Multi-scale prediction of MEMS gyroscope random drift based on EMD-SVR

To improve the prediction accuracy of micro-electromechanical systems(MEMS)gyroscope random drift series,a multi-scale prediction model based on empirical mode decomposition(EMD)and support vector regression(SVR)is proposed.Firstly,EMD is employed to decompose the raw drift series into a finite number of intrinsic mode functions(IMFs)with the frequency descending successively.Secondly,according to the time-frequency characteristic of each IMF,the corresponding SVR prediction model is established based on phase space reconstruction.Finally,the prediction results are obtained by adding up the prediction results of all IMFs with equal weight.The experimental results demonstrate the validity of the proposed model in random drift prediction of MEMS gyroscope.Compared with a single SVR model,the proposed model has higher prediction precision,which can provide the basis for drift error compensation of MEMS gyroscope.

Attention-Based Multi-Scale Prediction Network for Time-Series Data

Time series data is a kind of data accumulated over time,which can describe the change of phenomenon.This kind of data reflects the degree of change of a certain thing or phenomenon.The existing technologies such as LSTM and ARIMA are better than convolutional neural network in time series prediction,but they are not enough to mine the periodicity of data.In this article,we perform periodic analysis on two types of time series data,select time metrics with high periodic characteristics,and propose a multi-scale prediction model based on the attention mechanism for the periodic trend of the data.A loss calculation method for traffic time series characteristics is proposed as well.Multiple experiments have been conducted on actual data sets.The experiments show that the method proposed in this paper has better performance than commonly used traffic prediction methods(ARIMA,LSTM,etc.)and 3%-5%increase on MAPE.

Multi-scale persistent spatiotemporal transformer for long-term urban traffic flow prediction

Long-term urban traffic flow prediction is an important task in the field of intelligent transportation,as it can help optimize traffic management and improve travel efficiency.To improve prediction accuracy,a crucial issue is how to model spatiotemporal dependency in urban traffic data.In recent years,many studies have adopted spatiotemporal neural networks to extract key information from traffic data.However,most models ignore the semantic spatial similarity between long-distance areas when mining spatial dependency.They also ignore the impact of predicted time steps on the next unpredicted time step for making long-term predictions.Moreover,these models lack a comprehensive data embedding process to represent complex spatiotemporal dependency.This paper proposes a multi-scale persistent spatiotemporal transformer(MSPSTT)model to perform accurate long-term traffic flow prediction in cities.MSPSTT adopts an encoder-decoder structure and incorporates temporal,periodic,and spatial features to fully embed urban traffic data to address these issues.The model consists of a spatiotemporal encoder and a spatiotemporal decoder,which rely on temporal,geospatial,and semantic space multi-head attention modules to dynamically extract temporal,geospatial,and semantic characteristics.The spatiotemporal decoder combines the context information provided by the encoder,integrates the predicted time step information,and is iteratively updated to learn the correlation between different time steps in the broader time range to improve the model’s accuracy for long-term prediction.Experiments on four public transportation datasets demonstrate that MSPSTT outperforms the existing models by up to 9.5%on three common metrics.

Multi-Scale Location Attention Model for Spatio-Temporal Prediction of Disease Incidence

Due to the increasingly severe challenges brought by various epidemic diseases,people urgently need intelligent outbreak trend prediction.Predicting disease onset is very important to assist decision-making.Most of the exist-ing work fails to make full use of the temporal and spatial characteristics of epidemics,and also relies on multi-variate data for prediction.In this paper,we propose a Multi-Scale Location Attention Graph Neural Networks(MSLAGNN)based on a large number of Centers for Disease Control and Prevention(CDC)patient electronic medical records research sequence source data sets.In order to understand the geography and timeliness of infec-tious diseases,specific neural networks are used to extract the geography and timeliness of infectious diseases.In the model framework,the features of different periods are extracted by a multi-scale convolution module.At the same time,the propagation effects between regions are simulated by graph convolution and attention mechan-isms.We compare the proposed method with the most advanced statistical methods and deep learning models.Meanwhile,we conduct comparative experiments on data sets with different time lengths to observe the predic-tion performance of the model in the face of different degrees of data collection.We conduct extensive experi-ments on real-world epidemic-related data sets.The method has strong prediction performance and can be readily used for epidemic prediction.

Dynamic evolution and trend prediction of multi-scale green innovation in China

Numerous studies deal with spatial analysis of green innovation(GI).However,researchers have paid limited attention to analyzing the multi-scale evolution patterns and predicting trends of GI in China.This paper seeks to address this research gap by examining the multi-scale distribution and evolutionary characteristics of GI activities based on the data from 337 cities in China during 2000-2019.We used scale variance and the two-stage nested Theil decomposition method to examine the spatial distribution and inequalities of GI in China at multiple scales,including regional,provincial,and prefectural.Additionally,we utilized the Markov chain and spatial Markov chain to explore the dynamic evolution of GI in China and predict its long-term development.The findings indicate that GI in China has a multi-scale effect and is highly sensitive to changes in spatial scale,with significant spatial differences of GI decreasing in each scale.Furthermore,the spatiotemporal evolution of GI is influenced by both geospatial patterns and spatial scales,exhibiting the“club convergence”effect and a tendency to transfer to higher levels of proximity.This effect is more pronounced on a larger scale,but it is increasingly challenging to transfer to higher levels.The study also indicates a steady and sustained growth of GI in China,which concentrates on higher levels over time.These results contribute to a more precise understanding of the scale at which GI develops and provide a scientific basis and policy suggestions for optimizing the spatial structure of GI and promoting its development in China.

Rockburst Intensity Grade Prediction Model Based on Batch Gradient Descent and Multi-Scale Residual Deep Neural Network

Rockburst is a phenomenon in which free surfaces are formed during excavation,which subsequently causes the sudden release of energy in the construction of mines and tunnels.Light rockburst only peels off rock slices without ejection,while severe rockburst causes casualties and property loss.The frequency and degree of rockburst damage increases with the excavation depth.Moreover,rockburst is the leading engineering geological hazard in the excavation process,and thus the prediction of its intensity grade is of great significance to the development of geotechnical engineering.Therefore,the prediction of rockburst intensity grade is one problem that needs to be solved urgently.By comprehensively considering the occurrence mechanism of rockburst,this paper selects the stress index(σθ/σc),brittleness index(σ_(c)/σ_(t)),and rock elastic energy index(Wet)as the rockburst evaluation indexes through the Spearman coefficient method.This overcomes the low accuracy problem of a single evaluation index prediction method.Following this,the BGD-MSR-DNN rockburst intensity grade prediction model based on batch gradient descent and a multi-scale residual deep neural network is proposed.The batch gradient descent(BGD)module is used to replace the gradient descent algorithm,which effectively improves the efficiency of the network and reduces the model training time.Moreover,the multi-scale residual(MSR)module solves the problem of network degradation when there are too many hidden layers of the deep neural network(DNN),thus improving the model prediction accuracy.The experimental results reveal the BGDMSR-DNN model accuracy to reach 97.1%,outperforming other comparable models.Finally,actual projects such as Qinling Tunnel and Daxiangling Tunnel,reached an accuracy of 100%.The model can be applied in mines and tunnel engineering to realize the accurate and rapid prediction of rockburst intensity grade.

Multi-scale Incremental Analysis Update Scheme and Its Application to Typhoon Mangkhut(2018)Prediction

In the traditional incremental analysis update(IAU)process,all analysis increments are treated as constant forcing in a model’s prognostic equations over a certain time window.This approach effectively reduces high-frequency oscillations introduced by data assimilation.However,as different scales of increments have unique evolutionary speeds and life histories in a numerical model,the traditional IAU scheme cannot fully meet the requirements of short-term forecasting for the damping of high-frequency noise and may even cause systematic drifts.Therefore,a multi-scale IAU scheme is proposed in this paper.Analysis increments were divided into different scale parts using a spatial filtering technique.For each scale increment,the optimal relaxation time in the IAU scheme was determined by the skill of the forecasting results.Finally,different scales of analysis increments were added to the model integration during their optimal relaxation time.The multi-scale IAU scheme can effectively reduce the noise and further improve the balance between large-scale and small-scale increments in the model initialization stage.To evaluate its performance,several numerical experiments were conducted to simulate the path and intensity of Typhoon Mangkhut(2018)and showed that:(1)the multi-scale IAU scheme had an obvious effect on noise control at the initial stage of data assimilation;(2)the optimal relaxation time for large-scale and small-scale increments was estimated as 6 h and 3 h,respectively;(3)the forecast performance of the multi-scale IAU scheme in the prediction of Typhoon Mangkhut(2018)was better than that of the traditional IAU scheme.The results demonstrate the superiority of the multi-scale IAU scheme.

The application study on the multi-scales integrated prediction method to fractured reservoir description

In this paper,we implement three scales of fracture integrated prediction study by classifying it to macro-（ 1/4/λ）,meso-（ 1/100λ and 1/4λ） and micro-（ 1/100λ） scales.Based on the multi-scales rock physics modelling technique,the seismic azimuthal anisotropy characteristic is analyzed for distinguishing the fractures of meso-scale.Furthermore,by integrating geological core fracture description,image well-logging fracture interpretation,seismic attributes macro-scale fracture prediction and core slice micro-scale fracture characterization,an comprehensive multi-scale fracture prediction methodology and technique workflow are proposed by using geology,well-logging and seismic multi-attributes.Firstly,utilizing the geology core slice observation（Fractures description） and image well-logging data interpretation results,the main governing factors of fracture development are obtained,and then the control factors of the development of regional macro-scale fractures are carried out via modelling of the tectonic stress field.For the meso-scale fracture description,the poststack geometric attributes are used to describe the macro-scale fracture as well,the prestack attenuation seismic attribute is used to predict the meso-scale fracture.Finally,by combining lithological statistic inversion with superposed results of faults,the relationship of the meso-scale fractures,lithology and faults can be reasonably interpreted and the cause of meso-scale fractures can be verified.The micro-scale fracture description is mainly implemented by using the electron microscope scanning of cores.Therefore,the development of fractures in reservoirs is assessed by valuating three classes of fracture prediction results.An integrated fracture prediction application to a real field in Sichuan basin,where limestone reservoir fractures developed,is implemented.The application results in the study area indicates that the proposed multi-scales integrated fracture prediction method and the technique procedureare able to deal with the strong heterogeneity and multi-scales problems in fracture prediction.Moreover,the multi-scale fracture prediction technique integrated with geology,well-logging and seismic multi-information can help improve the reservoir characterization and sweet-spots prediction for the fractured hydrocarbon reservoirs.

A semi-analytical model for coupled flow in stress-sensitive multi-scale shale reservoirs with fractal characteristics

A large number of nanopores and complex fracture structures in shale reservoirs results in multi-scale flow of oil. With the development of shale oil reservoirs, the permeability of multi-scale media undergoes changes due to stress sensitivity, which plays a crucial role in controlling pressure propagation and oil flow. This paper proposes a multi-scale coupled flow mathematical model of matrix nanopores, induced fractures, and hydraulic fractures. In this model, the micro-scale effects of shale oil flow in fractal nanopores, fractal induced fracture network, and stress sensitivity of multi-scale media are considered. We solved the model iteratively using Pedrosa transform, semi-analytic Segmented Bessel function, Laplace transform. The results of this model exhibit good agreement with the numerical solution and field production data, confirming the high accuracy of the model. As well, the influence of stress sensitivity on permeability, pressure and production is analyzed. It is shown that the permeability and production decrease significantly when induced fractures are weakly supported. Closed induced fractures can inhibit interporosity flow in the stimulated reservoir volume (SRV). It has been shown in sensitivity analysis that hydraulic fractures are beneficial to early production, and induced fractures in SRV are beneficial to middle production. The model can characterize multi-scale flow characteristics of shale oil, providing theoretical guidance for rapid productivity evaluation.

Multi-scale physics-informed neural networks for solving high Reynolds number boundary layer flows based on matched asymptotic expansions

Multi-scale system remains a classical scientific problem in fluid dynamics,biology,etc.In the present study,a scheme of multi-scale Physics-informed neural networks is proposed to solve the boundary layer flow at high Reynolds numbers without any data.The flow is divided into several regions with different scales based on Prandtl's boundary theory.Different regions are solved with governing equations in different scales.The method of matched asymptotic expansions is used to make the flow field continuously.A flow on a semi infinite flat plate at a high Reynolds number is considered a multi-scale problem because the boundary layer scale is much smaller than the outer flow scale.The results are compared with the reference numerical solutions,which show that the msPINNs can solve the multi-scale problem of the boundary layer in high Reynolds number flows.This scheme can be developed for more multi-scale problems in the future.

Prediction model for corrosion rate of low-alloy steels under atmospheric conditions using machine learning algorithms

This work constructed a machine learning(ML)model to predict the atmospheric corrosion rate of low-alloy steels(LAS).The material properties of LAS,environmental factors,and exposure time were used as the input,while the corrosion rate as the output.6 dif-ferent ML algorithms were used to construct the proposed model.Through optimization and filtering,the eXtreme gradient boosting(XG-Boost)model exhibited good corrosion rate prediction accuracy.The features of material properties were then transformed into atomic and physical features using the proposed property transformation approach,and the dominant descriptors that affected the corrosion rate were filtered using the recursive feature elimination(RFE)as well as XGBoost methods.The established ML models exhibited better predic-tion performance and generalization ability via property transformation descriptors.In addition,the SHapley additive exPlanations(SHAP)method was applied to analyze the relationship between the descriptors and corrosion rate.The results showed that the property transformation model could effectively help with analyzing the corrosion behavior,thereby significantly improving the generalization ability of corrosion rate prediction models.

A Physics-informed Deep-learning Intensity Prediction Scheme for Tropical Cyclones over the Western North Pacific

Accurate prediction of tropical cyclone(TC)intensity is challenging due to the complex physical processes involved.Here,we introduce a new TC intensity prediction scheme for the western North Pacific(WNP)based on a time-dependent theory of TC intensification,termed the energetically based dynamical system(EBDS)model,together with the use of a long short-term memory(LSTM)neural network.In time-dependent theory,TC intensity change is controlled by both the internal dynamics of the TC system and various environmental factors,expressed as environmental dynamical efficiency.The LSTM neural network is used to predict the environmental dynamical efficiency in the EBDS model trained using besttrack TC data and global reanalysis data during 1982–2017.The transfer learning and ensemble methods are used to retrain the scheme using the environmental factors predicted by the Global Forecast System(GFS)of the National Centers for Environmental Prediction during 2017–21.The predicted environmental dynamical efficiency is finally iterated into the EBDS equations to predict TC intensity.The new scheme is evaluated for TC intensity prediction using both reanalysis data and the GFS prediction data.The intensity prediction by the new scheme shows better skill than the official prediction from the China Meteorological Administration(CMA)and those by other state-of-art statistical and dynamical forecast systems,except for the 72-h forecast.Particularly at the longer lead times of 96 h and 120 h,the new scheme has smaller forecast errors,with a more than 30%improvement over the official forecasts.

ST-LSTM-SA:A New Ocean Sound Velocity Field Prediction Model Based on Deep Learning

The scarcity of in-situ ocean observations poses a challenge for real-time information acquisition in the ocean.Among the crucial hydroacoustic environmental parameters,ocean sound velocity exhibits significant spatial and temporal variability and it is highly relevant to oceanic research.In this study,we propose a new data-driven approach,leveraging deep learning techniques,for the prediction of sound velocity fields(SVFs).Our novel spatiotemporal prediction model,STLSTM-SA,combines Spatiotemporal Long Short-Term Memory(ST-LSTM) with a self-attention mechanism to enable accurate and real-time prediction of SVFs.To circumvent the limited amount of observational data,we employ transfer learning by first training the model using reanalysis datasets,followed by fine-tuning it using in-situ analysis data to obtain the final prediction model.By utilizing the historical 12-month SVFs as input,our model predicts the SVFs for the subsequent three months.We compare the performance of five models:Artificial Neural Networks(ANN),Long ShortTerm Memory(LSTM),Convolutional LSTM(ConvLSTM),ST-LSTM,and our proposed ST-LSTM-SA model in a test experiment spanning 2019 to 2022.Our results demonstrate that the ST-LSTM-SA model significantly improves the prediction accuracy and stability of sound velocity in both temporal and spatial dimensions.The ST-LSTM-SA model not only accurately predicts the ocean sound velocity field(SVF),but also provides valuable insights for spatiotemporal prediction of other oceanic environmental variables.

Assessments of Data-Driven Deep Learning Models on One-Month Predictions of Pan-Arctic Sea Ice Thickness

In recent years,deep learning methods have gradually been applied to prediction tasks related to Arctic sea ice concentration,but relatively little research has been conducted for larger spatial and temporal scales,mainly due to the limited time coverage of observations and reanalysis data.Meanwhile,deep learning predictions of sea ice thickness(SIT)have yet to receive ample attention.In this study,two data-driven deep learning(DL)models are built based on the ConvLSTM and fully convolutional U-net(FC-Unet)algorithms and trained using CMIP6 historical simulations for transfer learning and fine-tuned using reanalysis/observations.These models enable monthly predictions of Arctic SIT without considering the complex physical processes involved.Through comprehensive assessments of prediction skills by season and region,the results suggest that using a broader set of CMIP6 data for transfer learning,as well as incorporating multiple climate variables as predictors,contribute to better prediction results,although both DL models can effectively predict the spatiotemporal features of SIT anomalies.Regarding the predicted SIT anomalies of the FC-Unet model,the spatial correlations with reanalysis reach an average level of 89%over all months,while the temporal anomaly correlation coefficients are close to unity in most cases.The models also demonstrate robust performances in predicting SIT and SIE during extreme events.The effectiveness and reliability of the proposed deep transfer learning models in predicting Arctic SIT can facilitate more accurate pan-Arctic predictions,aiding climate change research and real-time business applications.

Software Defect Prediction Method Based on Stable Learning

The purpose of software defect prediction is to identify defect-prone code modules to assist software quality assurance teams with the appropriate allocation of resources and labor.In previous software defect prediction studies,transfer learning was effective in solving the problem of inconsistent project data distribution.However,target projects often lack sufficient data,which affects the performance of the transfer learning model.In addition,the presence of uncorrelated features between projects can decrease the prediction accuracy of the transfer learning model.To address these problems,this article propose a software defect prediction method based on stable learning(SDP-SL)that combines code visualization techniques and residual networks.This method first transforms code files into code images using code visualization techniques and then constructs a defect prediction model based on these code images.During the model training process,target project data are not required as prior knowledge.Following the principles of stable learning,this paper dynamically adjusted the weights of source project samples to eliminate dependencies between features,thereby capturing the“invariance mechanism”within the data.This approach explores the genuine relationship between code defect features and labels,thereby enhancing defect prediction performance.To evaluate the performance of SDP-SL,this article conducted comparative experiments on 10 open-source projects in the PROMISE dataset.The experimental results demonstrated that in terms of the F-measure,the proposed SDP-SL method outperformed other within-project defect prediction methods by 2.11%-44.03%.In cross-project defect prediction,the SDP-SL method provided an improvement of 5.89%-25.46% in prediction performance compared to other cross-project defect prediction methods.Therefore,SDP-SL can effectively enhance within-and cross-project defect predictions.

An adaptive physics-informed deep learning method for pore pressure prediction using seismic data

Accurate prediction of formation pore pressure is essential to predict fluid flow and manage hydrocarbon production in petroleum engineering.Recent deep learning technique has been receiving more interest due to the great potential to deal with pore pressure prediction.However,most of the traditional deep learning models are less efficient to address generalization problems.To fill this technical gap,in this work,we developed a new adaptive physics-informed deep learning model with high generalization capability to predict pore pressure values directly from seismic data.Specifically,the new model,named CGP-NN,consists of a novel parametric features extraction approach(1DCPP),a stacked multilayer gated recurrent model(multilayer GRU),and an adaptive physics-informed loss function.Through machine training,the developed model can automatically select the optimal physical model to constrain the results for each pore pressure prediction.The CGP-NN model has the best generalization when the physicsrelated metricλ=0.5.A hybrid approach combining Eaton and Bowers methods is also proposed to build machine-learnable labels for solving the problem of few labels.To validate the developed model and methodology,a case study on a complex reservoir in Tarim Basin was further performed to demonstrate the high accuracy on the pore pressure prediction of new wells along with the strong generalization ability.The adaptive physics-informed deep learning approach presented here has potential application in the prediction of pore pressures coupled with multiple genesis mechanisms using seismic data.

Flood Velocity Prediction Using Deep Learning Approach

Floods are one of the most serious natural disasters that can cause huge societal and economic losses.Extensive research has been conducted on topics like flood monitoring,prediction,and loss estimation.In these research fields,flood velocity plays a crucial role and is an important factor that influences the reliability of the outcomes.Traditional methods rely on physical models for flood simulation and prediction and could generate accurate results but often take a long time.Deep learning technology has recently shown significant potential in the same field,especially in terms of efficiency,helping to overcome the time-consuming associated with traditional methods.This study explores the potential of deep learning models in predicting flood velocity.More specifically,we use a Multi-Layer Perceptron(MLP)model,a specific type of Artificial Neural Networks(ANNs),to predict the velocity in the test area of the Lundesokna River in Norway with diverse terrain conditions.Geographic data and flood velocity simulated based on the physical hydraulic model are used in the study for the pre-training,optimization,and testing of the MLP model.Our experiment indicates that the MLP model has the potential to predict flood velocity in diverse terrain conditions of the river with acceptable accuracy against simulated velocity results but with a significant decrease in training time and testing time.Meanwhile,we discuss the limitations for the improvement in future work.

Mapping Network-Coordinated Stacked Gated Recurrent Units for Turbulence Prediction

Accurately predicting fluid forces acting on the sur-face of a structure is crucial in engineering design.However,this task becomes particularly challenging in turbulent flow,due to the complex and irregular changes in the flow field.In this study,we propose a novel deep learning method,named mapping net-work-coordinated stacked gated recurrent units(MSU),for pre-dicting pressure on a circular cylinder from velocity data.Specifi-cally,our coordinated learning strategy is designed to extract the most critical velocity point for prediction,a process that has not been explored before.In our experiments,MSU extracts one point from a velocity field containing 121 points and utilizes this point to accurately predict 100 pressure points on the cylinder.This method significantly reduces the workload of data measure-ment in practical engineering applications.Our experimental results demonstrate that MSU predictions are highly similar to the real turbulent data in both spatio-temporal and individual aspects.Furthermore,the comparison results show that MSU predicts more precise results,even outperforming models that use all velocity field points.Compared with state-of-the-art methods,MSU has an average improvement of more than 45%in various indicators such as root mean square error(RMSE).Through comprehensive and authoritative physical verification,we estab-lished that MSU’s prediction results closely align with pressure field data obtained in real turbulence fields.This confirmation underscores the considerable potential of MSU for practical applications in real engineering scenarios.The code is available at https://github.com/zhangzm0128/MSU.

Product quality prediction based on RBF optimized by firefly algorithm

With the development of information technology,a large number of product quality data in the entire manufacturing process is accumulated,but it is not explored and used effectively.The traditional product quality prediction models have many disadvantages,such as high complexity and low accuracy.To overcome the above problems,we propose an optimized data equalization method to pre-process dataset and design a simple but effective product quality prediction model:radial basis function model optimized by the firefly algorithm with Levy flight mechanism(RBFFALM).First,the new data equalization method is introduced to pre-process the dataset,which reduces the dimension of the data,removes redundant features,and improves the data distribution.Then the RBFFALFM is used to predict product quality.Comprehensive expe riments conducted on real-world product quality datasets validate that the new model RBFFALFM combining with the new data pre-processing method outperforms other previous me thods on predicting product quality.

A modified stochastic model for LS+AR hybrid method and its application in polar motion short-term prediction

Short-term(up to 30 days)predictions of Earth Rotation Parameters(ERPs)such as Polar Motion(PM:PMX and PMY)play an essential role in real-time applications related to high-precision reference frame conversion.Currently,least squares(LS)+auto-regressive(AR)hybrid method is one of the main techniques of PM prediction.Besides,the weighted LS+AR hybrid method performs well for PM short-term prediction.However,the corresponding covariance information of LS fitting residuals deserves further exploration in the AR model.In this study,we have derived a modified stochastic model for the LS+AR hybrid method,namely the weighted LS+weighted AR hybrid method.By using the PM data products of IERS EOP 14 C04,the numerical results indicate that for PM short-term forecasting,the proposed weighted LS+weighted AR hybrid method shows an advantage over both the LS+AR hybrid method and the weighted LS+AR hybrid method.Compared to the mean absolute errors(MAEs)of PMX/PMY sho rt-term prediction of the LS+AR hybrid method and the weighted LS+AR hybrid method,the weighted LS+weighted AR hybrid method shows average improvements of 6.61%/12.08%and 0.24%/11.65%,respectively.Besides,for the slopes of the linear regression lines fitted to the errors of each method,the growth of the prediction error of the proposed method is slower than that of the other two methods.