Structural Similarity Measure Research Articles

Computationally efficient progressive approach for single-image super-resolution using generative adversarial network

Single-image super-resolution (SISR) refers to reconstructing a high-resolution image from given low-resolution observation. Recently, convolutional neural network (CNN)-based SISR methods have achieved remarkable results in terms of peak-signal-to-noise ratio and structural similarity measures. These models use pixel-wise loss functions to optimize their models, which results in blurry images. However, the generative adversarial network (GAN) has the ability to generate visually plausible solutions. The different GAN-based SISR methods obtain perceptually better SR results when compared to that with the existing CNN-based methods. However, the existing GAN-based SISR methods need a large number of training parameters in the architecture to obtain better SR performance, which makes them unsuitable for many real-world applications. We propose a computationally efficient enhanced progressive approach for SISR task using GAN, which we referred as E-ProSRGAN. In the proposed method, we introduce a novel design of residual block called enhanced parallel densely connected residual network, which helps to obtain better SR performance with less number of training parameters. The quantitative performance of the proposed E-ProSRNet (i.e., generator network of E-ProSRGAN) model is better for higher upscaling factors ×3 and ×4 for most of datasets when compared to the same obtained using different CNN-based methods whose trainable parameters are less than 7 M. In the case of upscaling factor ×2, E-ProSRNet obtains second highest structural similarity index measure values for Set5 and BSD100 datasets. The proposed E-ProSRGAN model generates SR samples with better high-frequency details and perception measures than that of the other existing GAN-based SISR methods with significant reduction in the number of training parameters for larger upscaling factor.

Fast and Lightweight Human Pose Estimation

Although achieving significant improvement on pose estimation, the major drawback is that most top-performing methods tend to adopt complex architecture and spend large computational cost to achieve higher performance. Due to the edge device’s limited resources, its top-performing methods are hard to maintain fast inference speed in practice. To address this issue, we proposed the fast and lightweight human pose estimation method to maintain high performance and bear the less computational cost. Especially, the proposed method consists of two parts, i.e., the fast and lightweight pose network (FLPN) for pose estimation and a novel lightweight bottleneck block for reducing computational cost, which can integrate the simple network and lightweight bottleneck into an efficient method for accurate pose estimation. In terms of lightweight bottleneck block, we introduce the structural similarity measurement (SSIM) to refine the appropriate ratio of intrinsic feature maps and reduce the model size. Furthermore, an attention mechanism is also adopted in our lightweight bottleneck block for modeling the contextual information. We demonstrate the performance of the proposed method with extensive experiments on the two standard benchmark datasets by comparing our method with state-of-the-art methods. On the COCO keypoint detection dataset, our proposed method attains a similar accuracy with these state-of-the-art methods, but the computational cost of these top-performing methods is more than 7 times that of ours.

A Graph-based Approach for Representing, Comparing, and Classifying Integer Programs

It has long been observed that model structure may play an important role in determining the effectiveness of certain solution techniques to mixed integer linear programs (MILPs). One implication is that solution techniques that work well for one class of MILP are often found to be effective on other “similar” problems. Despite the potential benefits, there is limited research in the area of recognizing similarity among MILPs. This paper seeks to address this gap by presenting a framework for classifying and comparing instances of MILPs, based on their mathematical structure. A new graph-based representation of MILPs is proposed, where decision variables and constraints are described by nodes, and arcs denote the presence of decision variables in certain constraints. Inspired by recent advances in the area of deep learning for graph-structured data, two methods of leveraging the MILP graph representations for classification and comparison are provided. In the first relational approach, a graph convolutional network (GCN) is employed to classify these so-called MILP graphs as having come from one of a known number of problem types. The second approach makes use of latent features learned by the GCN to compare graphs to one another directly. As part of the latter approach, we introduce a formal measure of graph-based structural similarity. Empirical studies indicate that both the classification and comparison procedures perform well on a test set. Additional properties of MILP graphs are also explored through a series of case studies.

A Novel AlphaSRGAN for Underwater Image Super Resolution

Obtaining clear images of underwater scenes with descriptive details is an arduous task. Conventional imaging techniques fail to provide clear cut features and attributes that ultimately result in object recognition errors. Consequently, a need for a system that produces clear images for underwater image study has been necessitated. To overcome problems in resolution and to make better use of the Super-Resolution (SR) method, this paper introduces a novel method that has been derived from the Alpha Generative Adversarial Network (AlphaGAN) model, named Alpha Super Resolution Generative Adversarial Network (AlphaSRGAN). The model put forth in this paper helps in enhancing the quality of underwater imagery and yields images with greater resolution and more concise details. Images undergo pre-processing before they are fed into a generator network that optimizes and reforms the structure of the network while enhancing the stability of the network that acts as the generator. After the images are processed by the generator network, they are passed through an adversarial method for training models. The dataset used in this paper to learn Single Image Super Resolution (SISR) is the USR 248 dataset. Training supervision is performed by an unprejudiced function that simultaneously scrutinizes and improves the image quality. Appraisal of images is done with reference to factors like local style information, global content and color. The dataset USR 248 which has a huge collection of images has been used for the study is composed of three collections of images—high (640 480) and low (80 60, 160 120, and 320 240). Paired instances of different sizes—2, 4 and 8—are also present in the dataset. Parameters like Mean Opinion Score (MOS), Peak Signal-to-Noise Ratio (PSNR), Structural Similarity (SSIM) and Underwater Image Quality Measure (UIQM) scores have been compared to validate the improved efficiency of our model when compared to existing works.

Adversarial Attack Based on Perturbation of Contour Region to Evade Steganalysis-Based Detection

Deep neural networks (DNN) are applied in various fields because they afford good performance. However, they seem vulnerable to adversarial examples. Therefore, studies are actively investigating adversarial defenses to improve the robustness of DNNs as well as adversarial attacks to generate more intensive adversarial perturbations. Most existing attack methods excessively modify images by generating overly large distortions or adding perturbations to regions with little impact on the DNN. As a result, the local smoothness of images is not maintained, and changes can be easily detected using a steganalysis-based detector. In this study, we propose a contour attack method to evade steganalysis-based detection. This method extracts the contour region from an image and adds perturbations only to applicable regions, thus maintaining the local smoothness. It can solve the problems mentioned above and effectively evade steganalysis-based detectors. Our experimental results demonstrate that the local smoothness is better than that in the case of original attack methods and that the detection evasion rate for a steganalysis detector is up to 19.9% higher. Further, structural similarity (SSIM) measurements and image comparisons demonstrate the improved imperceptibility of perturbations. In particular, the SSIM values for images subjected to the contour attack are close to 1.0.

Semantic integration of traditional and heterogeneous data sources (UML, XML and RDB) in OWL2 triplestore

With the success of the internet and the expansion of the amount of data in the web, the exchange of information from various heterogeneous and classical data sources becomes a critical need. In this context, researchers must propose integration solutions that allow applications to simultaneously access several data sources. In this perspective, we propose a semi-automatic integration approach of classical data sources via a global schema located in database management systems of RDF or OWL data, called triplestore. Our contribution is subdivided into three axes: 1) an automatic mapping solution that converts classical data sources such as UML, XML and RDB to local ontologies based on OWL2 language; 2) an alignment system of local ontologies based on syntactic, semantic and structural similarity measurement techniques in order to increase the probability of having real correspondences and real differences; 3) a fusion system of pre-existing local ontologies into a global ontology based on the alignment found in the previous step.

Cross-Modality Guided Contrast Enhancement for Improved Liver Tumor Image Segmentation

Tumor segmentation in Computed Tomography (CT) images is a crucial step in image-guided surgery. However, low-contrast CT images impede the performance of subsequent segmentation tasks. Contrast enhancement is then used as a preprocessing step to highlight the relevant structures, thus facilitating not only medical diagnosis but also image segmentation with higher accuracy. In this paper, we propose a goal-oriented contrast enhancement method to improve tumor segmentation performance. The proposed method is based on two concepts, namely guided image enhancement and image quality control through an optimization scheme. The proposed OPTimized Guided Contrast Enhancement (OPTGCE) scheme exploits both contextual information from the guidance image and structural information from the input image in a two-step process. The first step consists of applying a two-dimensional histogram specification exploiting contextual information in the corresponding guidance image, i.e. Magnetic Resonance Image (MRI). In the second step, an optimization scheme using a structural similarity measure to preserve the structural information of the original image is performed. To the best of our knowledge, this kind of contrast enhancement optimization scheme using cross-modal guidance is proposed for the first time in the medical imaging context. The experimental results obtained on real data demonstrate the effectiveness of the method in terms of enhancement and segmentation quality in comparison to some state-of-the-art methods based on the histogram.

Improved Deep Learning Based Method for Molecular Similarity Searching Using Stack of Deep Belief Networks.

Virtual screening (VS) is a computational practice applied in drug discovery research. VS is popularly applied in a computer-based search for new lead molecules based on molecular similarity searching. In chemical databases similarity searching is used to identify molecules that have similarities to a user-defined reference structure and is evaluated by quantitative measures of intermolecular structural similarity. Among existing approaches, 2D fingerprints are widely used. The similarity of a reference structure and a database structure is measured by the computation of association coefficients. In most classical similarity approaches, it is assumed that the molecular features in both biological and non-biologically-related activity carry the same weight. However, based on the chemical structure, it has been found that some distinguishable features are more important than others. Hence, this difference should be taken consideration by placing more weight on each important fragment. The main aim of this research is to enhance the performance of similarity searching by using multiple descriptors. In this paper, a deep learning method known as deep belief networks (DBN) has been used to reweight the molecule features. Several descriptors have been used for the MDL Drug Data Report (MDDR) dataset each of which represents different important features. The proposed method has been implemented with each descriptor individually to select the important features based on a new weight, with a lower error rate, and merging together all new features from all descriptors to produce a new descriptor for similarity searching. Based on the extensive experiments conducted, the results show that the proposed method outperformed several existing benchmark similarity methods, including Bayesian inference networks (BIN), the Tanimoto similarity method (TAN), adapted similarity measure of text processing (ASMTP) and the quantum-based similarity method (SQB). The results of this proposed multi-descriptor-based on Stack of deep belief networks method (SDBN) demonstrated a higher accuracy compared to existing methods on structurally heterogeneous datasets.

An Accurate Registration Method Based on Global Mixed Structure Similarity (GMSIM) for Remote Sensing Images

Although remote sensing image registration has been studied for several years, achieving accurate image registration remains a challenging task due to the complicated conditions surrounding remote sensing images. To improve the accuracy and robustness of image registration, we proposed a registration method based on the global mixed structure similarity (GMSIM) measure. This measure mixes the structure similarity in both the frequency domain and the intensity domain because phase-based structure similarity in the frequency domain is sensitive to intensity contrast and spatial translation, and gray-based structure similarity in the intensity domain is efficient to structure change. Feature-based registration methods are used to generate the initial registration parameters. After that, we calculate the final registration parameters by maximizing GMSIM. Quantum-behaved particle swarm optimization (QPSO) is utilized to solve the optimal results of GMSIM due to its high efficiency. The proposed method has been evaluated on several remote sensing images differing in scale, gray, and scene and compared with three state-of-the-art registration methods. Experimental results demonstrate the high accuracy of the proposed scheme.

STRUCTURAL SIMILARITY MEASURE OF USERS PROFILES BASED ON A WEIGHTED BIPARTITE GRAPHS

Abstract. The user profile is a very important tool in several fields such as recommendation systems, customization systems etc., it is used to narrow the number of data or results provided for a specific user, also to minimize the cost and the time of processing of multiple systems. Whatever the user profile model used, it’s updating and enrichment is a very essential step in the information research process in order to obtain more interesting and satisfactory results, which lead the information systems to develop several techniques aiming to enrich them based especially on similarity methods between user profiles. The similarity methods are used for several tasks such as the detection of duplicate profiles in online social network, also to answer the problem of cold start, and to predict users who can become friends as well as their future intentions, etc. In this paper, we propose a new approach to express the similarity between users profiles by developing a structural similarity measure to calculate the similarity between user profiles based on SimRank measure or similarity ,and the properties of bipartite graphs, in order to take advantage of the information provided by the relational structure between user profiles and their interests, our method is characterized by the similarity propagation between graph's nodes over iterations from source nodes to their successors, so our method finds profiles similar to the query profile, whether the links are direct or indirect between profiles.

PROMISCUOUS 2.0: a resource for drug-repositioning.

The development of new drugs for diseases is a time-consuming, costly and risky process. In recent years, many drugs could be approved for other indications. This repurposing process allows to effectively reduce development costs, time and, ultimately, save patients’ lives. During the ongoing COVID-19 pandemic, drug repositioning has gained widespread attention as a fast opportunity to find potential treatments against the newly emerging disease. In order to expand this field to researchers with varying levels of experience, we made an effort to open it to all users (meaning novices as well as experts in cheminformatics) by significantly improving the entry-level user experience. The browsing functionality can be used as a global entry point to collect further information with regards to small molecules (∼1 million), side-effects (∼110 000) or drug-target interactions (∼3 million). The drug-repositioning tab for small molecules will also suggest possible drug-repositioning opportunities to the user by using structural similarity measurements for small molecules using two different approaches. Additionally, using information from the Promiscuous 2.0 Database, lists of candidate drugs for given indications were precomputed, including a section dedicated to potential treatments for COVID-19. All the information is interconnected by a dynamic network-based visualization to identify new indications for available compounds. Promiscuous 2.0 is unique in its functionality and is publicly available at http://bioinformatics.charite.de/promiscuous2.

A Full-Spectrum Registration Method for Zhuhai-1 Satellite Hyperspectral Imagery.

Accurate registration is an essential prerequisite for analysis and applications involving remote sensing imagery. It is usually difficult to extract enough matching points for inter-band registration in hyperspectral imagery due to the different spectral responses for land features in different image bands. This is especially true for non-adjacent bands. The inconsistency in geometric distortion caused by topographic relief also makes it inappropriate to use a single affine transformation relationship for the geometric transformation of the entire image. Currently, accurate registration between spectral bands of Zhuhai-1 satellite hyperspectral imagery remains challenging. In this paper, a full-spectrum registration method was proposed to address this problem. The method combines the transfer strategy based on the affine transformation relationship between adjacent spectrums with the differential correction from dense Delaunay triangulation. Firstly, the scale-invariant feature transform (SIFT) extraction method was used to extract and match feature points of adjacent bands. The RANdom SAmple Consensus (RANSAC) algorithm and the least square method is then used to eliminate mismatching point pairs to obtain fine matching point pairs. Secondly, a dense Delaunay triangulation was constructed based on fine matching point pairs. The affine transformation relation for non-adjacent bands was established for each triangle using the affine transformation relation transfer strategy. Finally, the affine transformation relation was used to perform differential correction for each triangle. Three Zhuhai-1 satellite hyperspectral images covering different terrains were used as experiment data. The evaluation results showed that the adjacent band registration accuracy ranged from 0.2 to 0.6 pixels. The structural similarity measure and cosine similarity measure between non-adjacent bands were both greater than 0.80. Moreover, the full-spectrum registration accuracy was less than 1 pixel. These registration results can meet the needs of Zhuhai-1 hyperspectral imagery applications in various fields.

Performance evaluation of automatic object detection with post-processing schemes under enhanced measures in wide-area aerial imagery

Performance analysis of object detection combined with post-processing schemes are challenging especially that the spatial resolution of images is low in wide-area aerial imagery. In this paper, we present the quantitative results of ten object detection algorithms combined with several post-processing schemes including filtered dilation, heuristic filtering, sieving and closing, a three-stage scheme which involves thresholding with respect to area and compactness, and the proposed scheme of median filtering, opening and closing, followed by linear Gaussian filtering with nonmaximum suppression. We verified the sieving and closing as well as the three-stage scheme display better Fβ-score and PASCAL value via four vehicle detection algorithms. We evaluated combinations of ten object detection and segmentation methods with two post-processing schemes by adopting a set of recent evaluation metrics, i.e., Jaccard Index (JI), Fbw measure, the structure similarity measure (SSIM) and the enhanced alignment measure (EAM). Automatic detection outputs are compared with their ground truth in low-resolution aerial datasets. Classified detection results are established on ten algorithms each combined with the selected post-processing schemes. We take two widely used datasets (VIVID and VEDAI) for performance analysis, compare the detections and time cost of each algorithm either without or with the proposed scheme, and verified our approach via replacing either datasets or algorithms. Quantitative evaluation under a set of enhanced measures proves our test with validity, efficiency, and accuracy.

Structural Similarity Measurement Based Cost Function for Stereo Matching of Automotive Applications.

The human visual perception uses structural information to recognize stereo correspondences in natural scenes. Therefore, structural information is important to build an efficient stereo matching algorithm. In this paper, we demonstrate that incorporating the structural information similarity, extracted either from image intensity (SSIM) directly or from image gradients (GSSIM), between two patches can accurately describe the patch structures and, thus, provides more reliable initial cost values. We also address one of the major phenomenons faced in stereo matching for real world scenes, radiometric changes. The performance of the proposed cost functions was evaluated within two stages: the first one considers these costs without aggregation process while the second stage uses the fast adaptive aggregation technique. The experiments were conducted on the real road traffic scenes KITTI 2012 and KITTI 2015 benchmarks. The obtained results demonstrate the potential merits of the proposed stereo similarity measurements under radiometric changes.

An Adaptive Multisensor Image Fusion Method Based on Monogenic Features

Each kind of sensor is designed to adapt to a specific environment and usage scope. In this paper, an adaptive multisensor image fusion method based on monogenic features is proposed. For the proposed method, the monogenic features are extracted from the source images including monogenic amplitude, monogenic phase and monogenic orientation features. The energy matching similarity measure is used to measure the monogenic amplitude feature, and the complex coefficient structure similarity measure is used to characterize the monogenic phase and the monogenic orientation feature. Analyses the monogenic features in different types of regions, different fusion strategies are adopted for different characteristic regions. By means of visible and infrared image fusion, SAR and infrared image fusion experiments, the proposed method can effectively preserve a large amount of information and significantly improve the visual quality of the fused image, which can be evaluated with objective indicators.

Structural and Semantic Similarity Measurement of UML Use Case Diagram

Reusing software has several benefits ranging from reducing cost and risk, accelerating development, and its primary purposes are improving software quality. In the early stage of software development, reusing existing software artifacts may increase the benefit of reusing software because it uses mature artifacts from previous artifacts. One of software artifacts is diagram, and in order to assist the reusing diagram is to find the level of similarity of diagrams. This paper proposes a method for measuring the similarity of the use case diagram using structural and semantic aspects. For structural similarity measurement, Graph Edit Distance is used by transforming each factor and use case into a graph, while for semantic similarity measurement, WordNet, WuPalmer,and Levenshtein were used. The experimentation was conducted on ten datasets from variousprojects. The results of the method were compared with the results of assessments from experts.The measurement of agreement between experts and method was done by using Gwet’s AC1 andPearson correlation coefficient. Measurement results with Gwet’s AC1 diagram similarity are 0,60,which were categorized as “moderate" agreement and the result of measurement with Pearsonis 0.506 which means there is a significant correlation between experts and methods. The resultshowed that the proposed method can be used to find the similarity of the diagram, so finding andreuse of the diagram as a software component can be optimized.

Improving neighbor-based collaborative filtering by using a hybrid similarity measurement

Memory-based collaborative filtering is one of the recommendation system methods used to predict a user’s rating or preference by exploring historic ratings, but without incorporating any content information about users or items. It can be either item-based or user-based. Taking item-based Collaborative Filtering (CF) as an example, the way it makes predictions is accomplished in 2 steps: first, it selects based on pair-wise similarities a number of most similar items to the predicting item from those that the user has already rated on. Second, it aggregates the user’s opinions on those most similar items to predict a rating on the predicting item. Thus, similarity measurement determines which items are similar, and plays an important role on how accurate the predictions are. Many studies have been conducted on memory-based CFs to improve prediction accuracy, but none of them have achieved better prediction accuracy than state-of-the-art model-based CFs. In this paper, we proposed a new approach that combines both structural and rating-based similarity measurement. We found that memory-based CF using combined similarity measurement can achieve better prediction accuracy than model-based CFs in terms of lower MAE and reduce memory and time by using less neighbors than traditional memory-based CFs on MovieLens and Netflix datasets.

A comparative analysis of similarity measures akin to the Jaccard index in collaborative recommendations: empirical and theoretical perspective

Jaccard index, originally proposed by Jaccard (Bull Soc Vaudoise Sci Nat 37:241–272, 1901), is a measure for examining the similarity (or dissimilarity) between two sample data objects. It is defined as the proportion of the intersection size to the union size of the two data samples. It provides a very simple and intuitive measure of similarity between data samples. This research examines the measures that are akin to the Jaccard index and may be used for modelling affinity between users (or items) in collaborative recommendations. Particularly, the measures such as simple matching coefficient (SMC), Sorensen–Dice coefficient (SDC), Salton’s cosine index (SCI), and overlap coefficient (OLC) are compared and analysed in both theoretical and empirical perspectives with respect to the Jaccard index. Since these measures apprehend only the structural similarity information (overlapping information) between the data samples, these are very useful in situations where only the associations between users and items are available such as browsing or buying behaviours of the users on an e-commerce portal (i.e. unary rating data, a special case of ratings). Furthermore, a theoretical relation among these measures has been established. We have also derived an equivalent expression for each of these measures so that it can be directly applied for binary data samples in data mining/machine learning jargon. In order to compare and validate the effectiveness of these structural similarity measures, several experiments have been conducted using standardized benchmark datasets (MovieLens, FilmTrust, Epinions, Yahoo! Movies, and Yahoo! Music). Empirically obtained results demonstrate that the Salton’s cosine index (SCI) provides better accuracy (in terms of MAE, RMSE, and precision) for large datasets, whereas the overlap coefficient (OLC) results in more accurate recommendations for small datasets.

Kinetics-Induced Block Matching and 5-D Transform Domain Filtering for Dynamic PET Image Denoising

Dynamic positron emission tomography (PET) scans of short-time frames are required to quantitatively estimate the uptake of PET ligands. Because such short-frame scans tend to be noisy, we propose kinetics-induced block matching and 5-D transform domain filtering (KIBM5D) specialized for dynamic PET image denoising. In the proposed algorithm, kinetics-induced block matching (KIBM) and 5-D transform domain filtering are alternately repeated in two cascading stages. In each stage of KIBM5D, all time frames are included in a patch of the KIBM to collect similar patch-wise time activity curves. These similar 4-D patches are then five-dimensionally grouped and transformed to the 5-D spectrum. In the 5-D transform domain, the 5-D spectrum is shrunk by hard thresholding and Wiener filtering in the first and second stage of KIBM5D, respectively. The sparsity of the 5-D spectrum is improved because signals of similar 4-D patches are correlated, while noises of these are uncorrelated. To evaluate the performance of KIBM5D, we used both computer simulation data of a dynamic digital brain phantom using [18F]FDG kinetics, and experimental data of a normal healthy volunteer using [11C]MeQAA, and compared the results of KIBM5D, Gaussian filter (GF), bilateral filter, nonlocal means, block matching and 4-D filtering, and 4-D Gaussian filtering. For simulation data, KIBM5D performed superiorly to the other methods in terms of the peak signal to noise ratio and structural similarity measures, in all time frames. Additionally, KIBM5D generated the best image quality not only in simulations but also with human data. Accordingly, KIBM5D enables the efficient denoising of dynamic PET images.

An in silico Workflow that Yields Experimentally Comparable Inhibitors for Human Dihydroorotate Dehydrogenase.

Rheumatoid Arthritis [RA] is an autoimmune disease that can cause chronic inflammation of the joints. Human DiHydroOrotate DeHydrogenase [DHODH] is a clinically validated drug target for the treatment of Rheumatoid Arthritis. DHODH inhibition results in beneficial immunosuppressant and anti-proliferative effects. Leflunomide [LEF] and Brequinar Sodium [BREQ], drugs used in the treatment of RA, suppresses the immune cells responsible for inflammation but has several side-effects, most predominant being symptomatic liver damage and toxicity. An existing scaffold based on structural analogies with LEF and BREQ was used to screen out potent inhibitors of DHODH, in ZINC Database using 2D binary fingerprint. 10 structures similar to the scaffold were shortlisted due to their Tanimoto similarity coefficient. Selected structures were docked using the tools AutoDock, Ligand fit and iGEMDOCK with target human DHODH. High scoring compounds having similar interactions as that of scaffold were checked to evaluate their Drug-Likeliness. The five shortlisted compounds were then subjected to Molecular Dynamics Simulation studies for 50ns using GROMACS. Measures of structural similarity based on 2D Fingerprint Screening and Molecular Dynamics Simulation studies can suggest good leads for drug designing. The novelty of this study is that the workflow used here yields the same results that are at par with the experimental data. This suggests the use of the 2D fingerprint similarity search in various databases, followed by multiple docking algorithms and dynamics as a workflow that will lead to finding novel compounds that a structurally and functionally similar to LEF and BREQ.