Fully Automated Versions of Clinically Validated Nephrometry Scores Demonstrate Superior Predictive Utility versus Human Scores.

OBJECTIVE: To automate the generation of three validated nephrometry scoring systems on preoperative computerised tomography (CT) scans by developing artificial intelligence (AI)-based image processing methods. Subsequently, we aimed to evaluate the ability of these scores to predict meaningful pathological and perioperative outcomes. PATIENTS AND METHODS: A total of 300 patients with preoperative CT with early arterial contrast phase were identified from a cohort of 544 consecutive patients undergoing surgical extirpation for suspected renal cancer. A deep neural network approach was used to automatically segment kidneys and tumours, and then geometric algorithms were used to measure the components of the concordance index (C-Index), Preoperative Aspects and Dimensions Used for an Anatomical classification of renal tumours (PADUA), and tumour contact surface area (CSA) nephrometry scores. Human scores were independently calculated by medical personnel blinded to the AI scores. AI and human score agreement was assessed using linear regression and predictive abilities for meaningful outcomes were assessed using logistic regression and receiver operating characteristic curve analyses. RESULTS: The median (interquartile range) age was 60 (51-68) years, and 40% were female. The median tumour size was 4.2 cm and 91.3% had malignant tumours. In all, 27% of the tumours were high stage, 37% high grade, and 63% of the patients underwent partial nephrectomy. There was significant agreement between human and AI scores on linear regression analyses (R ranged from 0.574 to 0.828, all P < 0.001). The AI-generated scores were equivalent or superior to human-generated scores for all examined outcomes including high-grade histology, high-stage tumour, indolent tumour, pathological tumour necrosis, and radical nephrectomy (vs partial nephrectomy) surgical approach. CONCLUSIONS: Fully automated AI-generated C-Index, PADUA, and tumour CSA nephrometry scores are similar to human-generated scores and predict a wide variety of meaningful outcomes. Once validated, our results suggest that AI-generated nephrometry scores could be delivered automatically from a preoperative CT scan to a clinician and patient at the point of care to aid in decision making.

AI-generated R.E.N.A.L.+ Score Surpasses Human-generated Score in Predicting Renal Oncologic Outcomes.

OBJECTIVE: To determine whether we can surpass the traditional R.E.N.A.L. nephrometry score (H-score) prediction ability of pathologic outcomes by creating artificial intelligence (AI)-generated R.E.N.A.L.+ score (AI+ score) with continuous rather than ordinal components. We also assessed the AI+ score components' relative importance with respect to outcome odds. METHODS: This is a retrospective study of 300 consecutive patients with preoperative computed tomography scans showing suspected renal cancer at a single institution from 2010 to 2018. H-score was tabulated by three trained medical personnel. Deep neural network approach automatically generated kidney segmentation masks of parenchyma and tumor. Geometric algorithms were used to automatically estimate score components as ordinal and continuous variables. Multivariate logistic regression of continuous R.E.N.A.L. components was used to generate AI+ score. Predictive utility was compared between AI+, AI, and H-scores for variables of interest, and AI+ score components' relative importance was assessed. RESULTS: Median age was 60years (interquartile range 51-68), and 40% were female. Median tumor size was 4.2 cm (2.6-6.12), and 92% were malignant, including 27%, 37%, and 23% with high-stage, high-grade, and necrosis, respectively. AI+ score demonstrated superior predictive ability over AI and H-scores for predicting malignancy (area under the curve [AUC] 0.69 vs 0.67 vs 0.64, respectively), high stage (AUC 0.82 vs 0.65 vs 0.71, respectively), high grade (AUC 0.78 vs 0.65 vs 0.65, respectively), pathologic tumor necrosis (AUC 0.81 vs 0.72 vs 0.74, respectively), and partial nephrectomy approach (AUC 0.88 vs 0.74 vs 0.79, respectively). Of AI+ score components, the maximal tumor diameter ("R") was the most important outcomes predictor. CONCLUSION: AI+ score was superior to AI-score and H-score in predicting oncologic outcomes. Time-efficient AI+ score can be used at the point of care, surpassing validated clinical scoring systems.

Learning Log-Determinant Divergences for Positive Definite Matrices.

Representations in the form of Symmetric Positive Definite (SPD) matrices have been popularized in a variety of visual learning applications due to their demonstrated ability to capture rich second-order statistics of visual data. There exist several similarity measures for comparing SPD matrices with documented benefits. However, selecting an appropriate measure for a given problem remains a challenge and in most cases, is the result of a trial-and-error process. In this paper, we propose to learn similarity measures in a data-driven manner. To this end, we capitalize on the αß-log-det divergence, which is a meta-divergence parametrized by scalars α and ß, subsuming a wide family of popular information divergences on SPD matrices for distinct and discrete values of these parameters. Our key idea is to cast these parameters in a continuum and learn them from data. We systematically extend this idea to learn vector-valued parameters, thereby increasing the expressiveness of the underlying non-linear measure. We conjoin the divergence learning problem with several standard tasks in machine learning, including supervised discriminative dictionary learning and unsupervised SPD matrix clustering. We present Riemannian gradient descent schemes for optimizing our formulations efficiently, and show the usefulness of our method on eight standard computer vision tasks.

The Growing Role for Semantic Segmentation in Urology.

As the quantity and quality of cross-sectional imaging data increase, it is important to be able to make efficient use of the information. Semantic segmentation is an emerging technology that promises to improve the speed, reproducibility, and accuracy of analysis of medical imaging, and to allow visualization methods that were previously impossible. Manual image segmentation often requires expert knowledge and is both time- and cost-prohibitive in many clinical situations. However, automated methods, especially those using deep learning, show promise in alleviating this burden to make segmentation a standard tool for clinical intervention in the future. It is therefore important for clinicians to have a functional understanding of what segmentation is and to be aware of its uses. Here we include a number of examples of ways in which semantic segmentation has been put into practice in urology. PATIENT SUMMARY: This mini-review highlights the growing role of segmentation methods for medical images in urology to inform clinical practice. Segmentation methods show promise in improving the reliability of diagnosis and aiding in visualization, which may become a tool for patient education.

Automatic Segmentation of Kidneys and Kidney Tumors: The KiTS19 International Challenge.

Purpose: Clinicians rely on imaging features to calculate complexity of renal masses based on validated scoring systems. These scoring methods are labor-intensive and are subjected to interobserver variability. Artificial intelligence has been increasingly utilized by the medical community to solve such issues. However, developing reliable algorithms is usually time-consuming and costly. We created an international community-driven competition (KiTS19) to develop and identify the best system for automatic segmentation of kidneys and kidney tumors in contrast CT and report the results. Methods: A training and test set of CT scans that was manually annotated by trained individuals were generated from consecutive patients undergoing renal surgery for whom demographic, clinical and outcome data were available. The KiTS19 Challenge was a machine learning competition hosted on grand-challenge.org in conjunction with an international conference. Teams were given 3 months to develop their algorithm using a full-annotated training set of images and an unannotated test set was released for 2 weeks from which average Sørensen-Dice coefficient between kidney and tumor regions were calculated across all 90 test cases. Results: There were 100 valid submissions that were based on deep neural networks but there were differences in pre-processing strategies, architectural details, and training procedures. The winning team scored a 0.974 kidney Dice and a 0.851 tumor Dice resulting in 0.912 composite score. Automatic segmentation of the kidney by the participating teams performed comparably to expert manual segmentation but was less reliable when segmenting the tumor. Conclusion: Rapid advancement in automated semantic segmentation of kidney lesions is possible with relatively high accuracy when the data is released publicly, and participation is incentivized. We hope that our findings will encourage further research that would enable the potential of adopting AI into the medical field.

The state of the art in kidney and kidney tumor segmentation in contrast-enhanced CT imaging: Results of the KiTS19 challenge.

There is a large body of literature linking anatomic and geometric characteristics of kidney tumors to perioperative and oncologic outcomes. Semantic segmentation of these tumors and their host kidneys is a promising tool for quantitatively characterizing these lesions, but its adoption is limited due to the manual effort required to produce high-quality 3D segmentations of these structures. Recently, methods based on deep learning have shown excellent results in automatic 3D segmentation, but they require large datasets for training, and there remains little consensus on which methods perform best. The 2019 Kidney and Kidney Tumor Segmentation challenge (KiTS19) was a competition held in conjunction with the 2019 International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI) which sought to address these issues and stimulate progress on this automatic segmentation problem. A training set of 210 cross sectional CT images with kidney tumors was publicly released with corresponding semantic segmentation masks. 106 teams from five continents used this data to develop automated systems to predict the true segmentation masks on a test set of 90 CT images for which the corresponding ground truth segmentations were kept private. These predictions were scored and ranked according to their average Sørensen-Dice coefficient between the kidney and tumor across all 90 cases. The winning team achieved a Dice of 0.974 for kidney and 0.851 for tumor, approaching the inter-annotator performance on kidney (0.983) but falling short on tumor (0.923). This challenge has now entered an "open leaderboard" phase where it serves as a challenging benchmark in 3D semantic segmentation.

Image Descriptors for Weakly Annotated Histopathological Breast Cancer Data.

INTRODUCTION: Cancerous Tissue Recognition (CTR) methodologies are continuously integrating advancements at the forefront of machine learning and computer vision, providing a variety of inference schemes for histopathological data. Histopathological data, in most cases, come in the form of high-resolution images, and thus methodologies operating at the patch level are more computationally attractive. Such methodologies capitalize on pixel level annotations (tissue delineations) from expert pathologists, which are then used to derive labels at the patch level. In this work, we envision a digital connected health system that augments the capabilities of the clinicians by providing powerful feature descriptors that may describe malignant regions. MATERIAL AND METHODS: We start with a patch level descriptor, termed Covariance-Kernel Descriptor (CKD), capable of compactly describing tissue architectures associated with carcinomas. To leverage the recognition capability of the CKDs to larger slide regions, we resort to a multiple instance learning framework. In that direction, we derive the Weakly Annotated Image Descriptor (WAID) as the parameters of classifier decision boundaries in a Multiple Instance Learning framework. The WAID is computed on bags of patches corresponding to larger image regions for which binary labels (malignant vs. benign) are provided, thus obviating the necessity for tissue delineations. RESULTS: The CKD was seen to outperform all the considered descriptors, reaching classification accuracy (ACC) of 92.83%. and area under the curve (AUC) of 0.98. The CKD captures higher order correlations between features and was shown to achieve superior performance against a large collection of computer vision features on a private breast cancer dataset. The WAID outperform all other descriptors on the Breast Cancer Histopathological database (BreakHis) where correctly classified malignant (CCM) instances reached 91.27 and 92.00% at the patient and image level, respectively, without resorting to a deep learning scheme achieves state-of-the-art performance. DISCUSSION: Our proposed derivation of the CKD and WAID can help medical experts accomplish their work accurately and faster than the current state-of-the-art.

Public Perceptions of Artificial Intelligence and Robotics in Medicine.

Objective: To understand better the public perception and comprehension of medical technology such as artificial intelligence (AI) and robotic surgery. In addition to this, to identify sensitivity to their use to ensure acceptability and quality of counseling. Subjects and Methods: A survey was conducted on a convenience sample of visitors to the MN Minnesota State Fair (n = 264). Participants were randomized to receive one of two similar surveys. In the first, a diagnosis was made by a physician and in the second by an AI application to compare confidence in human and computer-based diagnosis. Results: The median age of participants was 45 (interquartile range 28-59), 58% were female (n = 154) vs 42% male (n = 110), 69% had completed at least a bachelor's degree, 88% were Caucasian (n = 233) vs 12% ethnic minorities (n = 31) and were from 12 states, mostly from the Upper Midwest. Participants had nearly equal trust in AI vs physician diagnoses. However, they were significantly more likely to trust an AI diagnosis of cancer over a doctor's diagnosis when responding to the version of the survey that suggested that an AI could make medical diagnoses (p = 9.32e-06). Though 55% of respondents (n = 145) reported that they were uncomfortable with automated robotic surgery, the majority of the individuals surveyed (88%) mistakenly believed that partially autonomous surgery was already happening. Almost all (94%, n = 249) stated that they would be willing to pay for a review of medical imaging by an AI if available. Conclusion: Most participants express confidence in AI providing medical diagnoses, sometimes even over human physicians. Participants generally express concern with surgical AI, but they mistakenly believe that it is already being performed. As AI applications increase in medical practice, health care providers should be cognizant of the potential amount of misinformation and sensitivity that patients have to how such technology is represented.

The Use of Immersive Environments for the Early Detection and Treatment of Neuropsychiatric Disorders.

Neuropsychiatric disorders are highly prevalent conditions with significant individual, societal, and economic impacts. A major challenge in the diagnosis and treatment of these conditions is the lack of sensitive, reliable, objective, quantitative tools to inform diagnosis, and measure symptom severity. Currently available assays rely on self-reports and clinician observations, leading to subjective analysis. As a step toward creating quantitative assays of neuropsychiatric symptoms, we propose an immersive environment to track behaviors relevant to neuropsychiatric symptomatology and to systematically study the effect of environmental contexts on certain behaviors. Moreover, the overarching theme leads to connected tele-psychiatry which can provide effective assessment.

Use of Computer Vision Tools to Identify Behavioral Markers of Pediatric Obsessive-Compulsive Disorder: A Pilot Study.

OBJECTIVES: The clinical presentation of pediatric obsessive-compulsive disorder (OCD) is heterogeneous, which is a stumbling block to understanding pathophysiology and to developing new treatments. A major shift in psychiatry, embodied in the Research Domain Criteria (RDoC) initiative of National Institute of Mental Health, recognizes the pitfalls of categorizing mental illnesses using diagnostic criteria. Instead, RDoC encourages researchers to use a dimensional approach, focusing on narrower domains of psychopathology to characterize brain-behavior relationships. Our aim in this multidisciplinary pilot study was to use computer vision tools to record OCD behaviors and to cross-validate these behavioral markers with standard clinical measures. METHODS: Eighteen youths with OCD and 21 healthy controls completed tasks in an innovation laboratory (free arrangement of objects, hand washing, arrangement of objects on contrasting carpets). Tasks were video-recorded. Videos were coded by blind raters for OCD-related behaviors. Children's Yale-Brown Obsessive Compulsive Scale (CY-BOCS) and other scales were administered. We compared video-recorded measures of behavior in OCD versus healthy controls and correlated video measures and clinical measures of OCD. RESULTS: Behavioral measures on the videos were significantly correlated with specific CY-BOCS dimension scores. During the free arrangement task, more time spent ordering objects and more moves of objects were both significantly associated with higher CY-BOCS ordering/repeating dimension scores. Longer duration of hand washing was significantly correlated with higher scores on CY-BOCS ordering/repeating and forbidden thoughts dimensions. During arrangement of objects on contrasting carpets, more moves and more adjustment of objects were significantly associated with higher CY-BOCS ordering/repeating dimension scores. CONCLUSION: Preliminary data suggest that measurement of behavior using video recording is a valid approach for quantifying OCD psychopathology. This methodology could serve as a new tool for investigating OCD using an RDoC approach. This objective, novel behavioral measurement technique may benefit both researchers and clinicians in assessing pediatric OCD and in identifying new behavioral markers of OCD. Clinical Trial Registry: Development of an Instrument That Monitors Behaviors Associated With OCD. NCT02866422. http://clinicaltrials.gov.

Bayesian Nonparametric Clustering for Positive Definite Matrices.

Symmetric Positive Definite (SPD) matrices emerge as data descriptors in several applications of computer vision such as object tracking, texture recognition, and diffusion tensor imaging. Clustering these data matrices forms an integral part of these applications, for which soft-clustering algorithms (K-Means, expectation maximization, etc.) are generally used. As is well-known, these algorithms need the number of clusters to be specified, which is difficult when the dataset scales. To address this issue, we resort to the classical nonparametric Bayesian framework by modeling the data as a mixture model using the Dirichlet process (DP) prior. Since these matrices do not conform to the Euclidean geometry, rather belongs to a curved Riemannian manifold,existing DP models cannot be directly applied. Thus, in this paper, we propose a novel DP mixture model framework for SPD matrices. Using the log-determinant divergence as the underlying dissimilarity measure to compare these matrices, and further using the connection between this measure and the Wishart distribution, we derive a novel DPM model based on the Wishart-Inverse-Wishart conjugate pair. We apply this model to several applications in computer vision. Our experiments demonstrate that our model is scalable to the dataset size and at the same time achieves superior accuracy compared to several state-of-the-art parametric and nonparametric clustering algorithms.

Tensor Dictionary Learning for Positive Definite Matrices.

Sparse models have proven to be extremely successful in image processing and computer vision. However, a majority of the effort has been focused on sparse representation of vectors and low-rank models for general matrices. The success of sparse modeling, along with popularity of region covariances, has inspired the development of sparse coding approaches for these positive definite descriptors. While in earlier work, the dictionary was formed from all, or a random subset of, the training signals, it is clearly advantageous to learn a concise dictionary from the entire training set. In this paper, we propose a novel approach for dictionary learning over positive definite matrices. The dictionary is learned by alternating minimization between sparse coding and dictionary update stages, and different atom update methods are described. A discriminative version of the dictionary learning approach is also proposed, which simultaneously learns dictionaries for different classes in classification or clustering. Experimental results demonstrate the advantage of learning dictionaries from data both from reconstruction and classification viewpoints. Finally, a software library is presented comprising C++ binaries for all the positive definite sparse coding and dictionary learning approaches presented here.

Efficient nearest neighbors via robust sparse hashing.

This paper presents a new nearest neighbor (NN) retrieval framework: robust sparse hashing (RSH). Our approach is inspired by the success of dictionary learning for sparse coding. Our key idea is to sparse code the data using a learned dictionary, and then to generate hash codes out of these sparse codes for accurate and fast NN retrieval. But, direct application of sparse coding to NN retrieval poses a technical difficulty: when data are noisy or uncertain (which is the case with most real-world data sets), for a query point, an exact match of the hash code generated from the sparse code seldom happens, thereby breaking the NN retrieval. Borrowing ideas from robust optimization theory, we circumvent this difficulty via our novel robust dictionary learning and sparse coding framework called RSH, by learning dictionaries on the robustified counterparts of the perturbed data points. The algorithm is applied to NN retrieval on both simulated and real-world data. Our results demonstrate that RSH holds significant promise for efficient NN retrieval against the state of the art.

Computer vision tools for low-cost and noninvasive measurement of autism-related behaviors in infants.

The early detection of developmental disorders is key to child outcome, allowing interventions to be initiated which promote development and improve prognosis. Research on autism spectrum disorder (ASD) suggests that behavioral signs can be observed late in the first year of life. Many of these studies involve extensive frame-by-frame video observation and analysis of a child's natural behavior. Although nonintrusive, these methods are extremely time-intensive and require a high level of observer training; thus, they are burdensome for clinical and large population research purposes. This work is a first milestone in a long-term project on non-invasive early observation of children in order to aid in risk detection and research of neurodevelopmental disorders. We focus on providing low-cost computer vision tools to measure and identify ASD behavioral signs based on components of the Autism Observation Scale for Infants (AOSI). In particular, we develop algorithms to measure responses to general ASD risk assessment tasks and activities outlined by the AOSI which assess visual attention by tracking facial features. We show results, including comparisons with expert and nonexpert clinicians, which demonstrate that the proposed computer vision tools can capture critical behavioral observations and potentially augment the clinician's behavioral observations obtained from real in-clinic assessments.

Tensor sparse coding for positive definite matrices.

In recent years, there has been extensive research on sparse representation of vector-valued signals. In the matrix case, the data points are merely vectorized and treated as vectors thereafter (for example, image patches). However, this approach cannot be used for all matrices, as it may destroy the inherent structure of the data. Symmetric positive definite (SPD) matrices constitute one such class of signals, where their implicit structure of positive eigenvalues is lost upon vectorization. This paper proposes a novel sparse coding technique for positive definite matrices, which respects the structure of the Riemannian manifold and preserves the positivity of their eigenvalues, without resorting to vectorization. Synthetic and real-world computer vision experiments with region covariance descriptors demonstrate the need for and the applicability of the new sparse coding model. This work serves to bridge the gap between the sparse modeling paradigm and the space of positive definite matrices.

Jensen-Bregman LogDet divergence with application to efficient similarity search for covariance matrices.

Covariance matrices have found success in several computer vision applications, including activity recognition, visual surveillance, and diffusion tensor imaging. This is because they provide an easy platform for fusing multiple features compactly. An important task in all of these applications is to compare two covariance matrices using a (dis)similarity function, for which the common choice is the Riemannian metric on the manifold inhabited by these matrices. As this Riemannian manifold is not flat, the dissimilarities should take into account the curvature of the manifold. As a result, such distance computations tend to slow down, especially when the matrix dimensions are large or gradients are required. Further, suitability of the metric to enable efficient nearest neighbor retrieval is an important requirement in the contemporary times of big data analytics. To alleviate these difficulties, this paper proposes a novel dissimilarity measure for covariances, the Jensen-Bregman LogDet Divergence (JBLD). This divergence enjoys several desirable theoretical properties and at the same time is computationally less demanding (compared to standard measures). Utilizing the fact that the square root of JBLD is a metric, we address the problem of efficient nearest neighbor retrieval on large covariance datasets via a metric tree data structure. To this end, we propose a K-Means clustering algorithm on JBLD. We demonstrate the superior performance of JBLD on covariance datasets from several computer vision applications.

Scalable active learning for multiclass image classification.

Machine learning techniques for computer vision applications like object recognition, scene classification, etc., require a large number of training samples for satisfactory performance. Especially when classification is to be performed over many categories, providing enough training samples for each category is infeasible. This paper describes new ideas in multiclass active learning to deal with the training bottleneck, making it easier to train large multiclass image classification systems. First, we propose a new interaction modality for training which requires only yes-no type binary feedback instead of a precise category label. The modality is especially powerful in the presence of hundreds of categories. For the proposed modality, we develop a Value-of-Information (VOI) algorithm that chooses informative queries while also considering user annotation cost. Second, we propose an active selection measure that works with many categories and is extremely fast to compute. This measure is employed to perform a fast seed search before computing VOI, resulting in an algorithm that scales linearly with dataset size. Third, we use locality sensitive hashing to provide a very fast approximation to active learning, which gives sublinear time scaling, allowing application to very large datasets. The approximation provides up to two orders of magnitude speedups with little loss in accuracy. Thorough empirical evaluation of classification accuracy, noise sensitivity, imbalanced data, and computational performance on a diverse set of image datasets demonstrates the strengths of the proposed algorithms.

Feasibility of intrafraction whole-body motion tracking for total marrow irradiation.

With image-guided tomotherapy, highly targeted total marrow irradiation (TMI) has become a feasible alternative to conventional total body irradiation. The uncertainties in patient localization and intrafraction motion of the whole body during hour-long TMI treatment may pose a risk to the safety and accuracy of targeted radiation treatment. The feasibility of near-infrared markers and optical tracking system (OTS) is accessed along with a megavoltage scanning system of tomotherapy. Three near-infrared markers placed on the face of a rando phantom are used to evaluate the capability of OTS in measuring changes in the markers' positions as the rando is moved in the translational direction. The OTS is also employed to determine breathing motion related changes in the position of 16 markers placed on the chest surface of human volunteers. The maximum uncertainty in locating marker position with the OTS is 1.5 mm. In the case of normal and deep breathing motion, the maximum marker position change is observed in anterior-posterior direction with the respective values of 4 and 12 mm. The OTS is able to measure surface changes due to breathing motion. The OTS may be optimized to monitor whole body motion during TMI to increase the accuracy of treatment delivery and reduce the radiation dose to the lungs.

Estimating 3D positions and velocities of projectiles from monocular views.

In this paper, we consider the problem of localizing a projectile in 3D based on its apparent motion in a stationary monocular view. A thorough theoretical analysis is developed, from which we establish the minimum conditions for the existence of a unique solution. The theoretical results obtained have important implications for applications involving projectile motion. A robust, nonlinear optimization-based formulation is proposed, and the use of a local optimization method is justified by detailed examination of the local convexity structure of the cost function. The potential of this approach is validated by experimental results.

Autonomous stair-climbing with miniature jumping robots.

The problem of vision-guided control of miniature mobile robots is investigated. Untethered mobile robots with small physical dimensions of around 10 cm or less do not permit powerful onboard computers because of size and power constraints. These challenges have, in the past, reduced the functionality of such devices to that of a complex remote control vehicle with fancy sensors. With the help of a computationally more powerful entity such as a larger companion robot, the control loop can be closed. Using the miniature robot's video transmission or that of an observer to localize it in the world, control commands can be computed and relayed to the inept robot. The result is a system that exhibits autonomous capabilities. The framework presented here solves the problem of climbing stairs with the miniature Scout robot. The robot's unique locomotion mode, the jump, is employed to hop one step at a time. Methods for externally tracking the Scout are developed. A large number of real-world experiments are conducted and the results discussed.