Unpredictable Errors Research Articles

Detailed analysis and simulation verification for reconstruction of plasma optical boundary with spectrometric technique on HL-2M tokamak

The plasma optical boundary reconstruction technique based on Hommen’s theory is promising for future tokamaks with high parameters. In this work, we conduct detailed analysis and simulation verification to estimate the ‘logic loophole’ of this technique. The finite-width effect and unpredictable errors reduce the technique’s reliability, which leads to this loophole. Based on imaging theory, the photos of a virtual camera are simulated by integrating the assumed luminous intensity of plasma. Based on Hommen’s theory, the plasma optical boundary is reconstructed from the photos. Comparing the reconstructed boundary with the one assumed, the logic loophole and its two effects are quantitatively estimated. The finite-width effect is related to the equivalent thickness of the luminous layer, which is generally about 2‒4 cm but sometimes larger. The level of unpredictable errors is around 0.65 cm. The technique based on Hommen’s theory is generally reliable, but finite-width effect and unpredictable errors have to be taken into consideration in some scenarios. The parameters of HL-2M are applied in this work.

Bottom-Up Clustering and Merging Strategy for Irregular Curvature Aero-Blade Surface Extraction

Surface extraction plays a significant role in blade reconstruction and measurement, improving manufacturing quality and reducing costs. Boundary extraction and region growth are the most common solutions. However, these methods treat points as complete objects and extract surfaces aggressively. Since the model and geometric constraints of the surfaces are usually blurring, these methods will lead to low accuracy results and dramatically impact the effectiveness of existing methods in practice. This paper presents a novel bottom-up irregular curvature surface extracting method called SuCMIS segmenting blade surface points from an unstructured scanning point cloud. SuCMIS applies adaptive multiple clustering methods based on the local flatness and normal deviation minimum, which improves the robustness to noise and unpredicted systematic errors. Then the curvature-based cluster merging process runs to reconstruct the blade surface. Differ to existing model-based method, SuCMIS converts surface extraction into a bottom-up process with multiply surfaces clustering and merging. It does not rely on evaluating the accuracy of the model and geometric constraints, which overcomes the natural defects of existing methods significantly. Experiments demonstrate SuCMIS’s efficiency and robustness. Compared to baseline methods, SuCMIS improves extracting accuracy with acceptable execution time, especially for complicated and large point clouds, such as blade surfaces.

Robust Lane Change Decision Making for Autonomous Vehicles: An Observation Adversarial Reinforcement Learning Approach

Reinforcementlearning holds the promise of allowing autonomous vehicles to learn complex decision making behaviors through interacting with other traffic participants. However, many real-world driving tasks involve unpredictable perception errors or measurement noises which may mislead an autonomous vehicle into making unsafe decisions, even cause catastrophic failures. In light of these risks, to ensure safety under perception uncertainty, autonomous vehicles are required to be able to cope with the worst case observation perturbations. Therefore, this paper proposes a novel observation adversarial reinforcement learning approach for robust lane change decision making of autonomous vehicles. A constrained observation-robust Markov decision process is presented to model lane change decision making behaviors of autonomous vehicles under policy constraints and observation uncertainties. Meanwhile, a black-box attack technique based on Bayesian optimization is implemented to approximate the optimal adversarial observation perturbations efficiently. Furthermore, a constrained observation-robust actor-critic algorithm is advanced to optimize autonomous driving lane change policies while keeping the variations of the policies attacked by the optimal adversarial observation perturbations within bounds. Finally, the robust lane change decision making approach is evaluated in three stochastic mixed traffic flows based on different densities. The results demonstrate that the proposed method can not only enhance the performance of an autonomous vehicle but also improve the robustness of lane change policies against adversarial observation perturbations.

The Lack of Philosophical Knowledge in Che Guevara’s Pedagogy: Fetishizing Love for Justice and Rage against Imperialism at the Expense of Logos

Most research on Ernesto “Che” Guevara has been concerned with emphasizing his ideological Marxist commitments and anti-imperial material objectives. These scholarly concerns usually constellate recycled subjective themes highlighting the revolutionary leader hating injustice, and loving justice, in tandem with the objective of eliminating imperialism and advancing a Third World project. In 2012, Che’s Apuntes filósoficos (Eng. Philosophical Notes) were published and highlighted that his exposure to philosophy regrettably occurred late in his life, and surprisingly, the difficulty he had in reading Marx and Hegel. The objective, therefore, of this multidisciplinary research navigating law, theology, philosophy, and politics is threefold. First, it alludes to and critiques the familiar pedagogy of Guevara emphasizing the importance of developing a “theory in action”, “learning through action”, being a “humanist”, and “leading by example”. Secondly, it considers the consequences of Che reifying emotion (eros) over reason (logos) thereby providing a possible answer to his “failed revolutionary story” in the Congo and Bolivia with his pedagogy involving an unstable compound mixing the emotion of compassion with rage thus clouding his reason. Finally, the third section highlights that we should not relegate emotion away from the sphere of political discourse, but rather harmonize it with reason to avoid chaotic and unpredictable errors based on subjective truths. Emphasizing the former at the expense of the latter—as maintained by a realist approach to International Relations and positivist jurisprudence accenting International Law—risks undermining scholarship challenging the immoral consequences arising from a naturalized assumption separating reason and revelation thus decriminalizing colonial practices characterizing the North and South.

A Downsampling Method Addressing the Modifiable Areal Unit Problem in Remote Sensing

Handling multiple scales efficiently is one avenue for processing big remote sensing imagery data. Unfortunately, imagery is also affected by the infamous modifiable areal unit problem, which creates unpredictable errors at different scales. We developed a downsampling method that attempts to keep the data distribution in a downsampled image constant, reducing the modifiable areal unit problem. We tested our method against classic downsampling methods (mean, central pixel selection, random) under a range of typical remote sensing scenarios. Under our experimental conditions, our downsampling method consistently outperformed the classical downsampling methods within a 95% confidence level. The downsampling method can be used in most typical situations where downsampling is needed, but it is likely to shine when used as a pyramid building policy in geocomputing platforms, such as Google Earth Engine.

Combining active and passive wind tunnel tests to determine the aerodynamic admittances of a bridge girder

In conventional buffeting analyses for long-span bridges, the aerodynamic admittance functions (AAF) with respect to the longitudinal (u-) and vertical (w-) turbulence components are usually assumed to be equivalent. This assumption could cause unpredictable errors due to complicated turbulence-structure interactions. This study proposes an experimental method to determine the u- and w- AAFs in the framework of three-dimensional buffeting theory. First, passive wind tunnel test is conducted to measure necessary aerodynamic parameters. Next, the turbulence characterized only by u-velocity fluctuations is generated in a multi-fan active-controlled wind tunnel to reproduce the u-velocity component in the passive wind tunnel test. The aim is to identify the u-AAF separately. Finally, the w-AAF is evaluated by combining the parameters measured in the active and passive wind tunnel tests. For a streamlined bridge girder, results show significant discrepancies between the u-AAF and w-AAF. The derivation degrees depend on the frequency and the angle of attack (AoA). This indicates the inaccuracy of the conventionally invoked assumption. In detail, the w-AAF is higher than the u-AAF at low frequencies, whereas the relationship reverses at higher frequencies. The proposed method is also applicable for other bluff-body structures, it is useful for improving the accuracy of buffeting analyses.

TimeStitch: Exploiting Slack to Mitigate Decoherence in Quantum Circuits

Quantum systems have the potential to demonstrate significant computational advantage, but current quantum devices suffer from the rapid accumulation of error that prevents the storage of quantum information over extended periods. The unintentional coupling of qubits to their environment and each other adds significant noise to computation, and improved methods to combat decoherence are required to boost the performance of quantum algorithms on real machines. While many existing techniques for mitigating error rely on adding extra gates to the circuit [ 13 , 20 , 56 ], calibrating new gates [ 50 ], or extending a circuit’s runtime [ 32 ], this article’s primary contribution leverages the gates already present in a quantum program without extending circuit duration. We exploit circuit slack for single-qubit gates that occur in idle windows, scheduling the gates such that their timing can counteract some errors. Spin-echo corrections that mitigate decoherence on idling qubits act as inspiration for this work. Theoretical models, however, fail to capture all sources of noise in Noisy Intermediate Scale Quantum devices, making practical solutions necessary that better minimize the impact of unpredictable errors in quantum machines. This article presents TimeStitch: a novel framework that pinpoints the optimum execution schedules for single-qubit gates within quantum circuits. TimeStitch, implemented as a compilation pass, leverages the reversible nature of quantum computation to boost the success of circuits on real quantum machines. Unlike past approaches that apply reversibility properties to improve quantum circuit execution [ 35 ], TimeStitch amplifies fidelity without violating critical path frontiers in either the slack tuning procedures or the final rescheduled circuit. On average, compared to a state-of-the-art baseline, a practically constrained TimeStitch achieves a mean 38% relative improvement in success rates, with a maximum of 106%, while observing bounds on circuit depth. When unconstrained by depth criteria, TimeStitch produces a mean relative fidelity increase of 50% with a maximum of 256%. Finally, when TimeStitch intelligently leverages periodic dynamical decoupling within its scheduling framework, a mean 64% improvement is observed over the baseline, relatively outperforming stand-alone dynamical decoupling by 19%, with a maximum of 287%.

Determining Exception Context in Assembly Operations from Multimodal Data.

Robot assembly tasks can fail due to unpredictable errors and can only continue with the manual intervention of a human operator. Recently, we proposed an exception strategy learning framework based on statistical learning and context determination, which can successfully resolve such situations. This paper deals with context determination from multimodal data, which is the key component of our framework. We propose a novel approach to generate unified low-dimensional context descriptions based on image and force-torque data. For this purpose, we combine a state-of-the-art neural network model for image segmentation and contact point estimation using force-torque measurements. An ensemble of decision trees is used to combine features from the two modalities. To validate the proposed approach, we have collected datasets of deliberately induced insertion failures both for the classic peg-in-hole insertion task and for an industrially relevant task of car starter assembly. We demonstrate that the proposed approach generates reliable low-dimensional descriptors, suitable as queries necessary in statistical learning.

Field Experience for Determination of Formaldehyde in Stack Emissions

Formaldehyde (H−CHO) is a chemical compound extremely common in many industrial productions. However, in 2004, it was reclassified as carcinogenic (H350) and mutagenic (H341). Therefore, stringent limitations on emissions were implemented; among them, the lowest limit (3 mg/m3) was adopted by some Italian Local Competent Authorities. Up to now, no European-validated method for emission control was available, and for this reason, a specific working group (WG 40) has been created in the framework of the European Committee for Standardization Technical Committees 264 (CEN TC 264) to publish a qualified method for the quantification of Formaldehyde emissions from stationary sources (i.e., power stations, incinerators, petrochemicals, and industrial plants that uses combustion for their energetic purposes). Some preliminary trial tests were conducted to evaluate (1) the sampling protocol, and (2) the analytical technique. From a measurement perspective, two methods were selected: EPA 323—VDI 3862-6 and VDI 3862-2. Every new method prepared by CEN shall be verified before publication in the field and in real conditions to verify its metrological properties (i.e., precision, biases, reproducibility, and repeatability), costs and the training needs for involved personnel. With this aim, two measuring campaigns were conducted, and some important conclusions emerged concerning the H−CHO sampling procedure. Due to high water levels normally present, condensation during sampling is critical and can cause unpredictable errors; wet traps (impingers) give good responses. The sampling in pure water appeared unstable, but using an H2SO4 solution solved this issue, thus being recommended.

In-Hospital Mortality From Cerebral Edema in MSUD During Newborn Screening Era: What Are We Missing and What More Can We Do?

In 1954, John Menkes described four siblings who died in the first three months of life from a neurometabolic disorder and whose urine had the odor of maple syrup. Decades after the recognition of this entity, and despite the advent of newborn screening and advancements in medical management, the classical form of maple syrup urine disease (MSUD) remains one of the most unpredictable and sinister inborn errors of metabolism (IEM). Mortality during metabolic crisis is estimated to be as high as 25%, and malignant cerebral edema is the most common cause of death. 1 Strauss K.A. Carson V.J. Soltys K. et al. Branched-chain α-ketoacid dehydrogenase deficiency (maple syrup urine disease): treatment, biomarkers, and outcomes. Mol Genet Metab. 2020; 129: 193-206 Crossref PubMed Scopus (44) Google Scholar

A survey on visual transfer learning using knowledge graphs

The information perceived via visual observations of real-world phenomena is unstructured and complex. Computer vision (CV) is the field of research that attempts to make use of that information. Recent approaches of CV utilize deep learning (DL) methods as they perform quite well if training and testing domains follow the same underlying data distribution. However, it has been shown that minor variations in the images that occur when these methods are used in the real world can lead to unpredictable and catastrophic errors. Transfer learning is the area of machine learning that tries to prevent these errors. Especially, approaches that augment image data using auxiliary knowledge encoded in language embeddings or knowledge graphs (KGs) have achieved promising results in recent years. This survey focuses on visual transfer learning approaches using KGs, as we believe that KGs are well suited to store and represent any kind of auxiliary knowledge. KGs can represent auxiliary knowledge either in an underlying graph-structured schema or in a vector-based knowledge graph embedding. Intending to enable the reader to solve visual transfer learning problems with the help of specific KG-DL configurations we start with a description of relevant modeling structures of a KG of various expressions, such as directed labeled graphs, hypergraphs, and hyper-relational graphs. We explain the notion of feature extractor, while specifically referring to visual and semantic features. We provide a broad overview of knowledge graph embedding methods and describe several joint training objectives suitable to combine them with high dimensional visual embeddings. The main section introduces four different categories on how a KG can be combined with a DL pipeline: 1) Knowledge Graph as a Reviewer; 2) Knowledge Graph as a Trainee; 3) Knowledge Graph as a Trainer; and 4) Knowledge Graph as a Peer. To help researchers find meaningful evaluation benchmarks, we provide an overview of generic KGs and a set of image processing datasets and benchmarks that include various types of auxiliary knowledge. Last, we summarize related surveys and give an outlook about challenges and open issues for future research.

2D scanning SERS probe for early biofilm boundary determination

Surface-enhanced Raman scattering (SERS) enables the biofilm detection by the characteristic Raman spectrum of extracellular polymeric substance (EPS). However, its clinical application in wound biofilm delineation is hindered by long sampling time and unpredictable sampling errors. To overcome these limitations, we propose a two dimensional (2D) scanning SERS probe that combines the advantages of galvo mirrors and a custom designed SERS active substrate. In this design, the SERS active substrate with dendritic nano-silver structure is fixed on the focal plane of the scan lens to maintain not only the required distance of the sampling plane but also the stable sampling condition as the excitation laser beam driven by the galvo mirrors scans quickly over the region of interest (ROI). Our benchtop study shows that the ± 3.75 mm offset between the sampling plane and the focal plane results in less than 10% change in both laser spot size and fluctuation in Raman peak intensity for the 2D scanning SERS probe, superior to the commercial Raman probe where 1700% change in laser spot size and 95% fluctuation in Raman peak intensity. Our in vitro study in two typical biofilms shows that the 2D SERS scanning probe can detect the biofilm as early as 4 h of cultivation and delineate the biofilm boundary with accuracy at 8 h of cultivation. Furthermore, this substrate is disposable, antibacterial, and capable of enhancing Raman intensity with consistency. Our studies imply the clinical potential of using the 2D SERS scanning probe for biofilm delineation in chronic wound management.

Intelligent deep learning-enabled autonomous small ship detection and classification model

Autonomous ship technologies have gained considerable interest due to the minimization of the challenging issues faced by the unpredictable errors of manual navigation, and therefore reduces human labor, increasing navigation security and profit margin. On autonomous shipping technologies, small ship detection is vital in ensuring shipping safety. With this motivation, this paper presents an efficient optimal mask regional convolutional neural network (Mask-CNN) technique for small ship detection (OMRCNN-SHD) on autonomous shipping technologies. Primarily, the data augmentation process is performed to resolve the issue of the limited number of real-world samples of small ships and helps to detect small ships in most cases accurately. Besides, the Mask RCNN with SqueezeNet model is used to detect ships and the hyperparameter tuning of the SqueezeNet model takes place by the use of the Adagrad optimizer. Furthermore, the Colliding Body's Optimization (CBO) algorithm with the weighted regularized extreme learning machine (WRELM) technique is employed to classify detected ships effectively. The comparative results analysis demonstrates the betterment of the OMRCNN-SHD technique over the current methods with the maximum accuracy of 98.63%.

Comparison of Time and Frequency Domain Solvers for Magnetic Resonance Coils at Different Field Strengths Using a Single Computational Platform

Rapid prototyping and safety assessments are essential in the modern development of radio frequency coils for magnetic resonance imaging. The use of 3D electromagnetic simulations can avoid expensive physical coil prototyping while providing quantities to determine local patient safety which is not measurable in vivo. Currently, 3D electromagnetic simulations are mostly solved on variations of two solver types, namely the time domain and the frequency domain solver. In this work, we compared these solvers and tested key simulation parameters using a single computational platform with state-of-the-art computational methods and computational human models. Our analysis included computational cost, B1+-field and power loss density for a range of common radio frequency setups used at different Larmor frequencies (field strengths, respectively) in magnetic resonance imaging systems. We found that a coarse mesh in a time solver has large unpredictable focal errors (>50%) due to partial volume artifacts while the frequency solver showed more linearity in the errors when reducing computational cost which could allow for more efficient simulations with reduced safety concerns. We expect our work to provide further insights into parameter and solver selection and contribute towards standardization in coil simulation in magnetic resonance imaging.

Finite-Time LOS Path Following of Unmanned Surface Vessels With Time-Varying Sideslip Angles and Input Saturation

In this article, a finite-time line-of-sight-based control (FTLC) scheme is presented for path following of unmanned surface vessels (USV) subject to unknown time-varying sideslip angles and input saturation as well as uncertainties induced by unknown internal dynamics and external disturbances. Specifically, finite-time observers (FTOBs) are introduced to acquire the sideslip angle and kinetic uncertainties. Finite-time line-of-sight guidance is developed by incorporating the FTOB and fractional power techniques. The profile of desired surge velocity is designed based on the hyperbolic tangent function of cross-track error. Nonlinear feedback is then introduced to attenuate the overshoot of surge velocity. Finite-time stability auxiliary systems are designed using fractional power to compensate for actuator constraints with finite-time convergence. The proposed FTLC scheme enables a USV to reach and follow a predefined path while satisfying spatial and dynamical specifications and obtaining finite-time stability and small overshoot in the presence of actuator limitations and uncertainties. All errors in the closed-loop system of USV converge to an arbitrarily small neighborhood of the origin within a finite settling time, which still holds in the presence of unpredictable errors. Three USV cases and ten simulation groups are included to demonstrate the effective performance of the FTLC.

Allelic dropout in PAH affecting the results of genetic diagnosis in phenylketonuria.

Phenylketonuria (PKU) is an inherited autosomal recessive disorder of phenylalanine metabolism. It is mainly caused by a deficiency in phenylalanine hydroxylase (PAH) and frequently diagnosed with Sanger sequencing. To some extent, allelic dropout can explain the inconsistency in genotype and phenotype. Three families were evaluated through DNA sequence analysis, multiplex ligation-dependent probe amplification (MLPA) and prenatal diagnosis technologies. The possibility of inconsistency in phenotype and genotype with c.331C>T variant was analysed. Through pedigree analysis, three mothers carried a homozygous c.331C>T variant, which was a false-positive result. New primers were used, and this error was caused by allelic dropout. In this case, c.158G>A was likely a benign variant. Sequence variants in primer-binding regions could cause allelic dropout, creating unpredictable errors in genotyping. Our results emphasised the need for careful measures to treat genotype-phenotype inconsistencies.

Randomized Compiling for Scalable Quantum Computing on a Noisy Superconducting Quantum Processor

The successful implementation of algorithms on quantum processors relies on the accurate control of quantum bits (qubits) to perform logic gate operations. In this era of noisy intermediate-scale quantum (NISQ) computing, systematic miscalibrations, drift, and crosstalk in the control of qubits can lead to a coherent form of error that has no classical analog. Coherent errors severely limit the performance of quantum algorithms in an unpredictable manner, and mitigating their impact is necessary for realizing reliable quantum computations. Moreover, the average error rates measured by randomized benchmarking and related protocols are not sensitive to the full impact of coherent errors and therefore do not reliably predict the global performance of quantum algorithms, leaving us unprepared to validate the accuracy of future large-scale quantum computations. Randomized compiling is a protocol designed to overcome these performance limitations by converting coherent errors into stochastic noise, dramatically reducing unpredictable errors in quantum algorithms and enabling accurate predictions of algorithmic performance from error rates measured via cycle benchmarking. In this work, we demonstrate significant performance gains under randomized compiling for the four-qubit quantum Fourier transform algorithm and for random circuits of variable depth on a superconducting quantum processor. Additionally, we accurately predict algorithm performance using experimentally measured error rates. Our results demonstrate that randomized compiling can be utilized to leverage and predict the capabilities of modern-day noisy quantum processors, paving the way forward for scalable quantum computing.Received 13 May 2021Accepted 3 September 2021DOI:https://doi.org/10.1103/PhysRevX.11.041039Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum algorithmsQuantum benchmarkingQuantum controlQuantum information with solid state qubitsQuantum Information

Development of Double-Sided Multipoint Press CNC and Operational Technology for Producing Freeform Molds

Many studies concerning the precision manufacturing of freeform concrete panels have been conducted, however, this process remains labor intensive taking significant amounts of time and cost. In particular, the precision in the shape of the panels produced tends to be low because of the manual work involved in producing the curves of those panels. This study documents the development of mold production technologies that can be used to produce precise curved surfaces on the upper and lower parts of a mold for freeform concrete panels. A double-sided multipoint press CNC (computer numerical control) produces curved upper and lower surfaces of a mold without the need for manual work, while the operational technology we developed to control this tool enhances the precision of the curves created. The precision of these technologies was verified through experiments. The difference between the shapes designed and those produced were found using 3D scans and quality inspections. Unpredictable errors can occur due to the size of certain curvatures, the elasticity of the silicone plate, and the rotational angle of the joints of the rods supporting the surfaces. To minimize errors, shape compensation was carried out through reverse engineering, leading to a maximum error of 2.887 mm, which is within the allowable error. The results achieved in this study are a significant step toward technologies that will produce increasingly precise freeform concrete panels.

Deep-Reinforcement-Learning-Based Latency Minimization in Edge Intelligence Over Vehicular Networks

A novel paradigm that combines federated learning with blockchain to empower edge intelligence over vehicular networks (FBVN) can enable latency-sensitive deep neural network-based applications to be executed in a distributed pattern. However, the complex environments in FBVN make the system latency much harder to minimize by traditional methods. In this article, we model the training and transmission latency of each autonomous vehicle (AV) and consensus latency of the blockchain in-edge side in FBVN. Considering the dynamic and time-varying wireless channel conditions, unpredictable packet error rate, and unstable data sets quality, we adopt duel deep <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -learning (DDQL) as the solving approach. We propose a federated DDQL algorithm, in which the learning agent is deployed on each AV side, and the sensing states on each AV do not need to be shared so that it increases scalability and flexibility for practical implementation. Simulation results show that the proposed algorithm has better performance in reducing system latency compared with the other schemes.

Systematic Partitioning of Proteins for Quantum-Chemical Fragmentation Methods Using Graph Algorithms

Quantum-chemical fragmentation methods offer an efficient approach for the treatment of large proteins, in particular if local target quantities such as protein-ligand interaction energies, enzymatic reaction energies, or spectroscopic properties of embedded chromophores are sought. However, the accuracy that is achievable for such local target quantities intricately depends on how the protein is partitioned into smaller fragments. While the commonly employed naı̈ve approach of using fragments with a fixed size is widely used, it can result in large and unpredictable errors when varying the fragment size. Here, we present a systematic partitioning scheme that aims at minimizing the fragmentation error of a local target quantity for a given maximum fragment size. To this end, we construct a weighted graph representation of the protein, in which the amino acids constitute the nodes. These nodes are connected by edges weighted with an estimate for the fragmentation error that is expected when cutting this edge. This allows us to employ graph partitioning algorithms provided by computer science to determine near-optimal partitions of the protein. We apply this scheme to a test set of six proteins representing various prototypical applications of quantum-chemical fragmentation methods using a simplified molecular fractionation with conjugate caps (MFCC) approach with hydrogen caps. We show that our graph-based scheme consistently improves upon the naı̈ve approach.