Correction Process Research Articles

A Statistical Model for Multisource Remote-Sensing Data Streams of Wildfire Aerosol Optical Depth

Increasingly frequent wildfires have significant impact on solar energy production as the atmospheric aerosols generated by wildfires diminish the incoming solar radiation. Atmospheric aerosols can be measured by aerosol optical depth (AOD), and multiple spatiotemporal AOD data streams are available from geostationary satellites. Although these multisource remote-sensing data streams are measurements of the same underlying AOD process, they often present heterogeneous characteristics, such as different measurement biases and errors, data missing rates, etc. It is usually not known which data source provides more accurate measurements, and simply averaging multiple data streams is not always the best practice. Hence, this paper proposes a statistical model that is capable of inferring the underlying true AOD process by simultaneously integrating heterogeneous multisource remote-sensing data streams and the advection-diffusion equation that governs the dynamics of the AOD process. A bias correction process is included in the model to account for the bias of the physics model and the truncation error of the Fourier series. The proposed approach is applied to California wildfires AOD data obtained from the GOES East (GOES-16) and GOES West (GOES-17) satellites operated by the National Oceanic and Atmospheric Administration. Comprehensive numerical examples are provided to demonstrate the predictive capabilities and model the interpretability of the proposed approach. History: Kwok-Leung Tsui served as the senior editor for this article. Funding: This work was funded by the U.S. National Science Foundation [Grant 2143695]. Data Ethics & Reproducibility Note: Our code requires packages that are not available on CodeOcean (for example, the Rfast package in R). Hence, code and sample data are provided on GitHub: https://github.com/gz-wei/Physics-Informed-Statistical-Modeling-for-Wildfire-Aerosols-Propagation . The online appendix is available at https://doi.org/10.1287/ijds.2021.0058 .

Support of Cancer Patients at the Stage of Early Rehabilitation: Possibilities of Postural Correction and Art Therapy Techniques

Introduction. Early rehabilitation of cancer patients after surgery plays an important role in their recovery and return to normal functioning. One of the tasks of this stage of treatment is to restore physical activity of the body, in particular, through postural correction. The medical aspects of this process are well described in the literature, however, the psychological aspects of the postural correction process are not sufficiently covered. Even fewer studies are devoted to restoring the psychological state of cancer patients. Purpose. Analysis of the possibilities of postural correction of cancer patients and the possibility of using art therapy techniques to normalize the psychological state during early rehabilitation.Theoretical justification. One of the key elements of postural correction is the restoration of the ability to maintain balance. For this purpose, special devices are used – stabilometric platforms. Another important element is the restoration of voluntary movements. For a more effective recovery, it is worth teaching patients the psychological adjustment to exercise movements. When the patient plans a movement, he forms a mental construct “task to be completed”, which promotes more precise movements. Restoration of their stable psychological state of cancer patients is possible, in particular, through art therapy techniques. One of the techniques, coloring mandalas, involves both hemispheres of the patients’ brains, triggering cognitive processes through the activation of fine motor skills. This provides a natural therapeutic process: the brain works initially on simple tasks and gradually moves on to more complex ones. The details of the mandala drawing are thought out in such a way that in the process of working on it, the patient focuses on his inner state – thoughts and feelings.Discussion. The importance of an integrated approach to the rehabilitation of cancer patients is increasingly emphasized in scientific papers. During the early rehabilitation period, the patient is in the most vulnerable state, both physically and psychologically. The use of psychological techniques can ensure that the patient can restore a more holistic image of himself both physically and internally.

Study on Welding Deformation Correction of TC4 Titanium Alloy Panel Parts

Aiming at the problem that TC4 titanium alloy panel parts after welding have large internal residual stress and obvious panel deformation, which can’t meet the requirements of the parts, the viscoelastic plastic model of titanium alloy panel parts is established by finite element analysis, and the welding deformation-thermal alignment collaborative simulation environment is established by ANSYS, and the welding deformation and thermal alignment process are analyzed by numerical simulation. The law of shape correction when the correction temperature is 600 °C, 650 °C, 700 °C and the holding time is 3600s, 5400s and 7200s, respectively, and the calculation formula of springback rate is established to evaluate the effect of thermal shape correction, so as to optimize the heat treatment correction process. The results show that the correction temperature and holding time have obvious influence on the correction effect. When the correction temperature is 700 °C and holding time is 7200s, the correction effect is the best, and the springback rate is controlled below 25%, which meets the requirements of machining accuracy.

Simulation of supersonic axisymmetric base flow with a data-driven turbulence model

Axisymmetric base flow involves massive flow separation which is challenging for a typical Reynolds-averaged Navier-Stokes (RANS) turbulence model. Furthermore, a supersonic condition imposes additional difficulties to a turbulence model in predicting strong compressibility effects associated with the flow separation phenomena. A data-driven approach is pursued here to improve a turbulence model. The Spalart-Allmaras model is corrected from an optimization process, and then the model correction is mapped to local flow features through a machine learning process. For the optimization-combined machine learning method, the field inversion and machine learning framework is adapted here with three major modifications. First, a zonal-field inversion method is suggested to avoid the undesired modification of attached flow in the optimization process for the model correction. Second, the RANS model is modified by adjusting a net balance between the production and destruction terms in the RANS equation. Third, the local Mach number is included in the machine learning process to incorporate compressibility effects of the supersonic flow. The current study indicates that the improved RANS model reduces the eddy viscosity in the separated region, compared to the baseline RANS model. The reduction of the eddy viscosity helps to predict the base expansion of the supersonic flow and the size of the recirculation region. Current computations are compared with relevant literature data including wake velocity profiles and the base pressure in the wide range of the supersonic Mach number.

Inversion of Forest above Ground Biomass in Mountainous Region Based on PolSAR Data after Terrain Correction: A Case Study from Saihanba, China

Accurate retrieval of forest above ground biomass (AGB) based on full-polarization synthetic aperture radar (PolSAR) data is still challenging for complex surface regions with fluctuating terrain. In this study, the three-step process of radiometric terrain correction (RTC), which includes polarization orientation angle correction (POAC), effective scattering area correction (ESAC), and angular variation effect correction (AVEC), is adopted as the technical framework. In the ESAC stage, a normalized correction factor is introduced based on local incidence angle and radar incidence angle to achieve accurate correction of PolSAR data information and improve the inversion accuracy of forest AGB. In order to verify the validity and robustness of this research method, the full-polarization SAR data of ALOS-2 and the ground measured AGB data collected in the Saihanba research area in 2020 were used for experiments. Our findings revealed that in the ESAC phase, the introduction of the normalized correction factor can effectively eliminate the ESA phenomenon and improve the correlation coefficients of the backscatter coefficient and AGB. Taking the data of 25 July 2020 as an example, ESAC increases the correlation coefficients between AGB and the backscattering coefficients of HH, HV, and VV polarization channels by 0.343, 0.296, and 0.382, respectively. In addition, the RTC process has strong robustness in different AGB statistical models and different date PolSAR data.

Development of an accreditation process for analytical methods to measure microplastics in drinking water for regulatory monitoring

Development of a laboratory accreditation program to ensure competency of laboratories performing analytical measurements is a key step in adopting new analytical measurement methods for regulatory decision-making. Here, we describe California's three-part accreditation process for spectroscopically measuring microplastics in drinking water, and show how data from a multi-laboratory method comparison study informed development of accreditation programs for the resulting methods, which can inform analogous future work for other analytes. The first part is periodic performance evaluation (PE) samples, in which laboratories are provided blind samples of known composition to quantify within acceptable performance limits. The second is inspection, or audit, assessing whether the laboratory has the proper equipment to conduct the work and whether it is correctly employing proper procedures. The third is implementation of a quality management system providing documentation that protocols demonstrated during inspection are continuously maintained. These fell into three broad categories: instrument maintenance; laboratory cleanliness, especially important for microplastics and one that must be accompanied by a blanks measurement and correction process; and training so samples are being processed by qualified analysts. An intercomparison exercise among 22 laboratories was necessary to determine what parameter permutations were important for PE samples, and expected accuracy from competent laboratories. The recommended PE sample composition was two size categories (20-50um and 500um-1mm), two polymer types, and two morphologies (fibers and non-fibers). Discussions among intercomparison exercise participants were key in determining the factors that most contributed to laboratory variability, and the focus for both on-site inspections and quality management systems.

Multisource remote sensing image fusion processing in plateau seismic region feature information extraction and application analysis – An example of the Menyuan Ms6.9 earthquake on January 8, 2022

Abstract A 6.9 magnitude earthquake hit Menyuan County, Haibei Prefecture, Qinghai Province, at 01:45 PM Beijing time on January 8, 2022 (17:45 PM GMT time on January 7, 2022). To explore the magnitude of the earthquake deformation and the affected area, this work combined optical remote sensing interpretation, interferometric synthetic aperture radar (InSAR) coseismic deformation extraction, and field surveys for research and analysis. Relying on the high-resolution Earth observation system of the Qinghai Remote Sensing Center for Natural Resources, high-resolution GF1D, GF2, and TRIPLESAT optical remote sensing images were acquired immediately after the earthquake. The airborne triangulation encryption method was used to carry out orthographic correction, fusion, and mosaic processing of digital orthophoto map (DOM) and digital surface model (DSM) images, and first-hand optical remote sensing images of the disaster areas were obtained. Based on differential InSAR (D-InSAR), small baseline subset InSAR (SBAS-InSAR) and lifting rail fusion methods, the coseismic deformation field and deformation rate of the lifting rail direction were obtained by using Sentinel-1A data processing before and after the earthquake. Combined with optical interpretation, InSAR deformation, and field investigation, the results show that the deformation trend of the line of sight (LOS) images to the north and south of the ascending and descending orbits show an obvious opposite trend. The surface shape variables are −50 to 45 cm and −65 to 72 cm, respectively, and the deformation rate before the earthquake reached 25 cm/year. The deformation field characteristics show that the earthquake was mainly due to thrust, and the coseismic deformation field fractured along the WNW‒ESE direction with a length of approximately 33 km. The areas affected by 10 mm, 20 cm, and 50 cm deformation magnitudes in the whole earthquake area were 975.14, 321.10, and 38.55 km2, respectively. Within 20 km, there were two main affected townships, namely, Sujitan Township and Huangcheng Mongolian Township. Within 50 km, there were four main affected towns and townships, namely, Sujitan Township, Mongolian Township of the Imperial city, Qingshizui town, and Haomen town.

TYPES OF MUSIC ACTIVITIES IN SCHOOL EDUCATION AND THEIR ROLE IN CORRECTIVE WORK WITH CHILDREN WITH SEVERE SPEECH DEFECTS

The article discusses the problems devoted to the importance of musical activity in kindergarten as a means of corrective work with children with severe speech impairments. The author identifies the main types of musical activity and explores their influence on the process of correction of speech disorders in preschool children.

Combined flat-field and frequency filter approach to correcting artifacts of multichannel two-photon microscopy.

Multiphoton microscopy (MPM) is a useful biomedical imaging tool for its ability to probe labeled and unlabeled depth-resolved tissue biomarkers at high resolution. Automated MPM tile scanning allows for whole-slide image acquisition but can suffer from tile-stitching artifacts that prevent accurate quantitative data analysis. We have investigated postprocessing artifact correction methods using ImageJ macros and custom Python code. Quantitative and qualitative comparisons of these methods were made using whole-slide MPM autofluorescence and second-harmonic generation images of human duodenal tissue. Image quality after artifact removal is assessed by evaluating the processed image and its unprocessed counterpart using the root mean square error, structural similarity index, and image histogram measurements. Consideration of both quantitative and qualitative results suggest that a combination of a custom flat-field-based correction and frequency filtering processing step provide improved artifact correction when compared with each method used independently to correct for tiling artifacts of tile-scan MPM images. While some image artifacts remain with these methods, further optimization of these processing steps may result in computational-efficient methods for removing these artifacts that are ubiquitous in large-scale MPM imaging. Removal of these artifacts with retention of the original image information would facilitate the use of this imaging modality in both research and clinical settings, where it is highly useful in collecting detailed morphologic and optical properties of tissue.

Short-Term Modulation of Online Monocular Visuomotor Function

Previous literature suggests that correcting ongoing movements is more effective when using the dominant limb and seeing with the dominant eye. Specifically, individuals are more effective at adjusting their movement to account for an imperceptibly perturbed or changed target location (i.e., online movement correction), when vision is available to the dominant eye. However, less is known if visual-motor functions based on monocular information can undergo short-term neuroplastic changes after a bout of practice, to improve online correction processes. Participants (n = 12) performed pointing movements monocularly and their ability to correct their movement towards an imperceptibly displaced target was assessed. On the first day, the eye associated with smaller correction amplitudes was exclusively trained during acquisition. While correction amplitude was assessed again with both eyes monocularly, only the eye with smaller correction amplitudes in the pre-test showed significant improvement in delayed retention. These results indicate that monocular visuomotor pathways can undergo short-term neuroplastic changes.

Management of Velopharyngeal Dysfunction (VPD) Following Cleft Palate Repair: A Comprehensive Decision-Making Process Based on Severity and Structural Deficiencies.

To describe a comprehensive decision-making process for surgical correction of structural Velopharyngeal Dysfunction (VPD) following cleft palate repair and evaluate its efficacy. Retrospective study. Tertiary care hospital. 300 consecutive patients with unilateral or bilateral cleft lip and palate (CLP) or isolated cleft palate (CP) diagnosed with clinical VPD following cleft palate repair between 2009 and 2014. Of these 206 patients had structural VPD and underwent surgical correction. Surgical corrections were carried out according to the comprehensive two stage decision making process developed by the investigators. Step 1 of decision-making involved visualisation of the VP sphincter function by nasoendoscopy. This was followed by step 2 which involved per-operative identification of scarring, tissue loss, hypoplasia and other structural deficiencies in the soft palate and septal mucoperiosteum. The choice of operation was then made from a repertoire of interrelated and escalating surgical procedures consisting of palate revision and pharyngoplasties ranging from most anatomical to the least. Evidence of postoperative restoration of VP function on nasoendoscopy, evaluation of speech for hypernasality, understandability, acceptability and symptoms of obstructive sleep apnea. Complete VP closure was demonstrated in 94% of patients treated using this algorithm. There was significant improvement in all speech parameters (p < 0.00001). Our comprehensive decision-making process is designed to effectively correct structural VPD according to the severity of structural and functional deficiencies in the soft palate and avoid over treatment.

Abstract B014: KDM4B mutations in human cancers

Abstract Homology-dependent-repair (HDR) is an essential process for the error-free correction of double-strand-breaks (DSBs). The histone demethylase KDM4B plays a role in the HDR repair process, wherein its H3K9 demethylase activity aids recruitment of repair factors such as the ATM checkpoint activator and KAT5 histone acetyltransferase and remodeler to the break site. Inhibition of KDM4B has been shown to disrupt the recruitment of ATM, and KAT5, affecting other downstream HDR factors and leading to widespread unrepaired DNA damage. Both over- and under-expression of KDM4B have implications for cancer severity, and changes in KDM4B expression have been shown to affect the expression of other oncogenes outside of the HDR pathway. We performed a pan-cancer analysis of the effects of KDM4B alterations in human cancers using data from the Catalogue of Somatic Mutations in Cancers (COSMIC). We find that KDM4B mutations occur in nearly every cancer. Further, there is a tendency of co-occurring mutations between KDM4B and several HDR genes the most significant being BRCA2. Machine learning tools did not predict any of the observed KDM4B mutations to be drivers. Our data suggests that although KDM4B does not display a driver phenotype it contributes to the destabilization of DNA damage repair machinery that causes cellular transformation and immortalization. Citation Format: Wesley A. Bush, Ruben C. Petreaca. KDM4B mutations in human cancers [abstract]. In: Proceedings of the AACR Special Conference in Cancer Research: DNA Damage Repair: From Basic Science to Future Clinical Application; 2024 Jan 9-11; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2024;84(1 Suppl):Abstract nr B014.

The influence of good governance on the tourism sector: The case of South Africa

Over the last decades, the tourism sector has contributed to the national and regional economies in South Africa, while governance levels have regressed over time. The study’s objective was to investigate the impact of good governance on the success and growth of the tourism sector in South Africa, a proxy for developing countries. The hypothesis is that good and effective governance could positively impact tourism growth. A quantitative research methodology was used with econometric methods such as an Autoregressive Distributed Lag Error Correction (ARDL-ECM) process. The estimation indicated a long-run relationship between the variables. The tourism sector contributes significantly to the South African economy, and the government should note the importance of good governance, as indicated through this study, in the success and development of the sector. Given tourism's potential to achieve some of the Sustainable Development Goals and positively influence economic growth and development, relevant parties are urged to pursue good governance in the sector.

Large Range of a High-Precision, Independent, Sub-Mirror Three-Dimensional Co-Phase Error Sensing and Correction Method via a Mask and Population Algorithm.

The emergence of segmented mirrors is expected to solve the design, processing, manufacturing, testing, and launching of space telescopes of large apertures. However, with the increase in the number of sub-mirrors, the sensing and correction of co-phase errors in segmented mirrors will be very difficult. In this paper, an independent three-dimensional method for sub-mirror co-phase error sensing and correction method is proposed. The method is based on a wide spectral modulation transfer function (MTF), mask, population optimization algorithm, and online model-free correction. In this method, the sensing and correction process of each sub-mirror co-phase error is independent of each other, so the increase in the number of sub-mirrors will not increase the difficulty of the method. This method can sense and correct the co-phase errors of three dimensions of the sub-mirror, including piston, tip, and tilt, even without modeling the optical system, and has a wide detection range and high precision. And the efficiency is high because the sub-mirrors can be corrected simultaneously in parallel. Simulation results show that the proposed method can effectively sense and correct the co-phase errors of the sub-mirrors in the range [-50λ, 50λ] in three dimensions with high precision. The average RMSE value in 100 experiments of the true co-phase error values and the experimental co-phase error values of one of the six sub-mirrors is 2.358 × 10-7λ.

Hybrid System for Image Restoration

The image processing field is considered one of the highly sensitive fields for accuracy due to the quality of the processing in view of the visual view of the user and due to the development in modern means of communication and the use of these means in the transfer of images and the impact of these means on several factors, including external, including those related to the quality of the source signal and the impact of the transmitted images by these conditions, digital correction processes have emerged to reach a high quality of the received image. Most of the studies and research on digital image correction have focused on the quality and time required for correction processes, and some have focused on using traditional optimization algorithms to obtain acceptable visual quality, while others have focused on shortening time regardless of quality, and due to the fact that all studies and research that have been viewed were focused on the use of speculative methods and hybrid algorithms to address distortion in images, as all weaknesses were related to time, quality and calculations because the size of the image data is large Very. The research aims to study digital images and then process images, optimization methods, genetic algorithms and accomplish an algorithm with high features. In this paper, the simple genetic algorithm is used in the process of correcting images of the type (.JPG), as this method is characterized by the fact that it includes many of the advantages of the previous methods in addition to additional features that provided quality, accuracy and shortening time in calculations. The paper has been completed in five phases: The first stage: Providing external protection for the system by entering the password. Second Stage: Creating the system's database. Third stage: Create (code book) in a new style based on the size of the file used. Fourth stage: Building the genetic algorithm for correction Fifth stage: Using a mathematical model to add distortion to a clear image, correct it and compare the results.

The Aesthetic Evaluation of the Brow-Eye Continuum After Correction of Severe Congenital Ptosis in Children With Extended Frontalis Muscle Advancement Technique.

Severe congenital ptosis is a common ocular deformity in pediatric patients that can significantly impact visual development and aesthetic appearance, leading to negative psychosocial outcomes. The frontalis muscle advancement technique is a well-established surgical treatment for severe congenital ptosis. Aesthetic changes of the brow-eye continuum often plays an important role in ptosis surgery. We conducted a single-center retrospective case series study of patients with severe congenital ptosis who underwent the frontalis muscle advancement technique at the Department of Plastic and Reconstructive Surgery, Xijing Hospital, Fourth Military Medical University between April 2020 and June 2021. The study aimed to evaluate the aesthetic changes of the eyebrow-eyelid continuum after surgery. The main outcome measurements included marginal reflex distance 1, palpebral fissure height, eyebrow position, upper eyelid to lower eyebrow distance, lower eyelid to upper eyebrow distance, and nasal base to lower eyelid distance. The study included 48 patients (66 eyelids), with 30 unilateral and 18 bilateral patients. Our analysis found that eyebrow height decreased by an average of 4.8% postoperatively relative to preoperatively in all patients. The frontalis muscle advancement technique has demonstrated effectiveness in achieving aesthetically pleasing outcomes in children with severe ptosis. It is crucial to pay careful attention to the brow-eye continuum during the correction process, as its harmony can greatly impact the final result.

APLICAÇÃO DE TÉCNICAS DE INTELIGÊNCIA ARTIFICIAL PARA CLASSIFICAÇÃO DE FUGA AO TEMA EM REDAÇÕES

ABSTRACT: The process of manual correction of essays causes some difficulties, among which we point out the time spent for correction and feedback to the student. For institutions such as elementary schools, universities, and the National High School Exam in Brazil (Enem), such activity demands time and cost for the evaluation of the texts produced. Going off-topic is one of the items evaluated in the Enem essay that can nullify the whole essay produced by the candidate. In this context, the automatic analysis of essays with the application of techniques and methods of Natural Language Processing, Text Mining, and other Artificial Intelligence techniques has shown to be promising in the process of automated evaluation of written language. The goal of this research is to compare different AI techniques for the classification of going off-topic in texts and identify the one with the best result to enable a smart correction system for essays. Therefore, computer experiments were carried out to classify these texts to normalize, identify patterns, and classify the essays in 1,320 Brazilian Portuguese essays on 119 different topics. The results indicate that the Convolutional Neural Network classifier obtained greater gain concerning the other classifiers analyzed, both in accuracy and about the results of false positives, the precision of metrics, Recall, and F1-Score. In conclusion, the solution validated in this research contributes to positively impacting the work of teachers and educational institutions, by reducing the time and costs associated with the essay evaluation process.

Identification and Correction of Improved GLR Algorithm in English Translation Teaching

Abstract In this paper, after clarifying the common types of errors in English translation teaching, in order to achieve the improvement of English translation teaching, combined with the GLR algorithm for English phrase recognition and analysis, PCFG English syntactic analysis model and HDSM lexicalization model are introduced for the optimization of GLR algorithm, which constitutes the PCFG-HDSM model. Analyze the process of English translation error recognition and correction with an improved GLR algorithm and realize the improvement of the GLR algorithm. Compare the performance of the English translation grammar analysis generator and determine the ratio of pure grammar analysis time to total analysis time. Examine the English translation accuracy of the improved GLR algorithm by combining the training corpus and evaluating it using LP and LR metrics. Analyze practical teaching applications by classifying the structure of English translation topics and using the improved GLR algorithm. The improved GLR algorithm is able to achieve more than 80% of English translation recognition and correction rates, which enhances students’ scores on English translation topics and promotes the development of English translation teaching.

Localization of Defects on PCBs with Diverse Acquisitions

The Printed Circuit Board (PCB) accommodates various Integrated Circuit (IC) components arranged in a specific layout of bond pads, lines, and tracks. Throughout the manufacturing process, irregularities or defects often occur during drilling, etching, stripping, and other stages, impacting the performance and functionality of the circuit board. Many of these defects are related to soldering pads and copper balance, identifying them through manual inspection is time-consuming and error-prone. This necessitates the use of Automated Optical Inspection (AOI). Practices like template matching often require two identical PCBs, which are compared using mathematical algorithms to detect differences. However, they are not resilient to viewpoint variations and non-rigid deformations. The current inspection process primarily focuses on rectifying PCB images captured with tilts ranging from 0 to 84 using homography principles. This correction process operates within a maximum run time of 7.96 s. The adjusted images then undergo analysis via a pattern-matching unit, where the system receives images of the same PCB pattern, each exhibiting different defects. Structural information mapping is performed using various spatial-domain feature-based matching algorithms. When evaluated using SSI and MSE metrics, the model achieved high matching percentages of 99.67%, 99.75%, and 99.30%, and low error rates of 0.343%, 0.358%, and 0.721% for three different types of PCB designs considered. Additionally, the model excels in precisely identifying the location of defects in the PCB images without using bounding boxes, in accordance with the description of the co-images through a segmentation approach. Overall, the proposed system effectively corrects skew, accurately detects abnormalities and outperforms traditional assessment systems.

Distributed Newton method for time-varying convex optimization with backward Euler prediction

&lt;p&gt;We investigated the challenge of unconstrained distributed optimization with a time-varying objective function, employing a prediction-correction approach. Our method introduced a backward Euler prediction step that used the differential information from consecutive moments to forecast the trajectory's future direction. This predicted value was then refined through an iterative correction process. Our analysis and experimental results demonstrated that this approach effectively addresses the optimization problem without requiring the computation of the Hessian matrix's inverse.&lt;/p&gt;