼0.041 dex, for the KOI and doppelgänger samples, respectively, for these elements. We conclude that the individual abundances at fixed T eff, , [Fe/H], and [Mg/H] are unremarkable for known planet hosts. Our results establish an upper limit on the abundance precision required to uncover any chemical signatures of planet formation in planet host stars.

A mathematical model for the spread of Omicron virus based on grey prediction algorithm

After two years of the Newcastle epidemic, the emergence of a mutant strain of Omicron virus has once again raised a high level of alarm worldwide, and it has rapidly replaced the Delta strain as the major strain in the world epidemic with high infectivity. In order to study the spread of the epidemic in a qualitative and quantitative manner, this paper uses relevant mathematical modeling ideas and methods, combined with the background of big data, to conduct relevant research and analysis in order to provide guidance for the actual fight against the epidemic and facilitate scientific research and response measures. In this paper, a gray prediction algorithm is used to predict the future epidemic data. A metabolic algorithm is introduced to recursively correct the prediction residuals and build a multilevel gray model. In this paper, to investigate the role of vaccines on epidemics, the R values under each dose of vaccine were calculated by selecting data from several countries and regions using fitted curve idealization. The prediction of the data yields the conclusion that vaccination is indeed directly effective in controlling the spread of the epidemic.