Visual Comparison Research Articles

Ensuring ethical integrity and bias reduction in machine learning models

This research focused on the multifaceted realm of machine learning algorithms, focusing on the pivotal themes of ethical concerns and bias mitigation (Zeba G. et al., 2021). Employing a dual-pronged research methodology, the study first evaluates algorithmic performance across diverse tasks, such as audio transcription, content moderation, and system implementation. The research uses quantitative assessments and visual comparisons to highlight nuanced improvements in algorithmic efficiency and accuracy. The second dimension involves an in-depth analysis of demographic contributions in tasks like image categorization and content moderation. By scrutinizing the geographical distribution of contributors and demographics like age and gender, the study aims to unravel potential correlations between algorithmic effectiveness and contributor demographics. The graphical representations provide valuable visual insights, including bias distribution across categories, evolution over time, and baseline and improved performance comparisons. The findings contribute to the discourse on responsible AI development, emphasizing the need for tailored enhancements and inclusive participant recruitment strategies. Complemented by comprehensive results and discussions, this research methodology lays a robust foundation for addressing ethical concerns and advancing bias mitigation strategies in machine learning algorithms.

Comparison of Data Visualization, Outlier Detection and Data Dimensionality Reduction Methods

With the deepening of the digital age of information, people's daily data is getting larger and larger, and it is more and more difficult to quantify and process. At this time, the data processing means becomes particularly important. This paper compares and analyzes some methods from data visualization to data dimensionality reduction to outlier detection. In this paper, two different types of datasets, ModelNet40, and red wine quality, are used to introduce the visualization method of the Farthest Point Sampling (FPS). This method can have a clear visual effect on the data dimension and scale, and allow users to observe the structure, type, and scale of the data. In data dimensionality reduction, the study uses Principal Component Analysis (PCA), T-Distributed Stochastic Neighbor Embedding (t-SNE), Triplets Manifold Approximation and Projection (TriMAP), Uniform Manifold Approximation and Projection (UMAP), Pairwise Controlled Manifold Approximation Projection (PaCMAP), and Autoencoder to compare their dimensionality reduction effects. Through these methods, this paper finds that different methods have different effects on different datasets. Therefore, in data dimensionality reduction, it can get twice the result with half the effort by choosing the appropriate method. Finally, this paper also detects outliers. Outliers in datasets will make it difficult for people to process data and make subsequent results inaccurate, so it is necessary to identify outliers. This paper involves methods such as isolation forest and Density-Based Spatial Clustering of Applications with Noise (DBSCAN). Through this paper, the methods of different datasets are analyzed and summarized.

AccuStripes: Visual exploration and comparison of univariate data distributions using color and binning

Understanding and analyzing univariate distributions of data in terms of their shapes as well as their specific characteristics, regarding gaps, spikes, or outliers, is crucial in many scientific disciplines. In this paper, we propose a design space composed of the visual channels position and color for representing accumulated distributions. The designs are a mixture of color-coded stripes with density lines. The width and coloring of the stripes is based on the applied binning technique. In a crowd-sourced experiment we explore a subspace, called the AccuStripes (i.e., “accumulated stripes”) design space, consisting of nine representations. These AccuStripes designs integrate three composition strategies (color only, overlay, filled curve) with three binning techniques, one uniform (UB) and two adaptive methods, namely Bayesian Blocks (BB) and Jenks’ Natural Breaks (NB). We evaluate the accuracy, efficiency, and confidence ratings of the nine AccuStripes designs for structural estimation and comparison tasks. Across all study tasks, the overlay composition was found to be most accurate and preferred by observers. Furthermore, the results demonstrate that while no binning method performed best in both identification and comparison, detection of structures using adaptive binning was the most accurate one. For validation we compared the best AccuStripes’ design, i.e., the overlay composition, to line charts. Our results show that the AccuStripes’ design outperformed the line charts in accuracy for all study tasks.

An improved nonlinear anisotropic model with p(x)‐growth conditions applied to image restoration and enhancement

This work proposes a novel nonlinear parabolic equation with ‐growth conditions for image restoration and enhancement. Based on the generalized Lebesgue and Sobolev spaces with variable exponent, we demonstrate the well‐posedness of the proposed model. As a first result, we prove the existence of a weak solution to our model when the reaction term is bounded by a suitable function. Secondly, we use the approximations method to establish the existence of a nonnegative weak SOLA (Solution Obtained as Limit of Approximations) solution to the proposed model. We illustrate our theoretical results in the context of image denoising and enhancement. Specifically, we present various numerical implementations on a set of grayscale images. To further enrich these simulations, we assess the efficiency of the proposed model on several color images. The obtained numerical results strongly suggest that our model outperforms existing state‐of‐the‐art methods in terms of both visual and quantitative comparison, demonstrating superior efficiency and robustness in noise removal and contrast enhancement.

Qualitative classification of thrombus images as a way to improve quantitative analysis of thrombus formation in flow chamber assays.

Thrombus formation in vitro under flow conditions is one of the most widely used methods to study haemostasis and to evaluate the activity of potential antithrombotic compounds. Assessment of the results of these experiments is often based on a quantification of microscopic images of thrombi. In a majority of reported analysis all thrombi visualised in an image are quantified as one homogenous class. In some protocols, qualitative assessment of thrombi morphology based on a visual comparison of evaluated images with representative images of predefined classes of thrombi are performed by experienced analysts. In presented paper we show how the quantitative analysis can be improved by classification of thrombi on the basis of defined morphological features prior to quantification and we suggest that machine learning-based approach can improve this way of analysis. We tested the applicability of machine learning-based segmentation and classification of thrombi images to improve the outcome of quantification of the results of flow chamber assays. For this, we used the public domain machine learning software Ilastik for bioimage analysis developed at the European Molecular Biology Laboratory. A model was trained to distinguish two classes of thrombi based on certain morphological features which apparently correspond to the stage of thrombus development. Thrombi formed in the presence of a model antiplatelet compound-abciximab or in control conditions were quantified with the use of this model and the results were compared to quantification where all thrombi were quantified as a homogenous class. Machine learning-based analysis was capable of effective distinguishing of two classes of morphologically distinct platelet aggregates. The use of the model which segmented and quantified only the objects recognized as compacted structures provided results which better mirrored the actual effect of an antiplatelet treatment than quantification based on all structures. Classification of thrombi enabled by machine learning increases the relevance of quantitative information and allows better evaluation of the results of in vitro thrombosis assays.

Predicting carbonate rock dissolution using multi-scale residual neural networks with prior knowledge

The factors that affect carbonate dissolution are complex, and it is crucial to acquire efficient and accurate knowledge of carbonate dissolution characteristics for CO2 capture and storage (CCS) projects. In current research, the most precise outcomes can be achieved through experimental or simulation techniques, but they are frequently computationally demanding and time-consuming. Data-driven machine learning methods can efficiently perform regression prediction tasks. In this paper, we propose a multi-scale hierarchical regression model for the dissolution problem based on residual neural networks, incorporating prior knowledge. We have developed new equations for carbonate rock dissolution and have incorporated the factors that influence this process into 3D image data by introducing Dissolution Degree (Dd) parameters. This allows the image data to include both the pore space structure and dissolution information with physical meaning. We utilize the pore phase and matrix phase grayscale thresholds (Pt, Mt) to eliminate voxel noise in the characteristic maps obtained from the model. This ensures that the predicted characteristics of carbonate rock dissolution are consistent with practical physics knowledge. We selected a total of 5 core samples to test the model. Among them, three samples are from the test set, and the additional two core samples selected have strong and weak correlations with the training set samples, respectively. The predictions were evaluated using semantic segmentation evaluation parameters, porosity, geometrical and topological structure parameters, Péclet and Damköhler numbers, porous media flow field simulations, and absolute permeability. The results of both visual comparisons and quantitative analyses demonstrated a high degree of consistency between predicted and experimental results, and the trained multi-scale hierarchical regression residual neural network with prior knowledge (MSR-Net) demonstrates good accuracy and generalization ability. The results of this study demonstrate that model based on MSR-Net can be utilized to predict the dissolution properties of the pore space in the formation where the core was extracted, along with the related formation.

A Comparison of 68Ga-PSMA PET/CT-Based Split Renal Function with 99mTc-MAG3 Renography in Patients with Metastatic Castration-Resistant Prostate Carcinoma Treated with 177Lu-PSMA.

Physiological PSMA expression in the cells of the proximal renal tubules and consecutive radiopharmaceutical binding and retention could potentially lead to radioligand-therapy-induced nephrotoxicity. Thus, patients with metastatic castration-resistant prostate cancer undergo 99mTc-Mercaptoacetyltriglycine (MAG3) renal scintigraphy to assess kidney function and to exclude renal obstruction as part of their workup for PSMA-targeted radioligand therapy (RLT). 99mTc-MAG-3 renal scintigraphy often requires an additional visit to the nuclear medicine department and patients spend 30-90 min in the department, which is inconvenient and takes up camera time. In addition, the patients are subjected to a baseline 68Ga-PSMA PET/CT to assess for PSMA-positive disease prior to targeted radioligand therapy. The aim of this retrospective cross-sectional study was to compare 99mTc-MAG-3-based split renal function (SRF) with 68Ga-PSMA-derived SRF. This retrospective cross-sectional study included 28 patients with histologically proven metastatic castration-resistant prostate cancer (mCRPC) who received 177Lu-PSMA617. A comparison between the split renal function using 68Ga-PSMA PET/CT and the 99mTc-MAG-3-derived split renal function was carried out in 56 kidneys (n = 56). The SRF on 68Ga-PSMA was calculated using the volume and the average standard uptake value (SUVmean) within each VOI calculated as previously described by Roser et al.: SRF = (VOLUMEright) ∗ SUVmeanright/(VOLUMEright ∗ SUVmeanright + VOLUMEleft ∗ SUVmeanleft). Paired tests and correlation coefficients were used to compare 68Ga-PSMA and 99mTc-MAG-3. A visual comparison of kidney morphology on both studies was also performed. The median SRF of the right kidney was 49.9% (range: 3-91%) using 68Ga-PSMA PET/CT and 50.5% (range: 0-94%) with 99mTc-MAG3 scintigraphy. Notably, there was a strong correlation between SRF measurements obtained from PSMA and 99mTcMAG3, with a Pearson correlation coefficient of 0.957 (p < 0.001). Both 99mTc-MAG3 and 68Ga-PSMA PET/CT studies identified morphological renal abnormalities; there were nine hydronephrotic kidneys, four shrunken kidneys and one obstructed kidney, and there was a strong positive correlation between 68Ga-PSMA kidney morphology and 99mTcMAG3 renal scintigraphy kidney morphology, with a correlation coefficient of 0.93. PSMA-derived split function demonstrated a high correlation with renal function assessed on diuretic 99mTc-MAG3 renograms. PET-derived split renal function may, therefore, be considered an alternative to diuretic renogram-based split function. Furthermore, both 99mTc-MAG3 and 68Ga-PSMA PET/CT studies identified morphological renal abnormalities such as hydronephrosis, shrunken and obstructed kidneys. This correlation underscores the potential utility of 68Ga-PSMA imaging as a valuable tool for assessing kidney morphology as an alternative to renogram split function in clinical practice.

Behavioral strategy shapes activation of the Vip-Sst disinhibitory circuit in visual cortex

In complex environments, animals can adopt diverse strategies to find rewards. How distinct strategies differentially engage brain circuits is not well understood. Here, we investigate this question, focusing on the cortical Vip-Sst disinhibitory circuit between vasoactive intestinal peptide-postive (Vip) interneurons and somatostatin-positive (Sst) interneurons. We characterize the behavioral strategies used by mice during a visual change detection task. Using a dynamic logistic regression model, we find that individual mice use mixtures of a visual comparison strategy and a statistical timing strategy. Separately, mice also have periods of task engagement and disengagement. Two-photon calcium imaging shows large strategy-dependent differences in neural activity in excitatory, Sst inhibitory, and Vip inhibitory cells in response to both image changes and image omissions. In contrast, task engagement has limited effects on neural population activity. We find that the diversity of neural correlates of strategy can be understood parsimoniously as the increased activation of the Vip-Sst disinhibitory circuit during the visual comparison strategy, which facilitates task-appropriate responses.

AiPE: A Novel Transformer-Based Pose Estimation Method

AiPE: A Novel Transformer-Based Pose Estimation Method

Applicability of a new method for mesoscopic structure segmentation of asphalt mixture based on two-dimensional image

The mechanical properties of the asphalt mixture largely depend on its internal structure. Studies in mixture mesostructure are of great significance for perfecting relevant theoretical systems and improving mixture design methods. However, efficient segmentation of mesostructure is an important precondition for mesoscale research about asphalt mixtures. Therefore, this article proposes a new method for mesostructure information acquisition that mainly improves the function of image preprocessing and separation of touching objects. A visual and quantitative comparison between the proposed and common methods is adopted. The result shows that the proposed method performs better in identifying small particles and retaining the fidelity of the boundary. Besides, the mesostructure of four types of asphalt mixtures are compared based on the proposed method. The result shows that the optimum sample size, which makes the measured 2D information efficiently close to the actual 3D information, is around 20–30. Compared to SUP25, the coordination number of AC20 is about 0.15–0.23 higher. Compared with the samples compacted by Marshall, the samples compacted by gyratory have a larger coordination number, about 0.12–0.21 higher, a larger fractal dimension, about 0.059–0.062 higher, a smaller uniformity of major axis orientation, about 1.53–1.28 lower, and a smaller uniformity of area distribution, about 0.063–0.12 lower.

Spatial and visual comparison analysis of health disparities in London neighbourhoods: the case of Southwark and Lambeth

Spatial and visual comparison analysis of health disparities in London neighbourhoods: the case of Southwark and Lambeth

Species delineation and hybrid identification using diagnostic nuclear markers for Mediterranean groupers Epinephelus marginatus and Mycteroperca rubra

Globally, groupers (Serranidae) are commercially important fish species. Hybridization within this family has been reported in captivity and natural environments, usually among congeneric species. However, intergeneric hybridization has been reported only occasionally. Given the commercial interest in these fish, artisanal or recreational fishermen easily notice “weird-looking” individuals. This is the case of an unidentified grouper noticed by a spearfisher in Lebanese Mediterranean waters. Visual comparisons raised the possibility that the observed specimen was a hybrid. Molecular analysis based on two mitochondrial and three nuclear markers was performed to investigate this potential hybrid’s affinity. The discordance of the phylogenetic gene trees of the mitochondrial and nuclear markers indicates that E. marginatus and M. rubra are potential parent species of a hybrid individual in our samples. The subsequent haploweb analysis based on the S7 nuclear marker reveals the affinity of the hybrid individual to both E. marginatus and M. rubra. In this specific hybridization case, the nuclear marker S7 emerges as a valuable diagnostic tool for species delineation and hybrid detection.

New method for collecting XPS and other spectra: A thought (Gedanken) experiment

We suggest a new approach for collecting data, with accompanying statistical analysis, that could be useful for assessing sample damage in X-ray Photoelectron Spectroscopy (XPS) and for target detection in XPS imagining. It is based on the concept of the ‘constant signal, variable time’ (CSVT) spectrum that is in many ways the opposite of the traditional approach of collecting ‘variable signal, constant time’ spectra. In many cases, CSVT spectra should allow better visual comparisons of spectra and also for more rigorous statistical analyses based on paired t-tests and sums-of-squares of errors. We discuss the possibility of taking both survey and narrow CSVT spectra and provide a statistical discussion of how the resulting data might be treated. As we have no ability to collect CSVT spectra with our XPS instrument, this paper is a thought (Gedanken) experiment. The ideas presented herein may also be transferable to other spectroscopies.

The Making of the Liveable City: The Overlooked Aspects of Smart Cities Design

This article examines the real potential of smart cities to offer a better experience to residents as people with more than just basic needs. This is done through a lens of design, urban encounters and on-site sensations. The topic is presented and discussed in four main themes; Facilitating the Making of Liveable City and Quality Experience, Mental Associations of the City, The Unique Intimacy of the Night Experience, Emotional Responses: Safety, Stress and Discomfort, and the Taste of the City: Character, Wayfinding and Monotony. This is done to facilitate analysis and communication. Nevertheless, the topics presented here should not be separated from one another. Various qualitative methods were used in the analysis of the Milton Keynes case study; this includes interviews, field observations and visual comparisons with other cases, allowing for a deeper understanding of the different capabilities of the different approaches. The results help to further fill the knowledge gap in the literature on the overlooked aspects of smart cities and provide better information for smart city design. Keywords: smart cities making, sustainability, city brain and smart cities metrics, smart cities standards, smart cities applications, governance, planning and policy

An Analysis of the Mean Chart Under OC Function for Correlated Data

In this paper, we determine and illustrate the effects of correlation between the observations on the operating characteristics curve, Type-I error and Average Run length. In addition, for different correlated coefficient the control limits have been developed. To study the effect of correlated observations the OC curves, Type-I error, ARL and factor A have been worked out using various equation and values are given in Tables 1 to 4. To give a visual comparison of OC function and ARL, curves have been drawn in Figures 1 to 6. It is found that correlation between observations seriously affected the OC, Type-I error, ARL and factor A for the mean chart when standards are known. When the center line and control limits are based on the large value. Thus, it will be healthy contribution in manufacturing process which tracks important product characteristics in industry.

Features of the development of the agricultural marketing system using information technologies

Forecasting prices for agricultural products is a complex, end-to-end and dynamic task of agricultural marketing. With constant development and changes in data sources, data types, data quality, data processing methods, model building methods, and model evaluation methods, agricultural price forecasting methods will also be updated and improved. An overview of the use of digital technologies is proposed, leading to profound changes in the functioning of economic factors, including in the agro-industrial complex. The article shows that the digital transformation (digitalization) of the agro-industrial market will lead to a change in the sectoral structure of the agro-industrial complex due to the replacement of traditional industries with new ones based on forecasts obtained using artificial intelligence systems. The paper provides an overview of specialized applied software products that are available on the Internet and are used to analyze financial data. An overview of modern information technologies, which allow convenient processing, systematization and visualization of data, as well as forecasting the movement of asset prices, was carried out. Scientific abstraction, analysis and synthesis methods, quantitative and qualitative assessment methods, which were used to determine the content of marketing concepts and its features in the activities of agro-industrial enterprises, as well as the method of source analysis served as the scientific and theoretical basis for deepening the research. When selecting sources for analysis, a search was made in open databases available in the global information network Internet, on the basis of which neural network training was carried out. The main functionalities of the created system are described, including a visual comparison of historical data, price movement forecasting using machine learning, and recommendations on the optimal content of the investment portfolio. The results obtained in the work substantiate the following basic propositions: - digitalization leads not only to technological, but also to organizational transformations in the agro-industrial complex; - the result of digital transformation will be a profound change in the model of the organization of the agro-industrial complex and its role in the national economy; - agribusiness needs to take measures to support the digital transformation of the agro-industrial market and the adaptation of the agro-industrial complex to the new digital system.

Klasik ve Bulanık Kenar Algılama Yöntemlerinin Karşılaştırılması

Edge detection is one of the challenging problems in image processing. Four different classical edge detection methods—Sobel, Prewitt, Roberts, and Canny—and type-1 and type-2 fuzzy logic-based edge detection methods are applied to analyze two separate datasets with various properties. The datasets are STARE which contains medical images of the retina and BIPED which contains images of the street. Furthermore, two separate hybrid fuzzy logic methods are implemented. The type-1 and type-2 fuzzy inference techniques are combined to produce the hybrid-1 and hybrid-2 approaches, using the "AND" and "OR" logic operators. We compare the simulation results for each technique using three different image quality metrics. These are Mean Square Error (MSE), Peak Signal Noise Ratio (PSNR), and Structural Similarity Index (SSIM). The type-2 fuzzy technique outperformed the hybrid-1 fuzzy method in visual quality metrics comparison, demonstrating superior blood vessel recognition on the STARE retinal image dataset—a dataset that more closely resembles the human visual system. Using the BIPED street image dataset, the hybrid-1 fuzzy approach outperformed the Roberts method. The hybrid-1 fuzzy technique showed good results in the second order for both kinds of datasets. Any data and general applications can take advantage of it.

Depth-based graphical tools and related tests for multivariate multi-sample problems

A notion of data depth is used to measure the centrality/outlyingness of a given point with respect to a given distribution or data cloud. Several depth-based graphical tools and nonparametric tests have been proposed for the comparison of two or more multivariate distributions. This article proposes graphical tools for the comparison of multiple multivariate distributions. These graphical tools can be considered as a generalization of the well-known depth versus depth plot (DD-plot) for the visual comparison of the two multivariate samples. Different types of variations in location, scale, skewness, or kurtosis among distributions give rise to different deviation patterns in the proposed plots. Based on these graphical tools we generalize the statistical tests for two sample location, scale, and homogeneity of species assemblages to the corresponding multi-sample problems. An extensive simulation study reveals that the performances of the proposed tests are superior to that of the existing tests. The proposed graphical tools and tests are illustrated with different simulated and real data sets.

Estimating the impact of adjuvant treatment with nivolumab on long-term survivorship rates compared with surveillance: Analyses of disease-free survival (DFS) from the phase 3 CheckMate-274 trial.

528 Background: Durable DFS and cure are the ultimate goals for the treatment of muscle invasive urothelial carcinoma (MIUC) with radical cystectomy. This analysis employed mixture cure models (MCMs) to estimate the underlying cure fraction among high-risk MIUC patients following radical resection in the Phase 3 CheckMate-274 study. Methods: MCMs were applied to patient-level DFS data from the trial (minimum follow-up: 31.6 months). Intention-to-treat (ITT) population and the subpopulation with tumor PD-L1 expression ≥1% were analyzed separately for nivolumab (NIVO) and placebo (PBO) arms. In MCMs, the patient populations were assumed to consist of two exclusive subgroups as cured and uncured. Cured subgroup was assumed to be free of disease recurrence and disease-related mortality risks. The uncured subgroup was at the risk of both disease recurrence and all-cause mortality. DFS for the cured subgroup was estimated using background mortality rates published by WHO matched to the trial’s demographic characteristics. DFS for the uncured subgroup was modelled using parametric distributions, which were characterized along with the cure fraction by maximum likelihood methods. Model selection was primarily based on clinical plausibility of estimated DFS for the uncured subgroup. Visual comparison of the fits from the MCMs to the reported DFS data from the trial and goodness-of-fit statistics also assisted model selection. Results: In the trial, 353 patients were treated with NIVO (mean age: 65.3; male: 75.1%; PD-L1≥1%: 39.7%) and 356 patients were in PBO control (mean age: 65.9; male: 77.2%; PD-L1≥1%: 39.9%). Selected models estimated almost all uncured patients to experience recurrence within 5 years. The estimated cure fraction in the ITT population ranged from 43.1%-45.1% in the NIVO arm (95% CI: 36.7%-51.6%), and 36.4%-37.0% in the PBO arm, (95% CI: 30.9%-43.0%) for clinically plausible models. Projected range of 10-year mean DFS for the ITT patients was 4.38-4.47 years in the NIVO arm and 3.61-3.64 years in the PBO arm. Estimated cure fractions in the PD-L1≥1% subpopulation ranged from 59.1%-61.0% in the NIVO arm (95% CI: 48.9%-72.0%), and 35.9%-36.9% in the PBO arm, (95% CI: 27.5%-45.9%). Projected range of 10-year mean DFS for the PD-L1≥1% subpopulation was 5.54-5.65 years in the NIVO arm and 3.54-3.57 years in the PBO arm. Conclusions: In the adjuvant treatment of MIUC, relative to radical resection only, systemic therapy with NIVO is associated with a 6-9 percentage points higher cure fraction in the ITT population. Tumor PD-L1≥1% expression was associated with higher cure fractions in the NIVO arm but had only negligible impact on the underlying cure fraction in the PBO arm. Clinical trial information: NCT02632409 .

Comparing Long Short-Term Memory and Random Forest Accuracy for Bitcoin Price Forecasting

Bitcoin’s daily value fluctuations are very dynamic. Understanding its rapid and intricate price movements demands advanced techniques for processing complex data. This research aims to compare the accuracy of two machine learning methods, Random Forest (RF) and Long Short-Term Memory (LSTM), in predicting Bitcoin price. This research employs RF and LSTM algorithms to forecast Bitcoin prices using a two-year Yahoo Finance dataset. The evaluation metrics used were accuracy based on Mean Absolute Percentage Error (MAPE) and computational power (CPU-Z). As a result of this research, the LSTM model demonstrates higher accuracy compared to the RF model. MAPE reveals LSTM’s precision of 99.8% and RF’s accuracy of 90.1%. Regarding computational time and resources, RF shows slightly better performance than LSTM. The visual comparison further emphasizes LSTM’s better performance in predicting Bitcoin prices, highlighting its potential for informed decision-making in cryptocurrency trading. This research contributes valuable insights into the effectiveness, strengths, and weaknesses of LSTM and RF models in predicting cryptocurrency trends.