Binary Partitioning Research Articles

Complex multi-material approach for dynamic simulations

Triangle meshes are the most common representation of an object in the field of computer graphics. Recently, they have found their way into the field of erosion simulation, where volumetric representation used to prevail. Real-life erosion scenes are usually formed of multiple materials and so a reliable means of material definition is needed. Unfortunately, coupling the material information with a triangle mesh is not as straightforward as in the volumetric case. This paper proposes an approach for multiple material definition based on space subdivision. Binary space partitioning (BSP) is used to simulate complex multi-material scenes. The approach allows the definition of a nontrivial scene composed of several materials, including the definition of a gradually changing material. A method for an automated creation of the BSP tree from input volumetric data is proposed. The construction algorithm extracts a triangle mesh as an intermediate product and uses its faces as the splitting planes of the BSP tree.

Pretreatment 18F-FDG PET Textural Features in Locally Advanced Non-Small Cell Lung Cancer: Secondary Analysis of ACRIN 6668/RTOG 0235.

In a secondary analysis of American College of Radiology Imaging Network (ACRIN) 6668/RTOG 0235, high pretreatment metabolic tumor volume (MTV) on (18)F-FDG PET was found to be a poor prognostic factor for patients treated with chemoradiotherapy for locally advanced non-small cell lung cancer (NSCLC). Here we utilize the same dataset to explore whether heterogeneity metrics based on PET textural features can provide additional prognostic information. Patients with locally advanced NSCLC underwent (18)F-FDG PET prior to treatment. A gradient-based segmentation tool was used to contour each patient's primary tumor. MTV, maximum SUV, and 43 textural features were extracted for each tumor. To address overfitting and high collinearity among PET features, the least absolute shrinkage and selection operator (LASSO) method was applied to identify features that were independent predictors of overall survival (OS) after adjusting for MTV. Recursive binary partitioning in a conditional inference framework was utilized to identify optimal thresholds. Kaplan-Meier curves and log-rank testing were used to compare outcomes among patient groups. Two hundred one patients met inclusion criteria. The LASSO procedure identified 1 textural feature (SumMean) as an independent predictor of OS. The optimal cutpoint for MTV was 93.3 cm(3), and the optimal SumMean cutpoint for tumors above 93.3 cm(3) was 0.018. This grouped patients into three categories: low tumor MTV (n = 155; median OS, 22.6 mo), high tumor MTV and high SumMean (n = 23; median OS, 20.0 mo), and high tumor MTV and low SumMean (n = 23; median OS, 6.2 mo; log-rank P < 0.001). We have described an appropriate methodology to evaluate the prognostic value of textural PET features in the context of established prognostic factors. We have also identified a promising feature that may have prognostic value in locally advanced NSCLC patients with large tumors who are treated with chemoradiotherapy. Validation studies are warranted.

History-driven firefly algorithm for optimisation in dynamic and uncertain environments

Due to dynamic and uncertain nature of many optimisation problems in real-world, the applied algorithm in this environment must be able to continuously track the changing optima over time. In this paper, we report a novel speciation-based firefly algorithm for dynamic optimisation, which improved its performance by employing prior landscape historical information. The proposed algorithm, namely history-driven speciation-based firefly algorithm HdSFA, uses a binary space partitioning BSP tree to capture the important information about the landscape during the optimisation process. By utilising this tree, the algorithm can approximate the fitness landscape and avoid wasting the fitness evaluation for some unsuitable solutions. The proposed algorithm is evaluated on the most well-known dynamic benchmark problem, moving peaks benchmark MPB, and also on a modified version of it, called MPB with pendulum-like motion among the environments PMPB, and its performance is compared with that of several state-of-the-art algorithms in the literature. The experimental results and statistical test prove that HdSFA outperforms most of the algorithms in different scenarios.

An Efficient Technique for Hardware/Software Partitioning Process in Codesign

Codesign methodology deals with the problem of designing complex embedded systems, where automatic hardware/software partitioning is one key issue. The research efforts in this issue are focused on exploring new automatic partitioning methods which consider only binary or extended partitioning problems. The main contribution of this paper is to propose a hybrid FCMPSO partitioning technique, based on Fuzzy C-Means (FCM) and Particle Swarm Optimization (PSO) algorithms suitable for mapping embedded applications for both binary and multicores target architecture. Our FCMPSO optimization technique has been compared using different graphical models with a large number of instances. Performance analysis reveals that FCMPSO outperforms PSO algorithm as well as the Genetic Algorithm (GA), Simulated Annealing (SA), Ant Colony Optimization (ACO), and FCM standard metaheuristic based techniques and also hybrid solutions including PSO then GA, GA then SA, GA then ACO, ACO then SA, FCM then GA, FCM then SA, and finally ACO followed by FCM.

The Three Postulates of the Theory of Everything

The three postulates of the posited dynamic and reversible theory of everything are: 1) the oscil-lating M-theory postulate for the oscillating matter structure, 2) the digital transitional Higgs-reversed Higgs fields postulate for the digital space structure, and 3) the reversible multiverse post-ulate for all physical laws and phenomena. The posited theory of everything based on the three postulates explains cosmology, the composition (baryonic matter, dark matter, and dark energy) in the universe, the periodic table of elementary particles (quarks, leptons, and bosons), the galaxy evolution, superconductivity, black hole, thermodynamic, and quantum mechanics. Oscillating M-theory is derived from oscillating membrane-string-particle whose space-time dimension number oscillates between 11D and 10D and between 10D and 4D. Space-time dimension number between 10 and 4 decreases with decreasing speed of light, decreasing vacuum energy, and in-creasing rest mass. The digital transitional Higgs-reversed Higgs fields are derived from digital attachment-detachment spaces which couple to particles. Under spontaneous symmetry breaking, the coupling of massless particle to zero-energy attachment space (the space for mass) produces the transitional nonzero-energy Higgs field-particle composite which under spontaneous symmetry restoring produces massive particle on zero-energy attachment space with the longitudinal component. The opposite of attachment space is detachment space as the space for kinetic energy and the nonzero-energy reverse Higgs field. The combination of n units of attachment space (de-noted as 1) and n units of detachment space (denoted as 0) brings about the three digital structures: binary partition space (1)n(0)n, miscible space (1 + 0)n, and binary lattice space (1 0)n to account for quantum mechanics, special relativity, and the force fields, respectively. In the third postulate, all physical laws and phenomena are permanently reversible in the multiverse, and temporary irreversible entropy increase is allowed. Our universe is an asymmetrical dual posi-tive-energy-negative-energy universe where the positive-energy universe on attachment space absorbed the interuniversal void on detachment space to result in the combination of attachment space and detachment space, while the negative-energy universe did not absorb the interuniversal void, resulting in temporary irreversible entropy increase through reversibility breaking, sym-metry violation, and low entropy beginning. Guided by the reversible negative-energy universe, our dual universe is a globally reversible cyclic dual universe.

A fast region segmentation algorithm on compressed gray images using Non-symmetry and Anti-packing Model and Extended Shading representation

Image segmentation is one of the fundamental steps in image analysis for object identification. The main goal of image segmentation is to recognize homogeneous regions within an image as distinct and belonging to different objects. Inspired by the idea of the packing problem, in this paper, we propose a fast O(Nα(N))-time algorithm for image segmentation by using Non-symmetry and Anti-packing Model and Extended Shading representation, which was called the NAMES-based algorithm, where N is the number of homogenous blocks and α(N) is the inverse of the Ackerman’s function and it is a very slowly growing function. We first put forward four extended Lemmas and two extended Theorems. Then, we present a new scanning method used to process each NAMES block. Finally, we propose a novel NAMES-based data structure used to merge two regions. With the same experimental conditions and the same time complexity, our proposed NAMES-based algorithm, which extends the popular hierarchical representation model to a new non-hierarchical representation model, has about 86.75% and 89.47% average execution time improvement ratio when compared to the Binary Partition Tree (BPT)-based algorithm and the Quadtree Shading (QS)-based algorithm which has about 55.4% execution time improvement ratio when the QS-based algorithm itself is compared to the previous fastest region segmentation algorithm by Fiorio and Gustedt whose O(N2)-time algorithm is run on the original N×N gray image. Further, the NAMES can improve the memory-saving by 28.85% (5.04%) and simultaneously reduce the number of the homogeneous blocks by 49.05% (36.04%) more than the QS (the BPT) whereas maintaining the satisfactory image quality. Therefore, by comparing our NAMES-based algorithm with the QS-based algorithm and the BPT-based algorithm, the experimental results presented in this paper show that the former has not only higher compression ratio and less number of homogenous blocks than the latter whereas maintaining the satisfactory image quality, but also can significantly improve the execution speed for image segmentation, and therefore it is a much more effective algorithm for image segmentation.

Hyperspectral Super-Resolution of Locally Low Rank Images From Complementary Multisource Data.

Remote sensing hyperspectral images (HSIs) are quite often low rank, in the sense that the data belong to a low dimensional subspace/manifold. This has been recently exploited for the fusion of low spatial resolution HSI with high spatial resolution multispectral images in order to obtain super-resolution HSI. Most approaches adopt an unmixing or a matrix factorization perspective. The derived methods have led to state-of-the-art results when the spectral information lies in a low-dimensional subspace/manifold. However, if the subspace/manifold dimensionality spanned by the complete data set is large, i.e., larger than the number of multispectral bands, the performance of these methods mainly decreases because the underlying sparse regression problem is severely ill-posed. In this paper, we propose a local approach to cope with this difficulty. Fundamentally, we exploit the fact that real world HSIs are locally low rank, that is, pixels acquired from a given spatial neighborhood span a very low-dimensional subspace/manifold, i.e., lower or equal than the number of multispectral bands. Thus, we propose to partition the image into patches and solve the data fusion problem independently for each patch. This way, in each patch the subspace/manifold dimensionality is low enough, such that the problem is not ill-posed anymore. We propose two alternative approaches to define the hyperspectral super-resolution through local dictionary learning using endmember induction algorithms. We also explore two alternatives to define the local regions, using sliding windows and binary partition trees. The effectiveness of the proposed approaches is illustrated with synthetic and semi real data.

Semiautomatic classification of cementitious materials using scanning electron microscope images

Segmentation and classification are prolific research topics in the image processing community. These topics have been increasingly used in the context of analysis of cementitious materials on images acquired with a scanning electron microscope. Indeed, there is a need to be able to detect and to quantify the materials present in a cement paste in order to follow the chemical reactions occurring in the material even days after the solidification. We propose a new approach for segmentation and classification of cementitious materials based on the denoising of the data with a block-matching three-dimensional (3-D) algorithm, binary partition tree (BPT) segmentation, support vector machines (SVM) classification, and interactivity with the user. The BPT provides a hierarchical representation of the spatial regions of the data, allowing a segmentation to be selected among the admissible partitions of the image. SVMs are used to obtain a classification map of the image. This approach combines state-of-the-art image processing tools with user interactivity to allow a better segmentation to be performed, or to help the classifier discriminate the classes better. We show that the proposed approach outperforms a previous method when applied to synthetic data and several real datasets coming from cement samples, both qualitatively with visual examination and quantitatively with the comparison of experimental results with theoretical ones.

Design Optimization of a Permanent Magnet Motor Derived From a General Magnetization Pattern

In this paper, a new topological design of permanent magnet (PM) motor with Halbach magnet is introduced and investigated. Based on this PM configuration, five typical types of PM arrangements are being considered by setting different combinations of parameters during the optimization process. To better evaluate the performance of different types of motors, a novel approach for the design optimization based on an improved Tabu search algorithm and finite element method is proposed. The improvements include the introduction of Tabu list with a binary space partitioning tree, solution density estimation, and an adaptive step vector for different search spaces. The optimal design and comparisons with conventional motors are reported to verify the efficiency and effectiveness of the proposed method.

Region-based urban road extraction from VHR satellite images using Binary Partition Tree

This paper provides a hierarchical method for urban road extraction. It consists of (1) obtaining the road region of interest from a VHR image, (2) hierarchically representing this road region of interest in a Binary Partition Tree (BPT), and extracting the roads based on this BPT at hierarchical levels. Besides using two existing geometrical features (i.e. compactness and elongation), we define two other structural features based on orientation histograms and morphological profiles to guide the region merging of BPT. The morphological profiles are constructed using a series of path openings, which facilitate modeling linear or curved structures. The proposed method was applied to two types of VHR images with different urban settings, corresponding to a Pléiades-B image of Wuhan, China, and a Quickbird image of Enschede, the Netherlands. Experimental results show that the proposed method was able to group adjacent small segments that have high spectral heterogeneity and low road-like geometrical properties to form more meaningful roads sections, and performed superior to the existing methods. Furthermore, we compared the proposed method with two other existing methods in the literature. We conclude that the proposed method can provide an effective means for extracting roads over densely populated urban areas from VHR satellite images.

INTEGRATION OF BUILDING KNOWLEDGE INTO BINARY SPACE PARTITIONING FOR THE RECONSTRUCTION OF REGULARIZED BUILDING MODELS

Abstract. Recent approaches for the automatic reconstruction of 3D building models from airborne point cloud data integrate prior knowledge of roof shapes with the intention to improve the regularization of the resulting models without lessening the flexibility to generate all real-world occurring roof shapes. In this paper, we present a method to integrate building knowledge into the data-driven approach that uses binary space partitioning (BSP) for modeling the 3D building geometry. A retrospective regularization of polygons that emerge from the BSP tree is not without difficulty because it has to deal with the 2D BSP subdivision itself and the plane definitions of the resulting partition regions to ensure topological correctness. This is aggravated by the use of hyperplanes during the binary subdivision that often splits planar roof regions into several parts that are stored in different subtrees of the BSP tree. We therefore introduce the use of hyperpolylines in the generation of the BSP tree to avoid unnecessary spatial subdivisions, so that the spatial integrity of planar roof regions is better maintained. The hyperpolylines are shown to result from basic building roof knowledge that is extracted based on roof topology graphs. An adjustment of the underlying point segments ensures that the positions of the extracted hyperpolylines result in regularized 2D partitions as well as topologically correct 3D building models. The validity and limitations of the approach are demonstrated on real-world examples.

Framework for monitoring the conversion of cultivated land to construction land using SAR image time series

The land cover change from cultivated land to construction land is a world issue since the urbanization process is extensively studied around the world. Chengdu, China, is a representative urbanization area, where cloud cover is very high most of the time, restricting the use of visible and near-infrared satellite data. Here, we present a novel framework for land change monitoring based on synthetic aperture radar (SAR) time series, which comprises three key components: (1) construction of pixel-level SAR image time series; (2) spatio-temporal similarity analysis based on morphological-structural characteristics of time series; and (3) iterative binary partition mean square error model analysis to ascertain change nodes. Experimental results showed that the proposed framework could effectively extract the change nodes and change pixels, with correctness of 85.82% and completeness of 84.78%, outperforming the time-series-only (non-spatial) method, as well as traditional classification methods, and the same framework using shorter Landsat TM image time series.

Untangling crop management and environmental influences on wheat yield variability in Bangladesh: An application of non-parametric approaches

In South Asia, wheat is typically grown in favorable environments, although policies promoting intensification in Bangladesh's stress-prone coastal zone have resulted in expanded cultivation in this non-traditional area. Relatively little is known about how to best manage wheat in these unique environments. Research is thus needed to identify ‘best-bet’ entry points to optimize productivity, but classical parametric analyses offer limited applicability to elucidate the relative importance of the multiple factors and interactions that influence yield under such conditions. This problem is most evident in datasets derived from farmer-participatory research, where missing values and skewed data are common. This paper examines the predictive power of three non-parametric approaches, including linear mixed effects models (LMMs), and two binary recursive partitioning methods: classification and regression trees (CARTs) and Random Forests. We collected yield, crop management, and environmental observations from 422 wheat fields in the 2012–13 season, across six production environments spanning southern Bangladesh, where nutrient rates and genotypes were imposed, but management of other production factors varied from farmer to farmer. Fields were grouped into categories including early- and late-sowing, depending on crop establishment before or after December 15, respectively, and in combination, across both early- and late-sowing groups. For each of these groups, we investigated how each non-parametric analysis predicted the factors influencing yield. All three approaches identified nitrogen rate and environment as the most important factors, regardless of sowing category. CART also identified assemblages of high- and low-yielding environments, although those located in saline and warmer thermal zones were not necessarily the lowest yielding, indicating that farmers can optimize crop management to overcome these constraints. The number of days farmers sowed wheat before or after December 15, days to maturity, and the number of irrigations and weedings also influenced yield, though each method weighted these factors differently. LMMs also indicated a slight yield advantage when farmers used stress-tolerant genotypes, though CART and Random Forests did not. One-to-one plots for observed vs. predicted yields from LMMs and Random Forests showed better performance by the former than the latter, with smaller root mean square and mean absolute error for the combined, early- and late-sowing groups, respectively. While the LMMs were superior in this case, Random Forests may still prove useful in the classification and interpretation of farm survey data in which no treatment interventions have been administered.

Dexamethasone exerts profound immunologic interference on treatment efficacy for recurrent glioblastoma

Background:Patients with recurrent glioblastoma have a poor outcome. Data from the phase III registration trial comparing tumour-treating alternating electric fields (TTFields) vs chemotherapy provided a unique opportunity to study dexamethasone effects on patient outcome unencumbered by the confounding immune and myeloablative side effects of chemotherapy.Methods:Using an unsupervised binary partitioning algorithm, we segregated both cohorts of the trial based on the dexamethasone dose that yielded the greatest statistical difference in overall survival (OS). The results were validated in a separate cohort treated in a single institution with TTFields and their T lymphocytes were correlated with OS.Results:Patients who used dexamethasone doses >4.1 mg per day had a significant reduction in OS when compared with those who used ⩽4.1 mg per day, 4.8 vs 11.0 months respectively (χ2=34.6, P<0.0001) in the TTField-treated cohort and 6.0 vs 8.9 months respectively (χ2=10.0, P<0.0015) in the chemotherapy-treated cohort. In a single institution validation cohort treated with TTFields, the median OS of patients who used dexamethasone >4.1 mg per day was 3.2 months compared with those who used ⩽4.1 mg per day was 8.7 months (χ2=11.1, P=0.0009). There was a significant correlation between OS and T-lymphocyte counts.Conclusions:Dexamethasone exerted profound effects on both TTFields and chemotherapy efficacy resulting in lower patient OS. Therefore, global immunosuppression by dexamethasone likely interferes with immune functions that are necessary for the treatment of glioblastoma.

RANDOM HYPERPLANE SEARCH TREES IN HIGH DIMENSIONS

Given a set S of n ≥ d points in general position in R d , a random hyperplane split is obtained by sampling d points uniformly at random without replacement from S and splitting based on their affine hull. A random hyperplane search tree is a binary space partition tree obtained by recursive application of random hyperplane splits. We investigate the structural distributions of such random trees with a particular focus on the growth with d . A blessing of dimensionality arises—as d increases, random hyperplane splits more closely resemble perfectly balanced splits; in turn, random hyperplane search trees more closely resemble perfectly balanced binary search trees. We prove that, for any fixed dimension d , a random hyperplane search tree storing n points has height at most (1 + O (1/sqrt( d ))) log 2 n and average element depth at most (1 + O (1/ d )) log 2 n with high probability as n → ∞. Further, we show that these bounds are asymptotically optimal with respect to d .

An enhanced K-SP algorithm with pruning strategies to solve the constrained shortest path problem

We propose an exact method to solve the constrained shortest path (CSP) problem. The new approach takes advantage of the binary partition strategy of a recent K shortest paths (K-SP) algorithm that allows posing numerous additional path constraints in the model without extra difficulty. We adapt and incorporate several pruning strategies from the literature on the CSP problem in this scheme and obtain a robust and scalable algorithm. The method is compared with the current best algorithm to solve the CSP problem and produces significant speedups in a wide range of network configurations. An example is given where the CSP problem is solved in road networks containing a million nodes and arcs.

Supramolecular assemblies underpin turnover of outer membrane proteins in bacteria.

Gram-negative bacteria inhabit a broad range of ecological niches. For Escherichia coli, this includes river water as well as humans and animals where it can be both a commensal and a pathogen1–3. Intricate regulatory mechanisms ensure bacteria have the right complement of β-barrel outer membrane proteins (OMPs) to enable adaptation to a particular habitat4,5. Yet no mechanism is known for replacing OMPs in the outer membrane (OM), a biological enigma further confounded by the lack of an energy source and the high stability6 and abundance of OMPs5. Here, we uncover the process underpinning OMP turnover in E. coli and show it to be passive and binary in nature wherein old OMPs are displaced to the poles of growing cells as new OMPs take their place. Using fluorescent colicins as OMP-specific probes, in combination with ensemble and single-molecule fluorescence microscopy in vivo and in vitro, as well as molecular dynamics (MD) simulations, we established the mechanism for binary OMP partitioning. OMPs clustered to form islands of ~0.5 μm diameter where their diffusion was restricted by promiscuous interactions with other OMPs. OMP islands were distributed throughout the cell and contained the Bam complex, which catalyses the insertion of OMPs in the OM7,8. However, OMP biogenesis occurred as a gradient that was highest at mid-cell but largely absent at cell poles. The cumulative effect is to push old OMP islands towards the poles of growing cells, leading to a binary distribution when cells divide. Hence the OM of a Gram-negative bacterium is a spatially and temporally organised structure and this organisation lies at the heart of how OMPs are turned over in the membrane.

Partitioned Shadow Volumes

AbstractReal‐time shadows remain a challenging problem in computer graphics. In this context, shadow algorithms generally rely either on shadow mapping or shadow volumes. This paper rediscovers an old class of algorithms that build a binary space partition over the shadow volumes. For almost 20 years, such methods have received little attention as they have been considered lacking of both robustness and efficiency. We show that these issues can be overcome, leading to a simple and robust shadow algorithm. Hence we demonstrate that this kind of approach can reach a high level of performance. Our algorithm uses a new partitioning strategy which avoids any polygon clipping. It relies on a Ternary Object Partitioning tree, a new data structure used to find if an image point is shadowed. Our method works on a triangle soup and its memory footprint is fixed. Our experiments show that it is efficient and robust, including for finely tessellated models.

Technical Framework of Feature Extraction Based on Pixel-Level SAR Image Time Series

This study proposes a novel technical framework of feature extraction based on pixel-level synthetic aperture radar (SAR) image time series, to exploit the application potential of SAR image data with low and medium spatial resolution. This framework comprises three key parts: 1) construction of the pixel-level SAR image time series using a new matching technique based on progressive binary partition; 2) pixel-level similarity measurement via dynamic time warping (DTW); and 3) a new spatiotemporal similarity analysis method that improves feature extraction by considering both the similarity of a feature’s pixel-level time series and its spatial correlation. Two locations, covered by 31 low-resolution (150 m) and 26 medium-resolution (30 m) ENVISAT ASAR images, respectively, were selected as test cases to validate the proposed framework. Results show that the framework can identify features with a high level of accuracy, completeness, and correctness, outperforming methods using multitemporal images, as well as the time series-only (nonspatial) method, and other methods of spatiotemporal similarity analysis that use alternative similarity measures.

Distribution of invasive and native riparian woody plants across the western USA in relation to climate, river flow, floodplain geometry and patterns of introduction

Management of riparian plant invasions across the landscape requires understanding the combined influence of climate, hydrology, geologic constraints and patterns of introduction. We measured abundance of nine riparian woody taxa at 456 stream gages across the western USA. We constructed conditional inference recursive binary partitioning models to discriminate the influence of eleven environmental variables on plant occurrence and abundance, focusing on the two most abundant non‐native taxa, Tamarix spp. and Elaeagnus angustifolia, and their native competitor Populus deltoides. River reaches in this study were distributed along a composite gradient from cooler, wetter higher‐elevation reaches with higher stream power and earlier snowmelt flood peaks to warmer, drier lower‐elevation reaches with lower power and later peaks. Plant distributions were strongly related to climate, hydrologic and geomorphic factors, and introduction history. The strongest associations were with temperature and then precipitation. Among hydrologic and geomorphic variables, stream power, peak flow timing and 10‐yr flood magnitude had stronger associations than did peak flow predictability, low‐flow magnitude, mean annual flow and channel confinement. Nearby intentional planting of Elaeagnus was the best predictor of its occurrence, but planting of Tamarix was rare. Higher temperatures were associated with greater abundance of Tamarix relative to P. deltoides, and greater abundance of P. deltoides relative to Elaeagnus. Populus deltoides abundance was more strongly related to peak flow timing than was that of Elaeagnus or Tamarix. Higher stream power and larger 10‐yr floods were associated with greater abundance of P. deltoides and Tamarix relative to Elaeagnus. Therefore, increases in temperature could increase abundance of Tamarix and decrease that of Elaeagnus relative to P. deltoides, changes in peak flow timing caused by climate change or dam operations could increase abundance of both invasive taxa, and dam‐induced reductions in flood peaks could increase abundance of Elaeagnus relative to Tamarix and P. deltoides.