Integrated Method Research Articles

The three-point form factor of Tr ϕ3 to six loops

We study the three-point form factor of the length-three half-BPS operator (Tr ϕ3) in planar N = 4 Super-Yang-Mills theory, using analyticity and integrability methods. We find that the functions describing the form factor in perturbation theory live in the same restrictive space of multiple polylogarithms as the one describing the form factor of the stress-tensor operator (Tr ϕ2). Furthermore, we find that the leading-order data in the collinear limit provided by the form factor operator product expansion (FFOPE) is enough to fix the form factor uniquely, at least through six loops. We perform various tests of our results using the subleading FFOPE corrections. We also analyze the form factor in the Regge limit where two Mandelstam invariants are large; we obtain a compact representation for the form factor in this limit which is valid to all orders in the coupling.

Integrative functional logistic regression model for genome-wide association studies.

Progress in rapid genomic sequencing techniques have transformed the field of disease biomarker identification by offering vast genetic information. The complexity of traits is not only influenced by single genetic loci but also by interactions among multiple genetic loci. When the dimensionality of SNP data is large, identifying a significant number of genetic variants associated with diseases becomes extremely challenging. To address these high-dimensionality issues, we employed functional data analysis techniques. Because there are a lot of ordered genetic variants spread out across a small space, multiple gene variations are handled as a continuous data set rather than discrete variables in some areas. This paper introduces a novel approach for analyzing the association of multiple genes within a region, by employing an integrative functional logistic regression model. The proposed technique has shown promising results in both simulation and real data analysis, indicating its ability to generate smooth signals and accurately estimate the coefficients of the function while recognizing the null regions. Integrative functional logistic regression method adopt functional data analysis and assume that high-dimensional genetic data follow a continuous process. It not only naturally accommodates correlations among adjacent SNPs but also avoids the unstable estimation of a large number of parameters. This is especially desirable with the rapidly increasing dimensions of SNP data but still limited sample size. In summary, the suggested approach offers a valuable new avenue for identifying disease-related genetic variants in GWAS.

Complementary Distant and Active Site Mutations Simultaneously Enhance Catalytic Activity and Thermostability of α-Galactosidase.

The industrial applications of enzymes are limited due to the activity-stability trade-off, which implies that the improvement of thermostability often accompanies decreased activity. This study presents a dual-strategy approach to simultaneously improve the catalytic efficiency and thermostability of α-galactosidase galV from Anoxybacillus vitaminiphilus WMF1. Our integrated method combines computational analysis with enzyme property prediction to selectively target and modify the catalytic region and residues that are distant from the active site. We identified and experimentally validated mutations that improve activity without compromising stability and further increased thermostability through additional distant-site mutations. The resulting mutant enzyme variant N549Q/T550N/Y634F demonstrated a 6.2-fold increase in catalytic efficiency and a 3.2-fold improvement in the half-life at 65 °C. Molecular dynamics (MD) simulations supported the structural basis for the observed enhancements. This approach offers a refined strategy for engineering α-galactosidases with improved industrial applicability, overcoming the traditional trade-offs between enzyme activity and stability. Hydrolytic activity toward raffinose family oligosaccharides (RFOs) was validated using soymilk as a model substrate, demonstrating significant practical potential.

Enhancing overall performances of large constructed wetlands using an integrated approach of numerical simulation and response surface method--Taking Bagong hybrid CWs as an example.

Constructed wetlands (CWs) with low carbon properties represented an effective approach for treating low-polluted water and improving water quality. Here, a research scheme was proposed to achieve maximum operation benefits of the large-scale CWs through parameter identification, operation simulation, evaluation, and analysis of the water quality process. Based on the two-dimensional water hydrodynamic model coupling with the Eco-Lab water quality module (with nutrients), simulation for Bagong hybrid CWs was successfully conducted. Variables were estimated using response surface design (RSD), and the values of model parameters were calibrated in accordance with central combination design (CCD) experiments. Ten key parameters in the water quality process affecting the overall pollutant removal of CWs were identified, and the water quality model of the CWs could be replicated well with the actual situation within the 95% confidence interval. The water purification effect of the CWs under five different influent flow conditions was simulated, and the maximum hydraulic loading (0.036m3·(m-2·h-1)) of the CWs was determined with the effluent water quality to meet the design requirements. The integrated method could effectively enhance the efficiency of parameter calibration and significantly reduce the simulation workload. The results of pollutants migration and transformation under different influent conditions could provide a universally applicable and valid method in engineering applications, and process a promising application prospect.

High performance ozone nanobubbles based advanced oxidation processes (AOPs) for degradation of organic pollutants under high pollutant loading.

Advanced Oxidation Processes (AOPs) have proven to be an effective solution for chemical wastewater treatment, particularly for degradation of organic pollutants, especially dyes. Ozonation is recognized as one of the most prevalent AOPs. Nevertheless, some cases show a lowered efficiency of O3 utilization which is attributed to its inadequate distribution in the treated water causing low residence time, low mass transfer coefficient as well as shorter half-life. This study demonstrates the application of ozone nanobubbles to enhance the degradation of organics under high pollution load conditions. We propose an integrated method that utilizes bulk nanobubbles to enhance the reactivity of ozone for the degradation of organics. We examined the degradation of organic pollutants under parameters such as varying pH levels, ozone concentrations and presence of salts and surfactants. The degradation of the organic pollutant by ozone nanobubbles (0.177 L mg-1min-1) demonstrated a threefold increase in reaction rate constants compared to microbubbles (0.025 L mg-1min-1). The plausible reason for these findings is (i) higher mass transfer coefficient (ii) higher ozone solubility (iii) NBs may act as a surface for chemical reaction (iv) NBs may increase the half-life of ozone. The presence of reactive oxygen species was verified using scavenging tests. This part of the studies revealed contribution of reactive oxygen species (ROSs) such as hydroxyl radical (•OH), superoxide radical anion (O2•-) and singlet oxygen (1O2) in the degradation process. The conditions that provide total degradation of 100% in 300s for both organic pollutants (Green rit and methylene blue dye) are: 5 LPM (Litre per minute) ozone flow rate, acidic pH, monovalent salts (NaCl, 2mM) and lower concentration of surfactants (CTAB and SDS, 0.3 CMC). A degradation mechanism has been outlined based on intermediates identified by LC-MS. This work presents a new method that combines AOPs with nanobubbles, which should lead to increased environmental sustainability and efficiency.

Hybrid model development through the integration of quantitative read-across (qRA) hypothesis with the QSAR framework: An alternative risk assessment of acute inhalation toxicity testing in rats.

Regulatory authorities frequently need information on a chemical's capacity to produce acute systemic toxicity in humans. Due to concerns about animal welfare, human relevance, and reproducibility, numerous international initiatives have centered on finding a substitute for using animals in acute systemic lethality testing. These substitutes include the more current in-silico and in vitro techniques. Meanwhile, Advances in artificial intelligence and computational resources have led to a rise in the speed and accuracy of machine learning algorithms. Therefore, new approach methodologies (NAMs) based on in-silico modeling are considered a suitable place to start, even though many non-animal testing approaches exist for evaluating the safety of chemicals. Eventually, in this investigation, we have developed a hybrid computational model for acute inhalational toxicity data. In this case study, two major in silico techniques, QSAR (quantitative structure-activity relationship) and qRA (quantitative read-across) predictions, were utilized in a hybrid manner to extract more insightful information about the compounds based on similarity as well as the physicochemical properties. The findings of this investigation demonstrate that the integrated method surpasses the traditional QSAR model in terms of statistical quality for inhalational toxicity data, with greater predictability and transferability, due to a much smaller number of descriptors used in the hybrid modeling process. This hybrid modeling technique is a promising alternative, which can be paired with other methods in an integrated manner for a more rational categorization and evaluation of inhaled chemicals as a substitute for animal testing for regulatory purposes in the future.

Revolutionizing Cesium Monitoring in Seawater through Electrochemical Voltammetry and Machine Learning

Monitoring radioactive cesium ions (Cs+) in seawater is vital for environmental safety but remains challenging due to limitations in the accessibility, stability, and selectivity of traditional methods. This study presents an innovative approach that combines electrochemical voltammetry using nickel hexacyanoferrate (NiHCF) thin-film electrode with machine learning (ML) to enable accurate and portable detection of Cs+. Optimizing the fabrication of NiHCF thin-film electrodes enabled the development of a robust sensor that generates cyclic voltammograms (CVs) sensitive to Cs⁺ concentrations as low as 1 ppb in synthetic seawater and 10 ppb in real seawater, with subtle changes in CV patterns caused by trace Cs⁺ effectively identified and analyzed using ML. Using 2D convolutional neural networks (CNNs), we classified Cs+ concentrations across eight logarithmic classes (0 - 106 ppb) with 100% accuracy and an F1-score of 1 in synthetic seawater datasets, outperforming the 1D CNN and deep neural networks. Validation using real seawater datasets confirmed the applicability of our model, achieving high performance. Moreover, gradient-weighted class activation mapping (Grad-CAM) identified critical CV regions that were overlooked during manual inspection, validating model reliability. This integrated method offers sensitive and practical solutions for monitoring Cs+ in seawater, helping to prevent its accumulation in ecosystems.

Advanced Android Malware Detection: Merging Deep Learning and XGBoost Techniques

The increasing importance of Android devices in our lives brings with it the need to secure personal information stored on these devices, such as contact details, documents, location data, and browser data. These devices are often targeted by attacks and malware designed to steal this data. In response, this work takes a novel approach to Android malware detection by integrating deep learning with traditional machine learning algorithms. An extensive experimental study was conducted using the DroidCollector network traffic analysis dataset. Eight different deep learning methods are analysed for malware classification. In the first phase, experiments were conducted on both original and stabilised datasets and the most effective methods were identified. In the second phase, the best performing deep learning methods were combined with XGBoost for classification. This hybrid approach increased classification success by 3-4%. The highest F1 and accuracy values obtained after 150 epochs of training with BiLSTM+XGBoost were 95.12% and 99.33% respectively. These results highlight the superiority of combining deep learning and traditional machine learning techniques over individual models and significantly improve classification accuracy. This integrated method provides a very important strategy for developing high-performance models for various applications.

Evaluating the Geodiversity, Geotourism, and Sustainable Development in Taihu Xishan National Geopark, China: An Integrated SWOT-AHP Method

Evaluating the Geodiversity, Geotourism, and Sustainable Development in Taihu Xishan National Geopark, China: An Integrated SWOT-AHP Method

Integrating Python and MATLAB for Digital Twin Applications in Aeroservoelasticity

The development of Digital Twin (DT) applications in intricate engineering areas has been greatly accelerated by the incorporation of sophisticated computational tools like Python and MATLAB. The goal of this research is to model, simulate, and analyze aeroservoelastic systems for Digital Twin implementations by utilizing the combined powers of Python and MATLAB. In order to achieve the real-time predictive skills needed for Digital Twins, aeroservoelasticity—which involves the coupled interplay of aerodynamic, structural, and control forces—presents special obstacles. This work successfully tackles these issues by fusing MATLAB's strong numerical and control system capabilities with Python's adaptability and library ecosystem. Using real-time sensor data streaming, and feedback control system implementation is used in this work. High-fidelity state-space modeling, sophisticated control design (such as PID and state feedback controllers), and system dynamics visualization are all done concurrently with MATLAB. In order to simulate and stabilize a highly flexible aeroelastic system, a continuous feedback loop was modeled in both environments, highlighting the platforms' complimentary advantages. Through the MATLAB Engine API for Python, the integrated method facilitates smooth data transmission between Python and MATLAB, guaranteeing real-time communication and model parameter synchronization. The efficiency of this dual-platform system is demonstrated by case studies on wing flutter suppression, limit cycle oscillation (LCO) mitigation, and control input optimization. The method is well suited for the dynamic needs of aeroservoelastic Digital Twins because of the results, which demonstrate a shorter error convergence time, improved stability, and computational economy. By utilizing MATLAB and Python's interoperability, this work establishes the groundwork for scalable, real-time Digital Twin solutions in aeronautical engineering. It highlights how crucial hybrid computational ecosystems are for bridging the gap between high- fidelity simulations and real-time predictive capabilities, opening the door for improvements in fault prediction, control optimization, and aeronautical system monitoring.

Identification of hypertension gene expression biomarkers based on the DeepGCFS algorithm.

Hypertension is a critical risk factor and cause of mortality in cardiovascular diseases, and it remains a global public health issue. Therefore, understanding its mechanisms is essential for treating and preventing hypertension. Gene expression data is an important source for obtaining hypertension biomarkers. However, this data has a small sample size and high feature dimensionality, posing challenges to biomarker identification. We propose a novel deep graph clustering feature selection (DeepGCFS) algorithm to identify hypertension gene biomarkers with more biological significance. This algorithm utilizes a graph network to represent the interaction information between genes, builds a GNN model, designs a loss function based on link prediction and self-supervised learning ideas for training, and allows each gene node to obtain a feature vector representing global information. The algorithm then uses hybrid clustering methods for gene module detection. Finally, it combines integrated feature selection methods to determine the gene biomarkers. The experiment revealed that all the ten identified hypertension biomarkers were significantly differentiated, and it was found that the classification performance of AUC can reach 97.50%, which is better than other literature methods. Six genes (PTGS2, TBXA2R, ZNF101, KCNJ2, MSRA, and CMTM5) have been reported to be associated with hypertension. By using GSE113439 as the validation dataset, the AUC value of classification performance was to be 95.45%, and seven of the genes (LYSMD3, TBXA2R, KLC3, GPR171, PTGS2, MSRA, and CMTM5) were to be significantly different. In addition, this algorithm's performance of gene feature vector clustering was better than other comparative methods. Therefore, the proposed algorithm has significant advantages in selecting potential hypertension biomarkers.

Methods for data extraction and data transformation in convergent integrated mixed methods systematic reviews.

The objective of this guidance paper is to describe data transformation involving qualitization, including when and how to undertake this process, and to clarify how it aligns with data extraction in order to expand on the current guidance for JBI convergent integrated mixed methods systematic reviews (MMSRs). The convergent integrated approach to MMSRs involves combining extracted data from both quantitative studies (including the quantitative components of mixed methods studies) and qualitative studies (including the qualitative components of mixed methods studies). This process requires data transformation, which can occur either by converting qualitative data into quantitative data (ie, quantitizing) or converting quantitative data into qualitative data (ie, qualitizing). Data transformation involving qualitization is poorly understood in the context of MMSRs, and there is confusion regarding how to undertake this process, with much of the literature specific to primary mixed methods studies. There is a need to expand current guidance and provide more practical advice to reviewers on how to undertake this process. The JBI MMSR Methodology Group took a multipronged approach to update its guidance. First, a structured search of the literature was conducted to determine what is known about data transformation, followed by analysis of a sample of systematic reviews that claimed to use the JBI convergent integrated approach to MMSRs. Approaches were summarized and used to inform the development of draft guidance. This guidance was iteratively revised following a series of online meetings, as well as presented to evidence synthesis experts at an international conference. Finally, the guidance was submitted to the JBI International Scientific Committee for discussion, feedback, and ratification. There is uncertainty in the literature regarding the process of data transformation within the context of MMSRs, with ill-defined approaches provided and variation in practice. In JBI convergent integrated MMSRs, it is recommended that data extraction from quantitative studies (or mixed method studies reporting quantitative findings) stays as close as possible to the data reported in the primary studies. Where data are absent or insufficient to meet the needs of the MMSR, systematic reviewers may need to construct the narrative representation using relevant data from the primary studies. Following data extraction, the process of qualitization occurs where extracted data (both quantitative and qualitative) are assembled, and reviewers are required to conduct detailed examination across data to identify likenesses and create categories based on similarities in meaning. To our knowledge, this is the most comprehensive guidance currently available for data extraction and qualitization for MMSRs. However, it is important to acknowledge the inherent variability in MMSRs and our methodology may need tailoring for certain situations. Further work will focus on examining how certainty and confidence in findings can be assessed within the framework of MMSRs.

Farnese palace in Caprarola, Italy: Towards a people-centred brand image in a cultural tourism market

The valorization of cultural identity-centered brand icons has become a requested action nowadays, promoting the marketing statement of local heritage sites that aren’t designated as UNESCO World Heritage. Thus, these sites might compete to enhance and safeguard cultural heritage and authentic cultural knowledge. Moreover, lessening the high negative impact of the customization approach on the conservation statement of the cultural asset, the research adopts a people-centered approach developing the interlinkages between cultural tourism marketing and conservative management to enhance the rapport between the community and the palace in a community-based cultural tourism manner. Therefore, this empirical study reviews the cultural significance of the Farnese Palace in Caprarola and its reflection on its marketing statement, developing its brand image. It applies an integrated method that combines quantitative and qualitative analysis. It mainly assesses 165 online questionnaires with the public audience. The findings of this study draw a proposal for generating a people-centered heritage branding image (logo and slogan) of the Farnese Palace in Caprarola that seeks to generate a lifelong learning memory for the community and a long-term brand image for the visitors’ mentality.

A sensitized dual-response ratiometric fluorescent sensor integrated smartphone platform for accurate discrimination and detection of tetracycline homologues based on N-CDs‒Eu3+ complex.

Asensitized dual-response ratiometric fluorescent sensor integrated smartphone platform for accurate discrimination and detection of tetracycline(TC) homologues was fabricated based on N-CDs-Eu3+ complex. In the sensing system, N-CDs act as a sensitizer of Eu3+ and significantly enhance the fluorescence of TC-Eu3+ complex approximate 40-fold owing to the synergistic effect of antenna effect (AE) and fluorescence resonance energy transfer (FRET). A paper sensor integrated with a smartphone platform is further fabricated for on-site measurement of TC. The proposed sensing platform exhibits an obvious color change from blue to red with limit of detection (LOD) of 1.5 and 63.2 nM for spectrofluorimetry and paper sensor, respectively. In addition, to eliminate the interference from TC homologues, a simple and effective sensor array was constructed by regulating thepH of the system. The different fluorescence responses to four tetracycline homologues used widely (TC, OTC, CTC, and DOX) were examined and dealt with principal component analysis, and accurate differentiation of TC homologues was therefore achieved. This work provides an integrated method for identification and synchronous quantitative detection of TCs, and a potential application for visual and on-site detection of TCs in environmental monitoring and food safety.

Source Apportionment and Analysis of Potentially Toxic Element Sources in Agricultural Soils Based on the Positive Matrix Factorization and Geo-Detector Models

The potentially toxic element pollution of agricultural soils has become a significant environmental threat to food safety and human health. Accurately identifying sources of potentially toxic element pollution is key to developing effective pollution prevention and control measures. In this study, regional potentially toxic element pollution of the soils in the Nanliujiang River Basin was analyzed using the positive matrix factorization (PMF) model and the geo-detector model. First, topsoil samples from the study area were collected to analyze eight potentially toxic elements in the soil, including As, Cd, Cr, Cu, Hg, Ni, Pb, and Zn. The PMF model was used to conduct source apportionment of the potentially toxic element data and identify the primary pollution sources and their contribution rates. Then, the geo-detector model was used to analyze the key factors affecting the spatial distribution of the potentially toxic elements and the influence of natural and human factors on the distribution of the potentially toxic elements. There are four potentially toxic element pollution sources of the agricultural soil in the study area: geological background, agricultural activities, industrial discharge, and river irrigation. The geological background contributed the most. The main factors affecting the spatial distribution of potentially toxic elements included agricultural activities, industrial discharge, and river irrigation. This integrated method can analyze the formation of potentially toxic element pollution in depth from the perspectives of source apportionment and spatial differentiation and provide a scientific basis and decision support for preventing and controlling potentially toxic element pollution in agricultural soils. This study provides a new method and scientific basis for identifying and preventing potentially toxic element pollution sources in agricultural soil and can guide the formulation of targeted soil pollution control measures.

CaVIT: An integrated method for image style transfer using parallel CNN and vision transformer

CaVIT: An integrated method for image style transfer using parallel CNN and vision transformer

A Comprehensive Survey on the Integrity of Localization Systems.

This survey extends and refines the existing definitions of integrity and protection level in localization systems (localization as a broad term, i.e., not limited to GNSS-based localization). In our definition, we study integrity from two aspects: quality and quantity. Unlike existing reviews, this survey examines integrity methods covering various localization techniques and sensors. We classify localization techniques as optimization-based, fusion-based, and SLAM-based. A new classification of integrity methods is introduced, evaluating their applications, effectiveness, and limitations. Comparative tables summarize strengths and gaps across key criteria, such as algorithms, evaluation methods, sensor data, and more. The survey presents a general probabilistic model addressing diverse error types in localization systems. Findings reveal a significant research imbalance: 73.3% of surveyed papers focus on GNSS-based methods, while only 26.7% explore non-GNSS approaches like fusion, optimization, or SLAM, with few addressing protection level calculations. Robust modeling is highlighted as a promising integrity method, combining quantification and qualification to address critical gaps. This approach offers a unified framework for improving localization system reliability and safety. This survey provides key insights for developing more robust localization systems, contributing to safer and more efficient autonomous operations.

An integrated modeling, verification, and code generation for uncrewed aerial systems: less cost and more efficiency.

Uncrewed Aerial Systems (UASs) are widely implemented in safety-critical fields such as industrial production, military operations, and disaster relief. Due to the diversity and complexity of implementation scenarios, UASs have become increasingly intricate. The challenge of designing and implementing highly reliable UASs while effectively controlling development costs and improving efficiency has been a pressing issue faced by academia and industry. To address this challenge, this article aims to examine an integrated method for modeling, verification, and code generation for UASs. This article begins to utilize Architecture Analysis and Design Language (AADL) to model UASs, proposing generic UAS models. Then, formal specifications describe a system's safety properties and functions based on these models. Finally, this article introduces a method to generate flight controller codes for UASs based on the verified models. Experiments demonstrate its effectiveness in pinpointing potential vulnerabilities in UASs during the early design phase and generating viable flight controller codes from the verified models. The proposed approach can also improve the efficiency of designing and verifying high-reliability UASs.

Photonics-assisted analog windowing and matched filtering.

In this paper, we propose an integrated method for windowing and matched filtering in the analog domain based on microwave photonic technology, which utilizes dispersion regulation of optical waveguide to achieve the windowing processing of broadband signals in the optical domain and the surface acoustic wave filter (SAWF) to achieve the following matched filtering processing in the radio frequency (RF) domain, thus realizing their integration processing in the analog domain. The proposed method is validated by simulation and experiment, in which the integrated processing of matched filtering and windowing in the analog domain for a linear frequency modulation (LFM) signal with a bandwidth of 1 GHz is carried out and the peak to sidelobe ratio (PSLR) of the output signal is -19.55 dB and the mainlobe width (MLW) broadens to 0.16 ns with the maximum achievable dispersion value. The proposed method can significantly reduce the pressure of signal processing at the back-end of the radar system and improve the response speed of the broadband radar system in detecting the targets.

A new discrete-geometry approach for integrative docking of proteins using chemical crosslinks.

The structures of protein complexes allow us to understand and modulate the biological functions of the proteins. Integrative docking is a computational method to obtain the structures of a protein complex, given the atomic structures of the constituent proteins along with other experimental data on the complex, such as chemical crosslinks or SAXS profiles. Here, we develop a new discrete geometry-based method, wall-EASAL, for integrative rigid docking of protein pairs given the structures of the constituent proteins and chemical crosslinks. The method is an adaptation of EASAL (Efficient Atlasing and Search of Assembly Landscapes), a state-of-the-art discrete geometry method for efficient and exhaustive sampling of macromolecular configurations under pairwise inter-molecular distance constraints. We provide a mathematical proof that the method finds a structure satisfying the crosslink constraints under a natural condition satisfied by energy landscapes. We compare wall-EASAL with IMP (Integrative Modeling Platform), a commonly used integrative modeling method, on a benchmark, varying the numbers, types, and sources of input crosslinks, and sources of monomer structures. The wall-EASAL method performs better than IMP in terms of the average satisfaction of the configurations to the input crosslinks and the average similarity of the configurations to their corresponding native structures. The ensembles from IMP exhibit greater variability in these two measures. Further, wall-EASAL is more efficient than IMP. Although the current study uses crosslinks, the method is general and any source of distance constraints can be used for integrative docking with wall-EASAL. However, the current implementation only supports binary rigid protein docking, i.e., assumes that the monomer structures are known and remain rigid. Additionally, the current implementation is deterministic, i.e., it does not account for uncertainties in the crosslinking data beyond using distance bounds. Neither of these appears to be a theoretical or algorithmic limitation of the EASAL methodology. Structures from wall-EASAL can be incorporated in methods for modeling large macromolecular assemblies, for example by suggesting rigid bodies or restraints for use in these methods. This will facilitate the characterization of assemblies and cellular neighborhoods at increased efficiency, accuracy, and precision. The wall-EASAL method is available at https://bitbucket.org/geoplexity/easal-dev/src/Crosslink and the benchmark is available at https://github.com/isblab/Integrative_docking_benchmark.