Computation Time Research Articles

NeuralCMS: A deep learning approach to study Jupiter's interior

NASA's Juno mission provided exquisite measurements of Jupiter's gravity field that together with the Galileo entry probe atmospheric measurements constrains the interior structure of the giant planet. Inferring its interior structure range remains a challenging inverse problem requiring a computationally intensive search of combinations of various planetary properties, such as the cloud-level temperature, composition, and core features, requiring the computation of sim \(10^9\) interior models. We propose an efficient deep neural network (DNN) model to generate high-precision wide-ranged interior models based on the very accurate but computationally demanding concentric MacLaurin spheroid (CMS) method. We trained a sharing-based DNN with a large set of CMS results for a four-layer interior model of Jupiter, including a dilute core, to accurately predict the gravity moments and mass, given a combination of interior features. We evaluated the performance of the trained DNN (NeuralCMS) to inspect its predictive limitations. NeuralCMS shows very good performance in predicting the gravity moments, with errors comparable with the uncertainty due to differential rotation, and a very accurate mass prediction. This allowed us to perform a broad parameter space search by computing only sim \(10^4\) actual CMS interior models, resulting in a large sample of plausible interior structures, and reducing the computation time by a factor of \(10^5\). Moreover, we used a DNN explainability algorithm to analyze the impact of the parameters setting the interior model on the predicted observables, providing information on their nonlinear relation.

A fast bootstrap algorithm for causal inference with large data.

Estimating causal effects from large experimental and observational data has become increasingly prevalent in both industry and research. The bootstrap is an intuitive and powerful technique used to construct standard errors and confidence intervals of estimators. Its application however can be prohibitively demanding in settings involving large data. In addition, modern causal inference estimators based on machine learning and optimization techniques exacerbate the computational burden of the bootstrap. The bag of little bootstraps has been proposed in non-causal settings for large data but has not yet been applied to evaluate the properties of estimators of causal effects. In this article, we introduce a new bootstrap algorithm called causal bag of little bootstraps for causal inference with large data. The new algorithm significantly improves the computational efficiency of the traditional bootstrap while providing consistent estimates and desirable confidence interval coverage. We describe its properties, provide practical considerations, and evaluate the performance of the proposed algorithm in terms of bias, coverage of the true 95% confidence intervals, and computational time in a simulation study. We apply it in the evaluation of the effect of hormone therapy on the average time to coronary heart disease using a large observational data set from the Women's Health Initiative.

Optimization of an inductor for electromagnetic levitation melting

Purpose The study aims to maximize the efficiency of the process under a given current condition by changing the geometry of the coil. This optimization is economically justified by reducing the cost of the process. Design/methodology/approach The paper presents the author’s optimization process for a case requiring long computational time. The presented optimization is based on a 3D simulation model of an electromagnetic levitation melting (ELM) inductor. Findings The result of the work is to find a suboptimal inductor geometry for ELM. Research limitations/implications To solve the presented problem, a procedure using an evolutionary algorithm was relied on. As for all global search algorithms, it is possible to find a local optimum instead of a global one. Practical implications The new inductor geometry for ELM, thanks to its higher process efficiency for its class of inductors, can lead to the reduction of the costs of the process by using this type of equipment. Originality/value The novelty of the article is a proprietary optimization algorithm and the use of an advanced 3D simulation model which was necessary due to the lack of symmetry of the ELM inductor.

Thermodynamics of Computations with Absolute Irreversibility, Unidirectional Transitions, and Stochastic Computation Times

Developing a thermodynamic theory of computation is a challenging task at the interface of nonequilibrium thermodynamics and computer science. In particular, this task requires dealing with difficulties such as stochastic halting times, unidirectional (possibly deterministic) transitions, and restricted initial conditions, features common in real-world computers. Here, we present a framework which tackles all such difficulties by extending the martingale theory of nonequilibrium thermodynamics to generic nonstationary Markovian processes, including those with broken detailed balance and/or absolute irreversibility. We derive several universal fluctuation relations and second-law-like inequalities that provide both lower and upper bounds on the intrinsic dissipation (mismatch cost) associated with any periodic process—in particular, the periodic processes underlying all current digital computation. Crucially, these bounds apply even if the process has stochastic stopping times, as it does in many computational machines. We illustrate our results with exhaustive numerical simulations of deterministic finite automata processing bit strings, one of the fundamental models of computation from theoretical computer science. We also provide universal equalities and inequalities for the acceptance probability of words of a given length by a deterministic finite automaton in terms of thermodynamic quantities, and outline connections between computer science and stochastic resetting. Our results, while motivated from the computational context, are applicable far more broadly. Published by the American Physical Society 2024

Digital twin-based tig welding quality prediction using electrode tip angle degradation influencing Industry 5.0 in manufacturing sector

Automation in tungsten inert gas (TIG) welding is important to achieve high production rates and quality in manufacturing industries. To improve the welding process and quality inspection methodologies, the intelligent welding robot and vision-based inspection system have been researched and deployed in many engineering fields. Hence to enhance the performance and production, a digital twin-based welding system with the prediction of weld quality based on the consideration of electrode tip angle degradation. The proposed system will capture real-time electrode tip angle and weld pool temperature using a forward looking infrared (FLIR) camera along with welding current and speed correlated with tensile strength as the output parameter. To validate the analysis, support vector machine (SVM) and random forest (RF) algorithms were implemented in which the RF model performs well on the prediction of welding quality by mapping with tensile strength. RF model confirms maximum accuracy of 90% with 0.29 seconds computation time to perform prediction on the next execution of welding operation. It is inferred that if the tip angle degradation increases consecutively welding current decreases drastically impacting the weld quality from good to poor. To forecast the need for immediate or scheduled maintenance to reduce the tip angle degradation, a linear regression algorithm is implemented to enable the inspection engineer to perform maintenance without delay in production.

Exploring Li-Ion Transport Properties of Li3TiCl6: A Machine Learning Molecular Dynamics Study

Abstract We performed large-scale molecular dynamics simulations based on a machine-learning force field (MLFF) to investigate the Li-ion transport mechanism in cation-disordered Li3TiCl6 cathode at six different temperatures, ranging from 25°C to 100°C. In this work, the deep neural network method and data generated by ab-initio molecular dynamics (AIMD) simulations were deployed to build a high-fidelity MLFF. Radial distribution functions, Li-ion mean square displacements (MSD), diffusion coefficients, ionic conductivity, activation energy, and crystallographic direction-dependent migration barriers were calculated and compared with corresponding AIMD and experimental data to benchmark the accuracy of the MLFF. Our MSD analysis captured both the self and distinct parts of Li-ion dynamics. The latter reveals that the Li-ions are involved in anti-correlation motion that was rarely reported for solid-state materials. The obtained trajectory from molecular dynamics infers that the Li-ion transportation is mainly through interstitial hopping, which was confirmed by intra- and inter-layer Li-ion displacement with respect to simulation time. Ionic conductivity (1.06 mS/cm) and activation energy (0.29eV) calculated by our simulation are highly comparable with that of experimental values. Overall, the MLFF-based simulation is a promising method to explain the intricate electrochemical properties of the Li3TiCl6 cathode with remarkably reduced computational time

Towards explainable traffic signal control for urban networks through genetic programming

The increasing number of vehicles in urban areas draws significant attention to traffic signal control (TSC), which can enhance the efficiency of the entire network by properly switching the phases of each signalized intersection. Fixed and max-pressure methods are commonly used in TSC systems owing to their high simplicity and good interpretability, but they respectively lack dynamic adaptability and automatic rule generation, possibly leading to low solution accuracy in complicated traffic environments. Meanwhile, meta-heuristic and black-box learning methods meet challenges in practice such as extensive computational time and poor interpretability. To this end, this paper proposes a new TSC method based on Genetic Programming (GP) to generate descriptive score rules automatically for switching phases of all signalized intersections in an urban transportation network. In the proposed method, switching phases of each signalized intersection type is formulated as a symbolic regression problem, and effective primitives are defined to facilitate GP to solve the problem. Experiments have been conducted on both synthetic and real-world networks. The results have validated the effectiveness of our proposed GP based method compared to several state-of-the-art TSC methods in terms of accuracy and interpretability.

Efficient optimization of an accelerator neutron source for neutron capture therapy using genetic algorithms.

In recent years, genetic algorithms have been applied in the field of nuclear technology design, producing superior optimization results compared to traditional methods. They can be employed in the design and optimization of beam shaping assemblies (BSA) BSA to obtain the desired neutron beams. But it should be noted that the direct combination of Monte Carlo methods with genetic algorithms requires a significant amount of computational resources and time. Design and optimize BSA more efficiently to achieve neutron beams that meet specified recommendations. We propose an approach of NSGA II with crucial variables which are identified by multivariate statistical techniques. This approach significantly reduces the problem sizes, thus reducing the time required for optimization. We illustrate this methodology using the example of BSA design for AB-BNCT. The computational efficiency has tripled with crucial variables. By using NSGA II, we obtained optimized models conforming to both the new and old version IAEA BNCT guidelines through a single optimization process and subjected them to phantom analysis. The results demonstrate that models obtained through this method can meet the IAEA recommendations with deep advantage depth (AD) and high absorbed ratio (AR). The genetic algorithm with crucial variables displays tremendous potential in addressing BSA optimization challenges.

A novel method for rapid estimation of active bone marrow dose for radiotherapy patients in epidemiological studies.

In a dedicated effort to improve the assessment of clonal hematopoiesis (CH) and study leukemia risk following radiotherapy, we are developing a large-scale cohort study among cancer patients who received radiation. To that end, it will be critical to analyze dosimetric parameters of red bone marrow (ABM) exposure in relation to CH and its progression to myeloid neoplasms, requiring reconstruction method for ABM doses of a large-scale patients rapidly and accurately. To support a large-scale cohort study on the assessment of clonal hematopoiesis and leukemia risk following radiotherapy, we present a new method for the rapid reconstruction of ABM doses of radiotherapy among cancer patients. The key idea of the presented method is to segment patient bones rapidly and automatically by matching a whole-body computational human phantom, in which the skeletal system is divided into 34 bone sites, to patient CT images via 3D skeletal registration. The automatic approach was used to segment site-specific bones for 40 radiotherapy patients. Also, we segmented the bones manually. The bones segmented both manually and automatically were then combined with the patient dose matrix calculated by the treatment planning system (TPS) to derive patient ABM dose. We evaluated the performance of the automatic method in geometric and dosimetric accuracy by comparison with the manual approach. The pelvis showed the best geometric performance [volume overlap fraction (VOF): 52% (mean) with 23% (σ) and average distance (AD): 0.8cm (mean) with 0.5cm (σ)]. The pelvis also showed the best dosimetry performance [absorbed dose difference (ADD): 0.7Gy (mean) with 1.0Gy (σ)]. Some bones showed unsatisfactory performances such as the cervical vertebrae [ADD: 5.2Gy (mean) with 10.8Gy (σ)]. This impact on the total ABM dose, however, was not significant. An excellent agreement for the total ABM dose was indeed observed [ADD: 0.4Gy (mean) with 0.4Gy (σ)]. The computation time required for dose calculation using our method was robust (about one minute per patient). We confirmed that our method estimates ABM doses across treatment sites accurately, while providing high computational efficiency. The method will be used to reconstruct patient-specific ABM doses for dose-response assessment in a large cohort study. The method can also be applied to prospective dose calculation within a clinical TPS to support clinical decision making at the point of care.

A digital twin model of the axial temperature field of a DC cable for millisecond calculations

The most important features of digital twin technology for transmission and transformation equipment are symbiotic evolution and state prediction. In constructing the digital twin model for DC cables, the transient and steady-state temperature fields need to be considered comprehensively in the modeling process to consider the multi-physical field coupling, mathematical model, operational data, and environmental conditions in specific cases, which makes it difficult to satisfy the real-time requirements of the digital twin. To solve this problem, in this paper, a digital twin technology architecture for DC cables is proposed, and a neural network learning model is constructed to minimize the latency due to the complexity of the model simulation. Moreover, an efficient digital twin model that is based on the model-driven approach is developed for the fast computation of the axial temperature field of DC cables. The use of the Sequence-to-Sequence residual neural network algorithm for the reduced-order multi-physics field coupling modeling reduces the computational time and ensures as much accuracy as possible up to the finite element model simulation. The simulation results show that the use of the digital twin model reduces the simulation time from 275 s to 0.56 s, and the relative error between the accuracy of the digital twin model and the finite element model for the axial temperature field of the DC cable is 0.46 %. Finally, verification of the reasonableness and feasibility of the proposed method is carried out via an experimental platform according to the standard of CIGRE TB496. In particular, the maximum value of the DC cable temperature is verified to have a small error compared with the result of the Sequence-to-Sequence calculation under specific working conditions.

RADIANTYOU: Personalized PCOS Prediction Partner

The abstract outlines a study aimed at addressing the challenge of detecting polycystic ovary syndrome (PCOS) in women, particularly in Asia where a significant portion of cases go undetected. PCOS is a complex hormonal disorder affecting reproductive health, characterized by irregular menstrual cycles, excessive androgen levels, and the presence of multiple cysts on the ovaries. The researchers employed machine learning techniques to develop a predictive model for early detection of PCOS. This approach leverages data on various physiological markers such as prolactin levels, blood pressure, thyroid-stimulating hormone (TSH), and pregnancy status. These factors are known to be associated with PCOS and can potentially serve as indicators for its presence. The abstract highlights the effectiveness of Random Forest, a machine learning algorithm, in accurately predicting PCOS with minimal computational time. This implies that the model developed by the researchers can reliably identify individuals at risk of PCOS, allowing for early intervention and management

FEM-Circuit co-simulation of superconducting synchronous wind generators connected to a DC network using the homogenized J-A formulation of the Maxwell equations

Abstract High-temperature superconductors (HTS) are greatly appealing for the development of high efficient, and high energy density power devices. They are particularly relevant for applications requiring light and compact machines such as wind power generation. In this context, to ensure the proper design of the superconducting machines and their reliable operation in power systems, it is then important to develop models that can accurately include their physics but also can describe properly their interaction with the system. Thus, one approach is the co-simulation. The goal of the present work is to put to use this numerical technique when superconducting components are involved. Here, the case study is a 15 MW hybrid superconducting synchronous generator (HTS rotor and conventional stator) coupled to a direct current (DC) network via a rectifier and its associated filter. The case study related to wind power application allows grasping the technical issues when employing co-simulation dealing with HTS machines. The FEM of the generator is done in COMSOL Multiphysics, which interacts with the circuit simulator Simulink through the built-in Functional Mock-up Unit (FMU). For the present study, a new version of the latest J-A formulation combined with homogenization technique is introduced allowing an even faster computation time compared to the T-A formulation. Distributed variables and global variables such as current density, magnetic flux density, and local losses for the former and voltage, current, electromagnetic torque, and power quality for the latter are estimated and compared for both formulations. The idea is to find the best-suited combination FEM-circuit under criteria of computational speed, accuracy, and numerical stability. It is then shown that all formulations generate an error of less than 5% on the machine parameters; and the J-A formulation with first order elements stands out with a significant 4-fold reduction in computational costs.

A computationally efficient gradient-enhanced healing model for soft biological tissues.

Soft biological tissues, such as arterial tissue, have the ability to grow and remodel in response to damage. Computational method plays a critical role in understanding the underlying mechanisms of tissue damage and healing. However, the existing healing model often requires huge computation time and it is inconvenient to implement finite element simulation. In this paper, we propose a computationally efficient gradient-enhanced healing model that combines the advantages of the gradient-enhanced damage model, the homeostatic-driven turnover remodeling model, and the damage-induced growth model. In the proposed model, the evolution of healing-related parameters can be solved explicitly. Additionally, an adaptive time increment method is used to further reduce computation time. The proposed model can be easily implemented in Abaqus, requiring only a user subroutine UMAT. The effectiveness of proposed model is verified through a semi-analytical example, and the influence of the variables in the proposed model is investigated using uniaxial tension and open-hole plate tests. Finally, the long-term development of aneurysms is simulated to demonstrate the potential applications of the proposed model in real biomechanical problems.

Towards efficient control synthesis for nonlinear wave energy conversion systems: impedance-matching meets the spectral-domain

AbstractExisting studies within the literature that focus on designing parametric energy-maximizing controllers for Wave Energy Converter (WEC) systems predominantly rely on the impedance-matching (IM) principle, originally developed for linear time-invariant systems. Alternatively, iterative optimization routines are commonly employed for nonlinear WECs. However, these approaches often face a trade-off between effectiveness in maximizing energy extraction and computational efficiency. To address this limitation, this study proposes a computationally efficient controller tuning method for analogous synthesis in the case of nonlinear WECs. The proposed approach combines a statistical linearization technique known as spectral-domain modeling with the IM principle, to synthesize a Proportional–Integrative (PI) controller for a nonlinear WEC. Furthermore, a comparison is performed with two other synthesis methods: one based on a standard (i.e. linear) frequency-domain representation of the WEC that incorporates the IM principle, and the other employing a gradient-free optimization routine applied to the nonlinear time-domain model of the WEC for PI parameter tuning through exhaustive numerical search. A discussion on the effectiveness of each tuning method in maximizing energy absorption is provided, including an appraisal of their associated computational time requirements. Numerical analyses demonstrate that the proposed method, which integrates spectral-domain modeling and IM, can achieve (almost) optimal PI controller design for a nonlinear WEC. Furthermore, this study addresses the inaccuracies inherent in the frequency-domain approach and significantly reduces the computational time compared to the exhaustive search procedure. The findings of this research represent a significant advancement towards the development of simple, effective, and efficient IM-based techniques for synthesis of controllers in nonlinear WEC systems

Metaheuristic and Heuristic Algorithms-Based Identification Parameters of a Direct Current Motor

Direct current motors are widely used in industry applications, and it has become necessary to carry out studies and experiments for their optimization. In this manuscript, a comparison between heuristic and metaheuristic algorithms is presented, specifically, the Steiglitz–McBride, Jaya, Genetic Algorithm (GA), and Grey Wolf Optimizer (GWO) algorithms. They were used to estimate the parameters of a dynamic model that approximates the actual responses of current and angular velocity of a DC motor. The inverse of the Euclidean distance between the current and velocity errors was defined as the fitness function for the metaheuristic algorithms. For a more comprehensive comparison between algorithms, other indicators such as mean squared error (MSE), standard deviation, computation time, and key points of the current and velocity responses were used. Simulations were performed with MATLAB/Simulink 2010 using the estimated parameters and compared to the experiments. The results showed that Steiglitz–McBride and GWO are better parametric estimators, performing better than Jaya and GA in real signals and nominal parameters. Indicators say that GWO is more accurate for parametric estimation, with an average MSE of 0.43%, but it requires a high computational cost. On the contrary, Steiglitz–McBride performed with an average MSE of 3.32% but required a much lower computational cost. The GWO presented an error of 1% in the dynamic response using the corresponding indicators. If a more accurate parametric estimation is required, it is recommended to use GWO; however, the heuristic algorithm performed better overall. The performance of the algorithms presented in this paper may change if different error functions are used.

ShaderPerFormer: Platform-independent Context-aware Shader Performance Predictor

The ability to model and predict the execution time of GPU computations is crucial for real-time graphics application development and optimization. While there are many existing methodologies for graphics programmers to provide such estimates, those methods are often vendor-dependent, require the platforms to be tested, or fail to capture the contextual influences among shader instructions. To address this challenge, we propose ShaderPerFormer, a platform-independent, context-aware deep-learning approach to model GPU performance and provide end-to-end performance predictions on a per-shader basis. To provide more accurate predictions, our method contains a separate stage to gather platform-independent shader program trace information. We also provide a dataset consisting of a total of 54,667 fragment shader performance samples on 5 different platforms. Compared to the PILR and SH baseline methods, our approach reduces the average MAPE across five platforms by 8.26% and 25.25%, respectively.

The Effects of Climate Change on Streamflow, Nitrogen Loads, and Crop Yields in the Gordes Dam Basin, Turkey

The Mediterranean region is highly vulnerable to climate change. Longer and more intense heatwaves and droughts are expected. The Gordes Dam in Turkey provides drinking water for Izmir city and irrigation water for a wide range of crops grown in the basin. Using the Soil and Water Assessment Tool (SWAT), this study examined the effects of projected climate change (RCP 4.5 and RCP 8.5) on the simulated streamflow, nitrogen loads, and crop yields in the basin for the period of 2031–2060. A hierarchical approach to define the hydrological response units (HRUs) of SWAT and the Fast Automatic Calibration Tool (FACT) were used to reduce computational time and improve model performance. The simulations showed that the average annual discharge into the reservoir is projected to increase by between 0.7 m3/s and 4 m3/s under RCP 4.5 and RCP 8.5 climate change scenarios. The steep slopes and changes in precipitation in the study area may lead to higher simulated streamflow. In addition, the rising temperatures predicted in the projections could lead to earlier spring snowmelt. This could also lead to increased streamflow. Projected nitrogen loads increased by between 8.8 and 25.1 t/year. The results for agricultural production were more variable. While the yields of poppy, tobacco, winter barley, and winter wheat will increase to some extent because of climate change, the yields of maize, cucumbers, and potatoes are all predicted to be negatively affected. Non-continuous and limited data on water quality and crop yields lead to uncertainties, so that the accuracy of the model is affected by these limitations and inconsistencies. However, the results of this study provide a basis for developing sustainable water and land management practices at the catchment scale in response to climate change. The changes in water quality and quantity and the ecological balance resulting from changes in land use and management patterns for economic benefit could not be fully demonstrated in this study. To explore the most appropriate management strategies for sustainable crop production, the SWAT model developed in this study should be further used in a multi-criteria land use optimization analysis that considers not only crop yields but also water quantity and quality targets.

Model and heuristics for the multi-manned assembly line worker integration and balancing problem

This paper examines the balancing of assembly lines with multi-manned stations and a heterogeneous workforce. Both topics received considerable attention in the literature, but not in an integrated fashion. Combining these two characteristics gives rise to a highly combinatorial Multi-manned Assembly Line Worker Integration and Balancing Problem. When considering multi-manned stations, the already coupled decisions on assigning tasks to heterogeneous workers and workers to stations must be further linked with task scheduling assessments. We propose a Mixed-Integer Linear Programming model and develop two heuristic solution procedures, which tackle the problem with a hierarchical decomposition approach. Computational tests on a large dataset indicate that the proposed method can obtain good primal bounds in short computational times. We demonstrate that these results can be applied to the monolithic model either as a warm start or in a proximity search procedure to obtain synergistic gains with statistically significant differences. From a managerial perspective, we show that multi-manned stations can reduce the assembly line's length even in the presence of a heterogeneous workforce, which is crucial for many industries manufacturing large-size products.

A simulation-based genetic algorithm for a semi-automated warehouse scheduling problem with processing time variability

For warehouse operations, efficiently scheduling the available resources is crucial to improve the productivity and customer satisfaction. This paper proposes a simulation-based evolutionary algorithm for order scheduling and multi-robot task assignment in a robotic mobile fulfillment system. The algorithm proactively deals with the effects of the processing time variability by evaluating schedules based on both its system performance as well as its robustness under uncertain conditions. The algorithm implements an efficient resource allocation method and a variance reduction technique to reduce the overall computational burden. The experimental results show that the techniques to reduce the computational time are effective and can significantly reduce the amount of simulations required for the fitness evaluation. If a candidate schedule is allocated insufficient simulation replications it can lead to an inaccurate estimate of its long-term average performance. This could lead to an average performance loss of 7.3 %. Furthermore, the proactive scheduler is able to generate schedules that are more robust compared to deterministically generated. A reduction in the average operational cost of about 5 % can be reached, compared to a deterministically generated schedule. The paper reveals the relevance of identifying and modeling uncertainty when designing schedules in an operational system, rather than looking for optimal schedules for ideal scenarios.

FastCCLasso: a fast and efficient algorithm for estimating correlation matrix from compositional data.

The composition and structure of microbial communities on the body surface are closely related to human health. The interaction relationship among microbes can help us understand the formation of the microecological environment and the biological mechanism by which microorganisms influence host health. With the help of high-throughput sequencing technologies, microbial abundances in a natural environment can be directly measured without the isolation of microorganisms in culture. Sequencing experiments in microbiome studies can measure the relative abundance of microbes, which is called compositional data. Although there are already many methods for correlation analysis for compositional data, the computation time or accuracy still needs to be improved for current microbiome studies. We develop a fast and efficient algorithm, called fastCCLasso, based on a penalized weighted least squares for inferring the correlation structure of microbes from compositional data in microbiome studies. We perform a large number of numerical experiments and the simulation results show that fastCCLasso outperforms its competitors in edge detection for inferring the correlation network. We also apply fastCCLasso for estimating microbial networks in microbiome studies and fastCCLasso provides a conservative network with comparable false discovery counts that are derived from shuffled data. FastCCLasso is open source and freely available from https://github.com/ShenZhang-Statistics/fastCCLasso under GNU LGPL v3.