Goal Of Accuracy Research Articles

TAToo: vision-based joint tracking of anatomy and tool for skull-base surgery.

Tracking the 3D motion of the surgical tool and the patient anatomy is a fundamental requirement for computer-assisted skull-base surgery. The estimated motion can be used both for intra-operative guidance and for downstream skill analysis. Recovering such motion solely from surgical videos is desirable, as it is compliant with current clinical workflows and instrumentation. We present Tracker of Anatomy and Tool (TAToo). TAToo jointly tracks the rigid 3D motion of the patient skull and surgical drill from stereo microscopic videos. TAToo estimates motion via an iterative optimization process in an end-to-end differentiable form. For robust tracking performance, TAToo adopts a probabilistic formulation and enforces geometric constraints on the object level. We validate TAToo on both simulation data, where ground truth motion is available, as well as on anthropomorphic phantom data, where optical tracking provides a strong baseline. We report sub-millimeter and millimeter inter-frame tracking accuracy for skull and drill, respectively, with rotation errors below [Formula: see text]. We further illustrate how TAToo may be used in a surgical navigation setting. We present TAToo, which simultaneously tracks the surgical tool and the patient anatomy in skull-base surgery. TAToo directly predicts the motion from surgical videos, without the need of any markers. Our results show that the performance of TAToo compares favorably to competing approaches. Future work will include fine-tuning of our depth network to reach a 1mm clinical accuracy goal desired for surgical applications in the skull base.

Limitations in Testing the Lense–Thirring Effect with LAGEOS and the Newly Launched Geodetic Satellite LARES 2

The new geodetic satellite LARES 2, cousin of LAGEOS and sharing with it almost the same orbital parameters apart from the inclination, displaced by 180 deg, was launched last year. Its proponents suggest using the sum of the nodes of LAGEOS and of LARES 2 to measure the sum of the Lense–Thirring node precessions independently of the systematic bias caused by the even zonal harmonics of the geopotential, claiming a final ≃0.2 percent total accuracy. In fact, the actual orbital configurations of the two satellites do not allow one to attain the sought for mutual cancellation of their classical node precessions due to the Earth’s quadrupole mass moment, as their sum is still ≃5000 times larger than the added general relativistic rates. This has important consequences. One is that the current uncertainties in the eccentricities and the inclinations of both satellites do not presently allow the stated accuracy goal to be met, needing improvements of 3–4 orders of magnitude. Furthermore, the imperfect knowledge of the Earth’s angular momentum S impacts the uncancelled sum of the node precessions, from 150 to 4900 percent of the relativistic signal depending on the uncertainty assumed in S. It is finally remarked that the real breakthrough in reliably testing the gravitomagnetic field of the Earth would consist in modeling it and simultaneously estimating one or more dedicated parameter(s) along with other ones characterising the geopotential, as is customarily performed for any other dynamical feature.

Using the internet “raises the bar” for precision in self‐produced question answering

AbstractWhen responding to queries for information, people control thegrain size(precision–coarseness) of the information they communicate based on competing goals of accuracy and informativeness (Goldsmith & Koriat,Behavioral and Brain Sciences, 1999,19, 167). Two experiments examined whether the act of searching for answers using the internet influences the granularity of the information people later choose to report. Participants who searched the internet for answers to general information questions later provided more precise (granular) estimates to questions in the absence of the internet when compared to participants who initially answered questions from memory and participants who initially were not asked any questions. These results indicate that searching the internet influences metacognitive processes underlying decisions about the granularity of the information we choose to communicate. The internet may “raise the bar” with respect to the informativeness of the information we feel obliged to offer.

High-order discontinuous Galerkin hydrodynamics with sub-cell shock capturing on GPUs

ABSTRACT Hydrodynamical numerical methods that converge with high-order hold particular promise for astrophysical studies, as they can in principle reach prescribed accuracy goals with higher computational efficiency than standard second- or third-order approaches. Here we consider the performance and accuracy benefits of Discontinuous Galerkin (DG) methods, which offer a particularly straightforward approach to reach extremely high order. Also, their computational stencil maps well to modern GPU devices, further raising the attractiveness of this approach. However, a traditional weakness of this method lies in the treatment of physical discontinuities such as shocks. We address this by invoking an artificial viscosity field to supply required dissipation where needed, and which can be augmented, if desired, with physical viscosity and thermal conductivity, yielding a high-order treatment of the Navier–Stokes equations for compressible fluids. We show that our approach results in sub-cell shock capturing ability, unlike traditional limiting schemes that tend to defeat the benefits of going to high order in DG in problems featuring many shocks. We demonstrate exponential convergence of our solver as a function of order when applied to smooth flows, such as the Kelvin–Helmholtz reference problem of Lecoanet et al. We also demonstrate excellent scalability of our GPU implementation up to hundreds of GPUs distributed on different compute nodes. In a first application to driven, subsonic turbulence, we highlight the accuracy advantages of high-order DG compared to traditional second-order accurate methods, and we stress the importance of physical viscosity for obtaining accurate velocity power spectra.

Improved 3D localization algorithm for large scale wireless sensor networks

As localization represents the main core of various wireless sensor network applications, several localization algorithms have been suggested in wireless sensor network research. In this article, we put forward an iterative bounding box algorithm enhanced by a Kalman filter to refine the unknown node’s estimated position. In fact, several research efforts are currently in progress to extend the 2D positioning algorithm in WSNs to 3D that reflects reality and the most practical applications. Subsequently, we replace a large number of GPS-equipped anchors with a single mobile anchor. In our studies, we consider the type of range-free sensor network exploiting the wireless sensors connectivity. We assess the performance of our algorithm using exhaustive experiments on several isotropic and anisotropic topologies. Our proposed algorithm can fulfill the joint goals of algorithm transparency and accuracy for various scenarios by evaluating parameters such as localization accuracy whilst changing other simulation parameters such as the effect of communication range, mobile anchor node position and sensor node deployment topology. It has been proven by the results of the experiments that the proposed algorithm effectively reduces the location error without requiring more equipment or increasing the communication cost.

Selecting and Composing Learning Rate Policies for Deep Neural Networks

The choice of learning rate (LR) functions and policies has evolved from a simple fixed LR to the decaying LR and the cyclic LR, aiming to improve the accuracy and reduce the training time of Deep Neural Networks (DNNs). This article presents a systematic approach to selecting and composing an LR policy for effective DNN training to meet desired target accuracy and reduce training time within the pre-defined training iterations. It makes three original contributions. First, we develop an LR tuning mechanism for auto-verification of a given LR policy with respect to the desired accuracy goal under the pre-defined training time constraint. Second, we develop an LR policy recommendation system (LRBench) to select and compose good LR policies from the same and/or different LR functions through dynamic tuning, and avoid bad choices, for a given learning task, DNN model, and dataset. Third, we extend LRBench by supporting different DNN optimizers and show the significant mutual impact of different LR policies and different optimizers. Evaluated using popular benchmark datasets and different DNN models (LeNet, CNN3, ResNet), we show that our approach can effectively deliver high DNN test accuracy, outperform the existing recommended default LR policies, and reduce the DNN training time by 1.6-6.7× to meet a targeted model accuracy.

Amplitude evaluation with pySecDec: A Higgs + three gluons example

We present an application of the major new features of pySecDec, a program designed to numerically calculate multi-loop integrals. One important new feature is the ability to integrate weighted sums of integrals in a way which is optimised to reach a given accuracy goal on the sums rather than on the individual integrals. Another feature is the option to perform asymptotic expansions. These new assets of the program represent an important step towards the efficient evaluation of multi-loop amplitudes in a largely automated way. We will illustrate them in a pedagogical example, through the calculation of the one-loop amplitude for Higgs plus jet production in the gluon channel, mediated by a top quark loop. Numerical results in the heavy top limit, compared to their analytic counterparts, are shown as well.

GENESIS: co-location of geodetic techniques in space

Improving and homogenizing time and space reference systems on Earth and, more specifically, realizing the Terrestrial Reference Frame (TRF) with an accuracy of 1 mm and a long-term stability of 0.1 mm/year are relevant for many scientific and societal endeavors. The knowledge of the TRF is fundamental for Earth and navigation sciences. For instance, quantifying sea level change strongly depends on an accurate determination of the geocenter motion but also of the positions of continental and island reference stations, such as those located at tide gauges, as well as the ground stations of tracking networks. Also, numerous applications in geophysics require absolute millimeter precision from the reference frame, as for example monitoring tectonic motion or crustal deformation, contributing to a better understanding of natural hazards. The TRF accuracy to be achieved represents the consensus of various authorities, including the International Association of Geodesy (IAG), which has enunciated geodesy requirements for Earth sciences. Moreover, the United Nations Resolution 69/266 states that the full societal benefits in developing satellite missions for positioning and Remote Sensing of the Earth are realized only if they are referenced to a common global geodetic reference frame at the national, regional and global levels. Today we are still far from these ambitious accuracy and stability goals for the realization of the TRF. However, a combination and co-location of all four space geodetic techniques on one satellite platform can significantly contribute to achieving these goals. This is the purpose of the GENESIS mission, a component of the FutureNAV program of the European Space Agency. The GENESIS platform will be a dynamic space geodetic observatory carrying all the geodetic instruments referenced to one another through carefully calibrated space ties. The co-location of the techniques in space will solve the inconsistencies and biases between the different geodetic techniques in order to reach the TRF accuracy and stability goals endorsed by the various international authorities and the scientific community. The purpose of this paper is to review the state-of-the-art and explain the benefits of the GENESIS mission in Earth sciences, navigation sciences and metrology. This paper has been written and supported by a large community of scientists from many countries and working in several different fields of science, ranging from geophysics and geodesy to time and frequency metrology, navigation and positioning. As it is explained throughout this paper, there is a very high scientific consensus that the GENESIS mission would deliver exemplary science and societal benefits across a multidisciplinary range of Navigation and Earth sciences applications, constituting a global infrastructure that is internationally agreed to be strongly desirable.Graphical

Adaptive piecewise Poly-Sinc methods for function approximation

We propose a new method of adaptive piecewise function approximation based on Sinc points. The adaptive method is a Lagrange interpolation scheme which utilizes Poly-Sinc interpolation to reach a preset level of accuracy for the approximation. We prove the exponential convergence of our algorithm. We derive an a priori error estimate for our adaptive method and show its exponential convergence. We use a statistical approach for partition refinement. The adaptive greedy piecewise Poly-Sinc algorithm is validated on continuous, singular, and piecewise functions. We demonstrate that Runge's phenomenon can be handled within a given accuracy goal.

Time-Efficient and Low-Cost Neural Network to detect plant disease on leaves and reduce food loss and waste

About 25% of the food grown never reaches consumers due to spoilage, and 11.5 billion pounds of produce from gardens are wasted every year. Diseases are a major cause of food loss as Asia loses 14.2% of its crops due to disease, which is equivalent to 43.8 billion dollars as of 1988-1990. Current solutions involve farmers manually looking for and treating diseased crops. These methods of tending crops are neither time-efficient nor feasible. I used a convolutional neural network to identify signs of plant disease on leaves for garden owners and farmers. The overall accuracy goal of 90% or higher was set to develop the most accurate models. The learning rates of 0.1, 0.01, and 0.001 were tested for the network. I hypothesized that the step size at each iteration or the learning rate of 0.001 would result in the highest accuracy, which was supported through testing. By using machine learning Python libraries, the solution met the standard accuracy goal and was evaluated by several performance metrics, including precision, recall, f-score, specificity, and overall accuracy rates. The model had an accuracy of 95%. By uploading a picture of the crops into the highly-accurate neural network, farmers and gardeners can receive results in seconds on whether or not their crops have a disease, and if they do, which ailment specifically.

Toward cooperative multi-agent video streaming perception

Video streaming perception ability is critical for AI applications on resource-constrained devices (agents), which prefers to offload video streams from devices to edge servers for real-time inference by deep neural networks (DNNs). Meanwhile, the multi-agent system (MAS) community is attempting to run DNNs on multiple cooperative agents to enable improved swarm intelligence-based tasks (e.g., drone swarm intelligence, self-driving fleet collaboration, and multi-agent robot cooperation). However, transferring video streaming perception capability from single-agent systems to MASs is extremely difficult due to spontaneous competition-induced trade-offs between the desired goals of accuracy, consistency, and capacity, which are three critical but conflicting measuring indexes. In this paper, we present the design and implementation of MASSIVE, an edge-assisted cooperative multi-agent video streaming perception system that simultaneously achieves all three desired goals. In our design, we consider the performance characteristics of video streaming perception and the insight of its periodic offloading pattern. On this basis, we develop a Pareto improvement scheduler to eliminate spontaneous competition among agents, allowing multi-objective optimization to achieve an ideal Pareto optimal state. Finally, we propose a virtual traffic shaper based on the mainstream 802.11 MAC protocol to ensure deterministic periodic video stream offloading in an uncertain wireless network. Our experiments demonstrate that MASSIVE achieves 122.7% accuracy and 1.8x capacity compared to the closest baseline on multiple actual cooperative vision tasks with even better consistency, and achieves an ideal Pareto optimal state in a wireless environment.

IHorology: Lowering the Barrier to Microsecond-Level Internet Time

High accuracy, synchronized clocks are essential to a growing number of Internet applications. Standard protocols and their associated server infrastructure typically enable client clocks to synchronize to the order of tens of milliseconds. We address one of the key challenges to high precision Internet timekeeping – the intrinsic contribution to clock error of underlying path asymmetry between client and time server, a fundamental barrier to microsecond level accuracy. We first exploit results of a unique measurement study to reliably quantify asymmetry by taking routing changes into account for the first time, and then to infer the impacts on timing. We then describe three approaches to addressing the path asymmetry problem: LBBE, SBBE and K-SBBE, each based on timestamp exchange with multiple servers, with the goal of tightening bounds on asymmetry for each client. We explore their capabilities and limitations through simulation and model-based argument. We show that substantial improvements are possible, and discuss whether, and how, the goal of microsecond accuracy might be attained.

TOPz: Photometric redshifts for J-PAS

Context. The importance of photometric galaxy redshift estimation is rapidly increasing with the development of specialised powerful observational facilities. Aims. We develop a new photometric redshift estimation workflow TOPz to provide reliable and efficient redshift estimations for the upcoming large-scale survey J-PAS which will observe 8500 deg2 of the northern sky through 54 narrow-band filters. Methods. TOPz relies on template-based photo-z estimation with some added J-PAS specific features and possibilities. We present TOPz performance on data from the miniJPAS survey, a precursor to the J-PAS survey with an identical filter system. First, we generated spectral templates based on the miniJPAS sources using the synthetic galaxy spectrum generation software CIGALE. Then we applied corrections to the input photometry by minimising systematic offsets from the template flux in each filter. To assess the accuracy of the redshift estimation, we used spectroscopic redshifts from the DEEP2, DEEP3, and SDSS surveys, available for 1989 miniJPAS galaxies with r < 22 magAB. We also tested how the choice and number of input templates, photo-z priors, and photometric corrections affect the TOPz redshift accuracy. Results. The general performance of the combination of miniJPAS data and the TOPz workflow fulfills the expectations for J-PAS redshift accuracy. Similarly to previous estimates, we find that 38.6% of galaxies with r < 22 mag reach the J-PAS redshift accuracy goal of dz/(1 + z) < 0.003. Limiting the number of spectra in the template set improves the redshift accuracy up to 5%, especially for fainter, noise-dominated sources. Further improvements will be possible once the actual J-PAS data become available.

EICO: Energy-Harvesting Long-Range Environmental Sensor Nodes With Energy-Information Dynamic Co-Optimization

Intensive research on energy-harvested sensor nodes has been driven by the challenges in achieving stringent design goals of battery lifetime, information accuracy, transmission distance, and cost. This challenge is further amplified by the inherent power-intensive nature of long-range communication when sensor networks are required to span vast areas, such as agricultural fields and remote terrain. Solar power is a common energy source in wireless sensor nodes, however, it is not reliable due to fluctuations in available power stemming from the changing seasons and weather conditions. This article tackles these issues by presenting a perpetually powered, energy-harvesting sensor node which utilizes a minimally sized solar cell and is capable of long-range communication by dynamically co-optimizing energy consumption and information transfer, termed as energy-information dynamic co-optimization (EICO). This energy-information intelligence is achieved by adaptive dutycycling of information transfer based on the total amount of energy available from the harvester and charge storage element to optimize the energy consumption of the sensor node, while employing in-sensor analytics (ISA) to minimize loss of information. This is the first reported sensor node < 35 cm2 in dimension, which is capable of long-range communication over >1 km at continuous information transfer rates of up to 1 packet/second which is enabled by EICO and ISA.

A laser tracker-based multilateration method for pre-alignment of High Energy Photon Source storage ring

High-precision pre-alignment of the magnet components is an important step in the construction and operation of the High Energy Photon Source (HEPS). In order to achieve 10μm pre-alignment accuracy of storage ring in transverse and vertical, four laser trackers were used for set up a four-station multilateration measurement system. A Rank-defect Free-network adjustment model was used to analysis the measurement accuracy of different arrangements of multilateration measurement system. By simulation, it shows when the four stations form a right-angled regular triangular pyramid the highest point measurement accuracy can be gotten. A multilateration measurement system formed by four laser tracker was built in the laboratory. Experiment results show that the absolute position measurement accuracy is within 7.1μm and the relative displacement measurement accuracy is better than 3μm in a 4 m × 1.2 m × 1.5 m volume, which can satisfy the real-time position feedback accuracy of the magnets in the process of ultra-high-precision pre-alignment. Then, a pre-alignment experiment for High Energy Photon Source based on this system was carried out, and finally the 10μm pre-alignment accuracy goal in transverse and vertical was achieved.

Intergroup Cascade Broad Learning System With Optimized Parameters for Chaotic Time Series Prediction

The prediction of chaotic time series can well describe the physical properties and influencing factors of a sequence of numerical data points in successive order and has played an increasingly crucial role in various scientific and engineering communities. These time series data require the prediction model to have strong dynamic feature representation ability, which often leads to excessive calculation burden. As an emerging and effective learning method, a broad learning system (BLS) can be trained quickly by incremental learning, and the system can be reconstructed without requiring a lengthy retraining process, which has been shown to facilitate superior time-saving performance. However, the historical information of time series data is often ignored, resulting in the lack of dynamic feature representation ability of the original BLS algorithm. In this article, a novel intergroup cascade BLS (ICBLS) method and its variant with optimized parameters, termed MOICBLS, are proposed, which can combine the previous knowledge with current information to determine the output results by constructing a novel intergroup cascade structure for the enhancement nodes. The new algorithms try to retain the time-saving advantage of BLS and greatly enhance the extraction ability of dynamic features of chaotic time series data. In addition, it cannot be ignored that the network structure parameters have an unquestionable impact on the performance of a BLS. In response, two conflicting goals of prediction accuracy and diversity are formulated as multiobjective optimization functions in the training phase to generate the optimized network structure parameters needed by multiple candidate models. The experimental results on two benchmark chaotic time series dataset, the Lorenz system and Rossler system, and a geomagnetic disturbance storm time chaotic time series dataset demonstrate that our proposed algorithms are effective for prediction of chaotic time series, and the prediction accuracy is better than some existing approaches.

Boosting the efficiency of parametric detection with hierarchical neural networks

Gravitational wave astronomy is a vibrant field that leverages both classic and modern data processing techniques for the understanding of the universe. Various approaches have been proposed for improving the efficiency of the detection scheme, with hierarchical matched filtering being an important strategy. Meanwhile, deep learning methods have recently demonstrated both consistency with matched filtering methods and remarkable statistical performance. In this work, we propose Hierarchical Detection Network (HDN), a novel approach to efficient detection that combines ideas from hierarchical matching and deep learning. The network is trained using a novel loss function, which encodes simultaneously the goals of statistical accuracy and efficiency. We discuss the source of complexity reduction of the proposed model, and describe a general recipe for initialization with each layer specializing in different regions. We demonstrate the performance of HDN with experiments using open LIGO data and synthetic injections, and observe with two-layer models a $79\%$ efficiency gain compared with matched filtering at an equal error rate of $0.2\%$. Furthermore, we show how training a three-layer HDN initialized using two-layer model can further boost both accuracy and efficiency, highlighting the power of multiple simple layers in efficient detection.

Forward-Solution Noninvasive Computational Arrhythmia Mapping: The VMAP Study.

The accuracy of noninvasive arrhythmia source localization using a forward-solution computational mapping system has not yet been evaluated in blinded, multicenter analysis. This study tested the hypothesis that a computational mapping system incorporating a comprehensive arrhythmia simulation library would provide accurate localization of the site-of-origin for atrial and ventricular arrhythmias and pacing using 12-lead ECG data when compared with the gold standard of invasive electrophysiology study and ablation. The VMAP study (Vectorcardiographic Mapping of Arrhythmogenic Probability) was a blinded, multicenter evaluation with final data analysis performed by an independent core laboratory. Eligible episodes included atrial and ventricular: tachycardia, fibrillation, pacing, premature atrial and ventricular complexes, and orthodromic atrioventricular reentrant tachycardia. Mapping system results were compared with the gold standard site of successful ablation or pacing during electrophysiology study and ablation. Mapping time was assessed from time-stamped logs. Prespecified performance goals were used for statistical comparisons. A total of 255 episodes from 225 patients were enrolled from 4 centers. Regional accuracy for ventricular tachycardia and premature ventricular complexes in patients without significant structural heart disease (n=75, primary end point) was 98.7% (95% CI, 96.0%-100%; P<0.001 to reject predefined H0 <0.80). Regional accuracy for all episodes (secondary end point 1) was 96.9% (95% CI, 94.7%-99.0%; P<0.001 to reject predefined H0 <0.75). Accuracy for the exact or neighboring segment for all episodes (secondary end point 2) was 97.3% (95% CI, 95.2%-99.3%; P<0.001 to reject predefined H0 <0.70). Median spatial accuracy was 15 mm (n=255, interquartile range, 7-25 mm). The mapping process was completed in a median of 0.8 minutes (interquartile range, 0.4-1.4 minutes). Computational ECG mapping using a forward-solution approach exceeded prespecified accuracy goals for arrhythmia and pacing localization. Spatial accuracy analysis demonstrated clinically actionable results. This rapid, noninvasive mapping technology may facilitate catheter-based and noninvasive targeted arrhythmia therapies. URL: https://www. gov; Unique identifier: NCT04559061.

Multiobjective whale optimization algorithm‐based feature selection for intelligent systems

With regard to large dimensions of contemporary data sets and restricted computational time of intelligent systems, reducing the dimensions of data sets is necessary. Feature selection is a practical way to remove a set of redundant, irrelevant, and noisy features. In this way, the speed of decision-making procedure will be increased while the accuracy of decisions will be retained. To this end, numerous attentions have been attracted to the topic and consequently, extensive range of methods has been proposed. Regarding the goals of the feature selection concept, the proposed algorithms in this field must be fast and accurate. Therefore, this paper proposes a light meanwhile accurate algorithm to fulfill the mentioned goals. The presented algorithm takes the speed advantage of Whale Optimization Algorithm (WOA) to propose a novel feature selection method for intelligent systems. Moreover, to reach the goal of accuracy, the proposed strategy considers three important fitness objectives, namely, the number of selected features, the accuracy of classification, and information gain. The proposed scheme considers an accurate multiobjective fitness function instead of manipulating the basic algorithm. The reason is that improving the basic algorithms, WOA in our case, may lead to loading more computational complexity. Also, to make the proposed algorithm as light as possible, this paper considers K-nearest neighbor algorithm as the main classifier. The proposed light feature selection algorithm is run on different data sets. Experimental results prove that this algorithm is able to reduce the number of features meanwhile it retains, and in some cases even increases, the accuracy of classification.

Framework for Testing Robustness of Machine Learning-Based Classifiers.

There has been a rapid increase in the number of artificial intelligence (AI)/machine learning (ML)-based biomarker diagnostic classifiers in recent years. However, relatively little work has focused on assessing the robustness of these biomarkers, i.e., investigating the uncertainty of the AI/ML models that these biomarkers are based upon. This paper addresses this issue by proposing a framework to evaluate the already-developed classifiers with regard to their robustness by focusing on the variability of the classifiers’ performance and changes in the classifiers’ parameter values using factor analysis and Monte Carlo simulations. Specifically, this work evaluates (1) the importance of a classifier’s input features and (2) the variability of a classifier’s output and model parameter values in response to data perturbations. Additionally, it was found that one can estimate a priori how much replacement noise a classifier can tolerate while still meeting accuracy goals. To illustrate the evaluation framework, six different AI/ML-based biomarkers are developed using commonly used techniques (linear discriminant analysis, support vector machines, random forest, partial-least squares discriminant analysis, logistic regression, and multilayer perceptron) for a metabolomics dataset involving 24 measured metabolites taken from 159 study participants. The framework was able to correctly predict which of the classifiers should be less robust than others without recomputing the classifiers itself, and this prediction was then validated in a detailed analysis.