Single-layer Model Research Articles

Hemispheric prediction of solar cycle 25 based on a deep learning technique

In the current work, single-and double-layered Long Short-Term Memory (LSTM) model have been developed and compared to find the most suitable one for hemispheric prediction of solar cycle 25. The smoothed Hemispheric Sunspot Number (HSN) reconstructed by Veronig et al. (2021) has been used to achieve the objective. The deep learning models are evaluated over different pairs of train and test set for both the hemispheres using the 5-fold cross-validation scheme, to determine the best effective model for hemispheric prediction of cycle 25. Our analysis reveals that the single-layered LSTM model achieves lower RMSE when predicting the test dataset. To prove the reliability of our suggested LSTM models, we have predicted the hemispheric profiles of solar cycles 21–24. From our analysis, we found that the single-layered LSTM model performed better in comparison to the double-layered LSTM model in predicting past solar cycles 21–24. Hence, hemispheric prediction of solar cycle 25 is carried out utilizing the single-layered LSTM model due to better performance capability during experimental analysis. This work founds that the northern hemisphere will peak with an amplitude of 56 ± 5 during July 2023 + 3 months while the southern hemisphere will have a maximum amplitude of 54 ± 4 during June 2023 + 2 months. So, it can be said that the southern HSN will peak before the northern HSN and that the peak of northern HSN will be slightly higher than the southern one.

Optimal Operation Strategy of Community Integrated Energy System Based on a Two-level Game

With the gradual transformation of the integrated energy system to intelligence and decentralization, users with distributed generation gradually replace traditional users. To realize the rationality of multi-agent power transactions in a community-integrated energy system and improve the income of each subject in the system, this paper presents the optimal operation strategy of a community-integrated energy system based on the two-level game. The first layer is a cooperative game between energy communities, which can promote the consumption of new energy in communities. The second layer is a master-slave game between operators and communities, which can promote effective interaction between the upper and lower levels. By using the Karush-Kuhn-Tucker condition, the two-layer model is transformed into a single-layer model and uses McCormick to relax the model. The example verifies that the trading strategy proposed in this paper can effectively improve the benefits of each energy community.

Evaluation of The Influence of an Aquaculture Basin on Water Resource Management Through The use of a Geographic Information System and The FREEWAT Modelling Tool: A Case Study in The El Tarf Region (Northeast Algeria)

The study area belongs to the Bouteldja plain in the northeast of Algeria that experiences a cold and rainy Mediterranean climate during winters alongside a hot and dry summer. As per the potentiometric map, the movement of groundwater is towards the east. During model development, a single-layer numerical model was created with the aid of the MODFLOW-2005 code and the FREEWAT modeling tool. Some GIS features were executed on the model in a steady-state condition through the hydrological year of 2020. MODFLOW Well (WEL) and MODFLOW Recharge (RCH) models were successively utilized to simulate groundwater extraction and recharge. Analysis of pumping test data indicates that the total contribution via the western boundary is lower than the term of extraction because of over-pumping. The simulation analyses of the water balance and groundwater recharge following the installation of the aquaculture basin, with or without pumping, demonstrate a reduction in hydraulic load in the area near the wells. As a result, the exploitation rate of these resources might amount to or even exceed their renewal rate. In conclusion, our work proposes a modeling approach to simulate the impact of an aquifer recharge management program by adding an aquaculture basin for a dual purpose: the development of fishery resources and agriculture in rural areas.

A global 5 km monthly potential evapotranspiration dataset (1982–2015) estimated by the Shuttleworth–Wallace model

Abstract. As the theoretical upper bound of evapotranspiration (ET) or water use by ecosystems, potential ET (PET) has always been widely used as a variable linking a variety of disciplines, such as climatology, ecology, hydrology, and agronomy. However, substantial uncertainties exist in the current PET methods (e.g., empiric models and single-layer models) and datasets because of unrealistic configurations of land surface and unreasonable parameterizations. Therefore, this study comprehensively considered interspecific differences in various vegetation-related parameters (e.g., plant stomatal resistance and CO2 effects on stomatal resistance) to calibrate and parametrize the Shuttleworth–Wallace (SW) model for forests, shrubland, grassland, and cropland. We derived the parameters using identified daily ET observations with no water stress (i.e., PET) at 96 eddy covariance (EC) sites across the globe. Model validations suggest that the calibrated model could be transferable from known observations to any location. Based on four popular meteorological datasets, relatively realistic canopy height, time-varying land use or land cover, and the leaf area index, we generated a global 5 km ensemble mean monthly PET dataset that includes two components of potential transpiration (PT) and soil evaporation (PE) for the 1982–2015 time period. Using this new dataset, the climatological characteristics of PET partitioning and the spatiotemporal changes in PET, PE, and PT were investigated. The global mean annual PET was 1198.96 mm with PT/PET of 41 % and PE/PET of 59 %, controlled moreover by PT and PE of over 41 % and 59 % of the globe, respectively. Globally, the annual PET and PT significantly (p<0.05) increase by 1.26 and 1.27 mm yr−1 over the last 34 years, followed by a slight decrease in the annual PE. Overall, the annual PET changes over 53 % of the globe could be attributed to PT, and the rest to PE. The new PET dataset may be used by academic communities and various agencies to conduct climatological analyses, hydrological modeling, drought studies, agricultural water management, and biodiversity conservation. The dataset is available at https://doi.org/10.11888/Terre.tpdc.300193 (Sun et al., 2023).

XCNN-SC: Explainable CNN for SARS-CoV-2 variants classification and mutation detection

The COVID-19 pandemic spread rapidly all over the world in 2019, causing the deaths of millions of people. One of the main challenges in controlling the pandemic was the high rate of virus mutation, which evaded the immune system and reduced the vaccine's effectiveness. Due to the differences in symptoms, transmission and mortality rate, and effective prevention strategies of each variant, identifying and classifying different variants is a great necessity. In the present study, 82802 whole genomes of Alpha, Beta, Delta, Eta, Epsilon, Lota, and Omicron variants of SARS-CoV-2 were obtained from the NCBI database. The label encoding method was applied to convert the genomic sequences to numeric sequences. Then, a single-layer 1D-CNN model was used to classify seven variants of SARS-CoV-2 and achieved 99.78% accuracy, 97.98% precision, 97.66% sensitivity, 99.95% specificity, and 98.68% F1-score. The max pool layer feature maps of this network were investigated to discover the sequence discriminative regions in SARS-CoV-2 variants and their effect on biological functional differences. The feature map examination led to the detection of three mutations; one of them was a missense mutation, which has been reported previously. The rest of the detected mutations were silent mutations. In conclusion, the achieved results indicated that CNN models can extract effective features to discriminate several SARS-CoV-2 variants. Also, investigation of CNN feature maps led to an explainable CNN revealing the learned knowledge of the network from the training database. This knowledge helped us to detect mutations and their functional effects in different variants.

Use of the 3D Equilibrium Equations in the Free-Edge Analyses for Laminated Structures with the Variable Kinematics Approach

This paper compares out-of-plane stresses evaluated with Hooke’s Law and the stress recovery technique, focusing on the free edges of composite plates and shells. The Carrera Unified Formulation and the finite element method are adopted to derive the governing equations. Lagrange polynomials are implemented in the equivalent single-layer, layer-wise, and variable kinematics approaches. The latter is used to refine structural models locally and reduce computational overheads. Laminated plates and shells subjected to uniaxial tension are considered. The out-of-plane stresses are compared with references from the existing literature for most cases. The results demonstrate that the stress recovery technique effectively calculates stresses and improves the accuracy of equivalent single-layer models. Furthermore, layer-wise models are needed for accurate results near the free-edge zone. Finally, variable kinematics theories are helpful in accurately detecting local phenomena along the structure’s thickness.

Optimizing Hyperparameters for Enhanced LSTM-Based Prediction System Performance

This research paper explores the application of deep learning and supervised machine learning algorithms, specifically Long Short-Term Memory (LSTM), for stock market prediction. The study focuses on the closing prices of three companies - Tata Steel, Apple, and Powergrid - using a dataset sourced from Yahoo Finance. Performance evaluation of the LSTM model employed RMSE, MAPE, and accuracy metrics, along with hyperparameter calibration to determine the optimal model parameters. The findings indicate that a single-layer LSTM model outperformed a multilayer LSTM model across all companies and evaluation metrics. Furthermore, a comparison with existing research demonstrated the superiority of the proposed model. The study emphasizes the effectiveness of LSTM models for stock price prediction, underscores the significance of proper hyperparameter tuning for optimal performance, and concludes that a single-layer LSTM model can yield superior results compared to a multilayer model.

Performance evaluation of the WRF model under different physical schemes for air quality purposes in Buenos Aires, Argentina

This work presents the performance evaluation of the Weather Research and Forecasting (WRF) model to estimate surface wind speed and direction, air temperature, and water vapor mixing ratio considering 22 configurations at high spatial resolution (1 km) during one week in winter and one week in spring, in order to determine the best-performing schemes for air quality purposes in the Metropolitan Area of Buenos Aires, Argentina. Results show that the use of urban schemes mostly affects wind speed and temperature. The single-layer urban canopy model (UCM) coupled with the Boulac planetary boundary layer (PBL) scheme exhibits the best results for wind speed. Wind direction and water vapor mixing ratio are more sensitive to the land surface model scheme, with results slightly improving with the Noah-MP land surface model. Wind speed and direction errors are larger when the former is lower. When removing from the analysis wind speed values below 2.6 m s–1 for the winter week and 3.1 m s–1 for the spring week, the root mean square errors for wind direction decreased between 50 and 72% of the original value, depending on the configuration and week. Overall, under the studied conditions, configurations including Noah-Mp land surface model or the combination of a simple UCM with BouLac PBL are suitable for air quality applications, as they reproduce both temperature and water vapor mixing ratio relatively well, with errors below 10% and Correlation values above 0.7, and are the best performing configurations for wind direction and speed, respectively.

Optimal configuration of a two-level integrated rural energy system for counting and biogas digester warming

This paper proposes a strategy to use wind power (WP) that cannot be fully consumed at the load side for biogas digester (BD) heat augmentation to improve the utilization rate of biomass while promoting the consumption of WP, in view of the anti-peak nature of WP and the low gas production of BD at night in winter. In this paper, based on the model of rural integrated energy system (RIES) with biogas digester heating, a double-layer optimization model with minimum investment cost in the upper layer and optimal operation in the lower layer is developed. And then the Karush–Kuhn–Tucker (KKT) condition is used to convert the lower layer model into the constraints of the upper layer model, The Big-M method is used to linearize the nonlinear problem, and the model is transformed into a single-layer mixed integer linearization model. Finally, a use case of the algorithm is established and the CPLEX solver is called to solve the problem.

Impact of Anthropogenic Heat on Urban Environment: A Case Study of Singapore with High-Resolution Gridded Data

Anthropogenic heat (AH) emissions have great impacts on urban climate. AH is usually spatially heterogeneous and depends on the urban land use type. Studies using high-resolution gridded data that can resolve spatially heterogeneous AH are still scarce. The present study uses AH data of a high spatial resolution of 200 m by 200 m and a temporal resolution of 1 h to investigate the impact of AH in Singapore in April 2016, particularly regarding the relative contribution of individual AH components. The WRF model coupled with a single-layer urban canopy model is employed. The WRF model can predict the 2-m air temperature and 2-m relative humidity with good agreement with the observation data, while the simulated 10-m wind speed has relatively large deviation from the observation data. The largest spatially averaged temperature increases caused by total AH (QF), AH from buildings (QB) and AH from traffic (QV) are 1.44 °C, 1.44 °C and 1.35 °C, respectively. The effects of AH on sensible heat flux and boundary layer height are largely consistent, with both QF and QB exhibiting significant effects at night, while the effects of QV are small. The effect of AH on the local circulations (sea and land breezes) in Singapore is small, while its effect on the urban heat island (UHI) circulations is more pronounced. Due to the UHI circulations, the sum of the effects on local temperatures caused by QB and QV may exceed that by QF in some areas. This finding can guide comprehensive mitigation measures of AH by not only focusing on land use type but also on the contribution of individual AH components, in order to ameliorate the impacts of urban overheating.

Microwave Heating for Synthesis of Carbonaceous Adsorbents for Removal of Toxic Organic and Inorganic Contaminants.

The residues obtained from the extraction of Inonotus obliquus fungus were used to produce carbonaceous adsorbents. The initial material was subjected to pyrolysis in a microwave oven. The adsorbents were characterized through elemental analysis, low-temperature nitrogen adsorption/desorption isotherms, and Boehm titration. The carbonaceous adsorbents were tested for the removal of NO2, methylene blue, and malachite green. The results indicated that the obtained carbonaceous adsorbents exhibited basic characteristics and possessed specific surface areas of 372 and 502 m2/g. The adsorption process of liquid contaminants was modeled using the single-layer Langmuir model. The maximum adsorption capacities were found to be 101 and 109 mg/g for methylene blue, and 75 and 77 mg/g for malachite green. The kinetic study demonstrated that the adsorption of methylene blue and malachite green was better described by a pseudo-second order model. The study affirmed that the adsorption of organic dyes onto the resultant carbonaceous adsorbents was both spontaneous and endothermic. The study also demonstrated that the presence of an air stream during the NO2 adsorption process and prehumidization of the adsorbent with humid air had a beneficial effect on the obtained sorption capacities. In conclusion, the study demonstrated that pyrolysis of the extraction residues from the fungus Inonotus obliquus yields highly effective, environmentally friendly, and cost-efficient carbonaceous adsorbents for the removal of both gaseous and liquid pollutants.

Reproduction of mode-locked pulses by spectrotemporal domain-informed deep learning.

The accurate reproduction of unique pulse states in a mode-locked fiber laser is an important scientific issue and has wide applications in the laser industry. We present what we believe to be a novel method for automatically and precisely reproducing targeted soliton states in a mode-locked fiber laser by spectrotemporal domain-informed deep learning. Targeted solitons are experimentally reproduced via a superior matching process with a spectrotemporal mean square error (MSE) of 3.99 × 10-5. The outstanding feature of our reproduction algorithm is that the pulse information in both the spectral and temporal domains is jointly adopted for reconstructing targeted soliton states from white noise, rather than establishing arbitrary mode-locked pulse states, as described in previous studies. Additionally, a single-layer perceptron model is proposed to retrieve the phase distribution of a mode-locked pulse, validating the physical completeness of our reproduction approach. Our approach advances ultrafast laser technology, enabling the precise control of pulse dynamics in applications such as optical communication and nonlinear optics.

A Novel Semi-Analytical Solution of Over-Damped Slug Test in a Three-Layered Aquifer System.

The slug test has been commonly used to estimate aquifer parameters. Previous studies on the slug test mainly focused on a single-layer aquifer. However, understanding the interaction between layers is particularly important when assessing aquifer parameters under certain circumstances. In this study, a new semi-analytical model on transient flow in a three-layered aquifer system with a partially penetrating well was developed for the slug test. The proposed model was solved using the Laplace transform method and the Goldstein-Weber transform method, where the semi-analytical solution for the model was obtained. The drawdowns of the proposed model were analyzed to understand the impacts of the different parameters on the drawdowns in a three-layered aquifer system. The results indicated that groundwater interactions between the layers have a significant impact on the slug test. In addition, a shorter and deeper well screen as well as a greater permeability ratio between the layers creates a greater interface flow between them, leading to a higher drawdown in the slug test. Finally, a slug test in a three-layered aquifer system was conducted in our laboratory to validate the new model, which indicated that the proposed model performed better in the interpretation of the experimental data than a previous model proposed by Hyder et al. (1994). We also proposed an empirical relationship to qualitatively identify the errors in the application of single-layer model for the analysis of response data in a three-layered aquifer system.

Fused-Deposition Modeling 3D Printing of Short-Cut Carbon-Fiber-Reinforced PA6 Composites for Strengthening, Toughening, and Light Weighting.

Additive manufacturing of carbon-fiber-reinforced polymer (CFRP) has been widely used in many fields. However, issues such as inconsistent fiber orientation distribution and void formation during the layer stacking process have hindered the further optimization of the composite material's performance. This study aimed to address these challenges by conducting a comprehensive investigation into the influence of carbon fiber content and printing parameters on the micro-morphology, thermal properties, and mechanical properties of PA6-CF composites. Additionally, a heat treatment process was proposed to enhance the interlayer bonding and tensile properties of the printed composites in the printing direction. The experimental results demonstrate that the PA6-CF25 composite achieved the highest tensile strength of 163 MPa under optimal heat treatment conditions: 120 °C for 7.5 h. This corresponds to a significant tensile strength enhancement of 406% compared to the unreinforced composites, which represents the highest reported improvement in the current field of CFRP-fused deposition 3D printing. Additionally, we have innovatively developed a single-layer monofilament CF-OD model to quantitatively analyze the influence of fiber orientation distribution on the properties of the composite material. Under specific heat treatment conditions, the sample exhibits an average orientation angle μ of 0.43 and an orientation angle variance of 8.02. The peak frequency of fiber orientation closely aligns with 0°, which corresponds to the printing direction. Finally, the study explored the lightweight applications of the composite material, showcasing the impressive specific energy absorption (SEA) value of 17,800 J/kg when implementing 3D-printed PA6-CF composites as fillers in automobile crash boxes.

FP-CNN: Fuzzy pooling-based convolutional neural network for lung ultrasound image classification with explainable AI

The COVID-19 pandemic wreaks havoc on healthcare systems all across the world. In pandemic scenarios like COVID-19, the applicability of diagnostic modalities is crucial in medical diagnosis, where non-invasive ultrasound imaging has the potential to be a useful biomarker. This research develops a computer-assisted intelligent methodology for ultrasound lung image classification by utilizing a fuzzy pooling-based convolutional neural network FP-CNN with underlying evidence of particular decisions. The fuzzy-pooling method finds better representative features for ultrasound image classification. The FPCNN model categorizes ultrasound images into one of three classes: covid, disease-free (normal), and pneumonia. Explanations of diagnostic decisions are crucial to ensure the fairness of an intelligent system. This research has used Shapley Additive Explanation (SHAP) to explain the prediction of the FP-CNN models. The prediction of the black-box model is illustrated using the SHAP explanation of the intermediate layers of the black-box model. To determine the most effective model, we have tested different state-of-the-art convolutional neural network architectures with various training strategies, including fine-tuned models, single-layer fuzzy pooling models, and fuzzy pooling at all pooling layers. Among different architectures, the Xception model with all pooling layers having fuzzy pooling achieves the best classification results of 97.2% accuracy. We hope our proposed method will be helpful for the clinical diagnosis of covid-19 from lung ultrasound (LUS) images.

A single-layer Peridynamic model for failure analysis of composite laminates

Computational efficiency is one of the major concerns when applying traditional Peridynamics (PD) to model laminated composites. This paper proposes a highly efficient bond-based PD model for characterizing the deformation and the progressive damage behavior of laminated composites by describing laminates with a single layer of material points. The computational cost is significantly decreased due to that far fewer material points are needed to be considered during the calculation in the single-layer material point model (SLMPM). The model is validated through simulations of deformation and progressive failure in composite laminates. The deformation response is compared to ABAQUS and conventional PD results, as well as the running time compared to conventional PD. The damage prediction results are verified by experiments. It has been demonstrated that the computational efficiency of the proposed model is highly improved compared to the traditional model.

Hybrid Lattice Boltzmann Approach for Simulation of High-Speed Flows

A lattice Boltzmann approach utilizing hybrid lattices for accurate simulation of high-speed transonic (TS) flows is presented in this study. Single-layer lattice models, such as D3Q19, are computationally efficient with low numerical dissipation, but are limited to simulate weakly compressible flows within subsonic Mach regime. Multilayer lattice models, such as D3Q33, are capable of simulating thermal and high-speed compressible flows in TS Mach regime, but suffer from a higher numerical dissipation and higher computational cost. To take full advantages of these two types of lattices, a simulation domain is divided into two regions, high-subsonic (HS) flow regions to be solved by single-layer lattices and TS flow regions to be solved by multilayer lattices. The interface connecting the HS and TS flow regions are represented by double-sided surfels to realize smooth flow transition and ensure satisfaction of fundamental conservation laws. The hybrid lattice Boltzmann approach is stable and robust, and it allows multiple HS/TS flow regions with arbitrary shapes. Extensive validation studies demonstrate that the proposed approach is capable of obtaining accurate aerodynamic prediction of flows with a wide range of Mach numbers, and preserving the low numerical dissipation advantage of single-layer lattices in aeroacoustic computations.

A novel approach for the mechanical response of cement concrete pavement structure considering the interlaminar interface shear slip effect

The traditional theoretical analysis method has many problems such as cumbersome calculation and low efficiency, and there is a relative lack of research on the simplified mechanical model in the field of road engineering. To further improve and enrich the existing theoretical analysis of pavement structures, and to realize the rapid analysis of the mechanical behavior of cement concrete pavement structure (CCPS), based on the state-space method, a new approach is proposed to analyze the mechanical response of the CCPS, taking the interlaminar interface shear slip effect into account. The CCPS is considered as a two-layered Euler beam. A state equation is established to investigate the static responses of the CCPS with explicit consideration of the interlaminar interface shear slip effect under the action of an arbitrary vertical load and is solved by matrix theory. Subsequently, the present solution is validated by the literature published and the numerical simulation. In addition, the effects of the interlayer shear stiffness, thickness of the base course, stiffness of Winkler foundation springs, and bending stiffness on the deformations of the CCPS, and the influence of external loads on the interlayer distributing shear forces are revealed. It is indicated that the interlaminar interface shear slip effect exhibits a significant influence on the deflection and bending deformation of the CCPS. Moreover, the proposed solution can not only be employed conveniently for the consideration of any interlaminar contact conditions and vertical load distributions but also be reduced to obtain the responses of a single-layer mechanical model.

Prediction of Feed Efficiency and Performance-Based Traits in Fish via Integration of Multiple Omics and Clinical Covariates.

Fish aquaculture is a rapidly expanding global industry, set to support growing demands for sources of marine protein. Enhancing feed efficiency (FE) in farmed fish is required to reduce production costs and improve sector sustainability. Recognising that organisms are complex systems whose emerging phenotypes are the product of multiple interacting molecular processes, systems-based approaches are expected to deliver new biological insights into FE and growth performance. Here, we establish 14 diverse layers of multi-omics and clinical covariates to assess their capacities to predict FE and associated performance traits in a fish model (Oncorhynchus tshawytscha) and uncover the influential variables. Inter-omic relatedness between the different layers revealed several significant concordances, particularly between datasets originating from similar material/tissue and between blood indicators and some of the proteomic (liver), metabolomic (liver), and microbiomic layers. Single- and multi-layer random forest (RF) regression models showed that integration of all data layers provide greater FE prediction power than any single-layer model alone. Although FE was among the most challenging of the traits we attempted to predict, the mean accuracy of 40 different FE models in terms of root-mean square errors normalized to percentage was 30.4%, supporting RF as a feature selection tool and approach for complex trait prediction. Major contributions to the integrated FE models were derived from layers of proteomic and metabolomic data, with substantial influence also provided by the lipid composition layer. A correlation matrix of the top 27 variables in the models highlighted FE trait-associations with faecal bacteria (Serratia spp.), palmitic and nervonic acid moieties in whole body lipids, levels of free glycerol in muscle, and N-acetylglutamic acid content in liver. In summary, we identified subsets of molecular characteristics for the assessment of commercially relevant performance-based metrics in farmed Chinook salmon.

Comparison of multilayer and single-layer coronary plaque models on stress/strain calculations based on optical coherence tomography images.

Mechanical stress and strain conditions are closely related to atherosclerotic plaque progression and rupture and have been under intensive investigations in recent years. It is well known that arteries have a three-layer structure: intima, media and adventitia. However, in vivo image-based multilayer plaque models are not available in the current literature due to lack of multilayer image segmentation data. A multilayer segmentation and repairing technique was introduced to segment coronary plaque optical coherence tomography (OCT) image to obtain its three-layer vessel structure. A total of 200 OCT slices from 20 patients (13 male; 7 female) were used to construct multilayer and single-layer 3D thin-slice models to calculate plaque stress and strain and compare model differences. Our results indicated that the average maximum plaque stress values of 20 patients from multilayer and single-layer models were 385.13 ± 110.09kPa and 270.91 ± 95.86kPa, respectively. The relative difference was 42.2%, with single-layer stress serving as the base value. The average mean plaque stress values from multilayer and single-layer models were 129.59 ± 32.77kPa and 93.27 ± 18.20kPa, respectively, with a relative difference of 38.9%. The maximum and mean plaque strain values obtained from the multilayer models were 11.6% and 19.0% higher than those from the single-layer models. Similarly, the maximum and mean cap strains showed increases of 9.6% and 12.9% over those from the single-layer models. These findings suggest that use of multilayer models could improve plaque stress and strain calculation accuracy and may have large impact on plaque progression and vulnerability investigation and potential clinical applications. Further large-scale studies are needed to validate our findings.