Statistical Modeling Methods Research Articles

Selection of aerodynamic characteristics and engine parameters of a maneuverable aircraft under epistemic uncertainty

At the preliminary stage of aircraft design, it is usually required to solve the problem of insufficient initial data for applying traditional algoristic-type mathematical programming models. In many cases, numerous input parameters cannot be accurately specified at the time of making design decisions. If the inaccuracy of parameters is not taken into account, the actual values of target functions may differ significantly from the calculated ones when solving optimization problems. In this regard, the issue of current interest is the development of algorithms to improve the reliability of design decisions under conditions of epistemological uncertainty when experts engage in the formation of initial data. The paper considers the problem of selecting aerodynamic characteristics and engine parameters of maneuverable aircraft under conditions of uncertainty associated with inaccuracy of expert data. The applied problem under consideration is further complicated by the necessity to include “black box” models in the algorithms being developed. The paper proposes algorithms that apply the uncertainty theory together with “black box” models that implement optimization calculation techniques derived from previous engineering practice of aircraft design. Using these algorithms, experts are able to set uncertain parameters whereby the lack of data is factored in using uncertainty distribution functions. In cases of monotonicity of uncertain parameters in target functions, application of the uncertainty theory provides a significant reduction in computational costs compared to the method of statistical modeling in optimization calculations. The paper presents the results of computational studies of the developed algorithms. A genetic algorithm (mathematical optimization solver) is used to optimize the search for design solutions. Pareto frontiers are obtained for different confidence levels enabling to make design decisions including values of aerodynamic characteristics and engine parameters of maneuverable aircraft.

Estimation of the Service Life of Approach Slabs of Road Bridges Based on the Statistical Modeling Method

The article discusses the durability and reliability of a separate element – bridge approach slab, which is justified by the need to maintain a satisfactory technical condition of Ukrainian bridges in general and traffic safety on public roads with limited funding during martial law. The scope of the research is forecasting the residual service life of bridge elements (on the example of approach slabs) using probabilistic methods. Approach slabs are designed to smoothly and safely connect the road approach embankment with the bridge to gradually equalize the elastic modulus of the carriageway from a less rigid asphalt pavement on an elastic base to a more rigid one on a reinforced concrete slab. The main defects in the destruction of approach slabs are: changes in the longitudinal profile of the road due to the collapse and subsidence of the soil under the approach slabs; longitudinal and transverse cracks in the asphalt concrete pavement on the bridge approaches; and potholes that lead to an increase in the additional dynamic load on the bridge deck.

Comparing performances of different statistical models and multiple threshold methods in a nested association mapping population of wheat.

Nested association mapping (NAM) populations emerged as a multi-parental strategy that combines the high statistical power of biparental linkage mapping with greater allelic richness of association mapping. Several statistical models have been developed for marker-trait associations (MTAs) in genome-wide association studies (GWAS), which ranges from simple to increasingly complex models. These statistical models vary in their performance for detecting real association with the avoidance of false positives and false negatives. Furthermore, significant threshold methods play an equally important role for controlling spurious associations. In this study, we compared the performance of seven different statistical models ranging from single to multi-locus models on eight different simulated traits with varied genetic architecture for a NAM population of spring wheat (Triticum aestivum L.). The best identified model was further used to identify MTAs for 11 different agronomic and spectral reflectance traits, which were collected on the NAM population between 2014 and 2016. The "Bayesian information and linkage disequilibrium iteratively nested keyway (BLINK)" model performed better than all other models observed based on QQ plots and detection of real association in a simulated data set. The results from model comparison suggest that BLINK controls both false positives and false negatives under the different genetic architecture of simulated traits. Comparison of multiple significant threshold methods suggests that Bonferroni correction performed superior for controlling false positives and false negatives and complements the performance of GWAS models. BLINK identified 45 MTAs using Bonferroni correction of 0.05 for 11 different phenotypic traits in the NAM population. This study helps identify the best statistical model and significant threshold method for performing association analysis in subsequent NAM population studies.

Повышение ВРП экономики Иркутской области на основе роста уровня энергетической эффективности регионального промышленного комплекса

Energy efficiency of fuel and energy consumption is an important indicator of regional economy. The article provides an empirical study of electricity consumption, gross regional product, and electricity consumption per capita in Russia’s regions in 2021. The analysis focused on the role of the Irkutsk Region in the development of Russia’s energy balance and economy. The authors mapped the electric intensity as part of gross regional product and found out that it is very low in the Irkutsk Region, despite the fact that this region is one of the largest consumers of electricity in Russia. The analysis revealed a national need for a better theoretical basis in energy efficiency. The research featured the increase in economic indicators of the Irkutsk Region in conditions of leveling the regional energy efficiency to average indicators. The authors used the methods of statistical research, expert assessments, modeling, and forecasting. They analyzed electric intensity by type of economic activity in various regions of the Siberian Federal District. As a result, they associated the low electric intensity of the gross regional product in Irkutsk with its industrial sector, which uses a lot of electricity and provides a significant share of the gross regional product. They modelled some changes in the volumes of Irkutsk’s gross regional product with an increase in energy efficiency in the industrial power consumption sector. As a result, the gross regional product increased by 57%, rising from 1,268 billion rubles to 2,000 billion rubles. The result was achieved by an increase in the industrial sector from 494 billion rubles to 1,226 billion rubles.

Enhancing Manufacturing Processing Stability and Efficiency with Linear-Regression Analysis: Modeling on a Flow-Drill Screw (FDS) Joining Process

The instability (in processing time) in the flow-drill screwing process is undesired but inescapable due to variations in material property, gauge, and process parameters. A substantial number of materials and lab labor need to be used to test and control the variability of the real manufacturing joining process. To enhance the stability and efficiency of the screwing process, this study seeks multi-disciplinary collaboration by applying linear-regression modeling. Six hundred and forty-eight data points were collected and split into an 80% training set for model building and a 20% test set for model validation. A multiple linear-regression model was built. The results indicated that, compared to variable base level (6000 rpm rotational speed and 1100 N downforce), higher rotational speed (8000 rpm, 7000 rpm), greater downforce (1200 N, 1300 N), and their interaction were significantly associated with passage (processing) time, while the switch point did not significantly affect passage time. The interaction plot and effect size were adopted to provide measurements of the effect magnitude on processing time. The coefficient of determination indicated that 86% of the variability in the passage time can be explained by this model. Statistical analysis, such as data visualization, statistical modeling, and other data-driven analysis methods, can be used to detect underlying relationships between variables, investigate variations, and make predictions in the manufacturing process. The outcomes from the data-driven analysis can benefit from improving the economical manufacturing system, refining the processing setting, and reducing test material costs, labor, and lead time.

Ada-XG-CatBoost: A Combined Forecasting Model for Gross Ecosystem Product (GEP) Prediction

The degradation of the ecosystem and the loss of natural capital have seriously threatened the sustainable development of human society and economy. Currently, most research on Gross Ecosystem Product (GEP) is based on statistical modeling methods, which face challenges such as high modeling difficulty, high costs, and inaccurate quantitative methods. However, machine learning models are characterized by high efficiency, fewer parameters, and higher accuracy. Despite these advantages, their application in GEP research is not widespread, particularly in the area of combined machine learning models. This paper includes both a GEP combination model and an explanatory analysis model. This paper is the first to propose a combined GEP prediction model called Ada-XGBoost-CatBoost (Ada-XG-CatBoost), which integrates the Extreme Gradient Boosting (XGBoost), Categorical Boosting (CatBoost) algorithms, and SHapley Additive exPlanations (SHAP) model. This approach overcomes the limitations of single-model evaluations and aims to address the current issues of inaccurate and incomplete GEP assessments. It provides new guidance and methods for enhancing the value of ecosystem services and achieving regional sustainable development. Based on the actual ecological data of a national city, data preprocessing and feature correlation analysis are carried out using XGBoost and CatBoost algorithms, AdaGrad optimization algorithm, and the Bayesian hyperparameter optimization method. By selecting the 11 factors that predominantly influence GEP, training the model using these selected feature datasets, and optimizing the Bayesian parameters, the error gradient is then updated to adjust the weights, achieving a combination model that minimizes errors. This approach reduces the risk of overfitting in individual models and enhances the predictive accuracy and interpretability of the model. The results indicate that the mean squared error (MSE) of the Ada-XG-CatBoost model is reduced by 65% and 70% compared to the XGBoost and CatBoost, respectively. Additionally, the mean absolute error (MAE) is reduced by 4.1% and 42.6%, respectively. Overall, the Ada-XG-CatBoost combination model has a more accurate and stable predictive performance, providing a more accurate, efficient, and reliable reference for the sustainable development of the ecological industry.

Machine Learning versus Cox Models for Predicting Overall Survival in Patients with Osteosarcoma: A Retrospective Analysis of the EURAMOS-1 Clinical Trial Data.

Since the mid-1980s, there has been little progress in improving survival of patients diagnosed with osteosarcoma. Survival prediction models play a key role in clinical decision-making, guiding healthcare professionals in tailoring treatment strategies based on individual patient risks. The increasing interest of the medical community in using machine learning (ML) for predicting survival has sparked an ongoing debate on the value of ML techniques versus more traditional statistical modelling (SM) approaches. This study investigates the use of SM versus ML methods in predicting overall survival (OS) using osteosarcoma data from the EURAMOS-1 clinical trial (NCT00134030). The well-established Cox proportional hazard model is compared to the extended Cox model that includes time-varying effects, and to the ML methods random survival forests and survival neural networks. The impact of eight variables on OS predictions is explored. Results are compared on different model performance metrics, variable importance, and patient-specific predictions. The article provides comprehensive insights to aid healthcare researchers in evaluating diverse survival prediction models for low-dimensional clinical data.

Reinforcement learning for occupant behavior modeling in public buildings: Why, what and how?

Effective control of energy consumption in public buildings holds paramount significance for global sustainable development. However, uncertainty in occupant behavior during operational phase often leads to a substantial discrepancy between the designed and actual energy consumption. While there is existing research on occupant behavior in public buildings utilizing stochastic modeling, statistical modeling, data mining, and agent-based modeling methods, the connotations and formation mechanisms have not been systematically revealed, rendering these developed models weak in applicability and reliability in practical scenarios. Reinforcement learning, which can perceive aspects of external environment and learn from stochastic interactions spontaneously, has been distinguished as a promising method for occupant behavior modeling. This research aims to develop a paradigm for reinforcement learning application in occupant behavior modeling in public buildings. Semi-structured interviews and literature review were combined to collect relevant information, while reasons for using reinforcement learning and applicable algorithms were discerned through qualitative analysis. Finally, detailed frameworks were proposed and validated through focus groups, offering a comprehensive guide that will serve as a reference for future research. This includes steps for collecting occupant-related data, selecting appropriate algorithms, and training and deploying reinforcement learning agents effectively. This research innovatively proposed a “panorama” of reinforcement learning for occupant behavior modeling in public buildings, laying a solid foundation for indoor environment and energy efficiency improvement in public building operations.

Advanced statistical methods for hazard modeling in cardiothoracic surgery: a comprehensive review of techniques and approaches.

Hazard modeling in cardiothoracic surgery, crucial for understanding patient outcomes, utilizes survival analysis like the Cox proportional hazards model. Kaplan-Meier curves are employed in survival analysis to represent the probability of survival over time. While Cox assumes proportional hazards, the Fine-Gray model deals with competing risks. Parametric models (e.g., Weibull) specify survival distributions, unlike Cox. Bayesian analysis integrates prior knowledge with data. Machine learning, including decision trees and support vector machines, enhances risk prediction by analyzing extensive datasets. However, it is important to note that whatever new approaches one may adopt will enhance the quality of risk assessment and not the risk assessment as such. Preprocessing is vital for data quality in complex cardiovascular datasets, alongside robust validation methods like cross-validation for model reliability across patient cohorts.

Singularities of Diffuse Wave Fields in Scattering Media with Refractive Index Gradients

The subject of this paper is the radiative transfer in media with gradients of the refractive index. Asymptotic expressions of the intensity distributions in the vicinity of singular directions are derived. Critical conditions for the appearance of singular intensity distributions in fields of scattered radiation in a medium are formulated. It is shown that singular radiation fields in such media can be generated, among other things, by non-singular configurations of radiation sources. The obtained results are verified by direct comparison with the results of numerical calculations using the Monte Carlo statistical modeling method.

Simulating Climatic Patterns and Their Impacts on the Food Security Stability System in Jammu, Kashmir and Adjoining Regions, India

This study investigated the historical climate data and future projections under the SSP5-8.5 scenario for Jammu, Kashmir (J&K), and its adjoining regions in India. Agriculture is a critical economic pillar of this region, making it highly vulnerable to climate change. This study focused on temperature and precipitation trends. Statistical analysis and modeling methods, including cloud computing, were employed to predict changes and assess their impact on agricultural productivity and water resources. The results indicated that by 2100, the mean maximum and minimum temperatures are projected to increase by approximately 2.90 °C and 2.86 °C, respectively. Precipitation variability is expected to rise, with a mean increase of 2.64 × 10−6 mm per day. These changes have significant consequences for crop yield, water stress, and ecosystem dynamics. An analysis of Gross Primary Productivity (GPP) as a proxy for agricultural productivity using linear regression revealed a concerning trend. Although the total GPP of the study area remained stable over time, it declined by −570 g yr−1 in 2010, coinciding with a 1 °C temperature rise. Projections based on the expected 3 °C temperature increase by 2100 suggest a total GPP loss of −2500 g yr−1. These findings highlight the urgent need for proactive adaptation measures, including sustainable agricultural practices, improved water management, and enhanced socioeconomic infrastructure, to mitigate the impact of climate change and ensure long-term resilience and food security in the region.

Algorithm for Assessing the Characteristics of a Waveguide Slot Antenna Array when Changing Antenna Element Phasing

Introduction. When operating antennas in various radio-electronic systems, the influence of phase shifter (PS) failures on the characteristics of phased array antennas, waveguide-slot phased array antennas (WSPAA) in particular, should be taken into account. A review of publications shows a lack of research studies into failures of these elements.Aim. Research of WSPAA characteristics in the event of PS failures, when their phase takes a value equal to zero instead of the required value.Materials and methods. Statistical modeling methods were used to study the impact of PS failures on WSPAA characteristics. Calculations were carried out using a PC and the Mathcad 15 applied mathematics package.Results. An algorithm for statistical modeling of the impact of PS failures on WSPAA characteristics is proposed. A relationship that connects the radiation pattern with the statistical sample volume and the number of failed PSs is presented. Malfunctions of emitters from 5 to 35 out of 50 elements were investigated. Changes in the following characteristics were obtained: standard deviation - from 0.064 to 0.18; relative values: radiation pattern width - from 8 to 18 %; level of side lobes - from 13 to 59 %; radiation power - from 0.9 to 0.3.Conclusion. The results obtained can be generalized and used in radio-electronic systems with antenna arrays at the stage of their development. Future work will address the influence of PS failures with phases being established randomly and with random values, as well as PS failures in which power does not pass into the emitter. Another important area concerns compensation of distortions resulting from failures of antenna elements.

DriverDetector: An R package providing multiple statistical methods for cancer driver genes detection and tools for downstream analysis

Identifying driver genes in cancer is a difficult task because of the heterogeneity of cancer as well as the complex interactions among genes. As sequencing data become more readily available, there is a growing need for detecting cancer driver genes based on statistical and mathematical modeling methods. Currently, plenty of driver gene identification algorithms have been published, but they fail to achieve consistent results. In order to obtain gene sets with high confidence, we present DriverDetector, an R package providing a convenient workflow for cancer driver genes detection and downstream analysis. We develop the background mutation rate calculating module based on the distance between genes in covariate space and binomial test, followed by the driver gene selection module which integrates 11 methods, including two already recognized approaches, a de novo method, and five variants of Fisher's method which are applied to driver gene identification for the first time. Through verification on 12 TCGA datasets, each method is able to identify a set of confirmed driver genes while the number of resulting genes vary significantly across different methods. For robust driver genes detection, a voting strategy based on 10 of the statistical methods is further applied. Results show that the collective prediction based on the voting strategy demonstrates superiority in achieving the consistency of prediction while ensuring a reasonable number of predicted genes and confirmed drivers. By comparing the results of each cancer dataset, we also find that sample size has a huge impact on the number of predicted genes. For downstream analysis, DriverDetector automatically generates plenty of plots and tables to elaborate the results. We propose DriverDetector as a user-friendly tool promoting early diagnosis of cancer and the development of targeted drugs.

Statistical modeling of 3D fiber geometry in pultruded GFRP composite: A multi-scale approach

The fiber geometry is a crucial determinant of the fiber reinforced polymer composites’ mechanical properties. Specifically, the manufacturing process of stretching and gradual curving in pultruded composites invariably results in complex 3D fiber geometries. Despite its significance, there is still lacking a statistical method to accurately describe these spatially curved fiber shapes. This paper presents a novel multi-scale mathematical approach for modeling the complex 3D fiber geometry in pultruded glass fiber reinforced polymer (GFRP) composites, which includes the analysis of fiber misalignment and waviness at two scales. At the mesoscopic level, a modified elliptical symmetry angular Gaussian (ESAG) model effectively characterizes the fiber misalignment. Simultaneously, at the micro scale, a cosine series representation is employed for capturing local fiber waviness. The approach is verified with XCT scanning results of pultruded GFRP specimens. The current statistical modeling method provides a multi-scale approach for geometry analysis and further simulation of pultruded composite materials.

Using lifestyle information in polygenic modeling of blood pressure traits: a simple method to reduce bias.

Complex traits are determined by the effects of multiple genetic variants, multiple environmental factors, and potentially their interaction. Predicting complex trait phenotypes from genotypes is a fundamental task in quantitative genetics that was pioneered in agricultural breeding for selection purposes. However, it has recently become important in human genetics. While prediction accuracy for some human complex traits is appreciable, this remains low for most traits. A promising way to improve prediction accuracy is by including not only genetic information but also environmental information in prediction models. However, environmental factors can, in turn, be genetically determined. This phenomenon gives rise to a correlation between the genetic and environmental components of the phenotype, which violates the assumption of independence between the genetic and environmental components of most statistical methods for polygenic modeling. In this work, we investigated the impact of including 27 lifestyle variables as well as genotype information (and their interaction) for predicting diastolic blood pressure, systolic blood pressure, and pulse pressure in older individuals in UK Biobank. The 27 lifestyle variables were included as either raw variables or adjusted by genetic and other non-genetic factors. The results show that including both lifestyle and genetic data improved prediction accuracy compared to using either piece of information alone. Both prediction accuracy and bias can improve substantially for some traits when the models account for the lifestyle variables after their proper adjustment. Our work confirms the utility of including environmental information in polygenic models of complex traits and highlights the importance of proper handling of the environmental variables.

ОПТИМІЗАЦІЯ ТЕМПЕРАТУРИ ПРИГОТУВАННЯ, ВМІСТУ ЕНЕРГОЗБЕРІГАЮЧОЇ ДОБАВКИ ТА АСФАЛЬТОБЕТОННОЇ КРИХТИ ПІД ЧАС ВИГОТОВЛЕННЯ ТЕПЛИХ АСФАЛЬТОБЕТОННИХ СУМІШЕЙ

Introduction. The article investigates the effect of the preparation temperature, the amount of energy-saving additive and the amount of asphalt crumb on the physical and mechanical properties of warm asphalt mixtures. The method of experimental and statistical modeling was used in the study, and mathematical models describing the dependence of water saturation and compressive strength of asphalt concrete were developed. Based on the analysis of the results obtained, the areas of optimal values of the preparation temperature, the amount of energy-saving additive, and the amount of asphalt crumb during the production of warm asphalt mixtures were determined. In this case, the resulting mixture meets the standard requirements for hot fine-grained asphalt mixtures in terms of physical and mechanical properties. Problem statement. Studies by the authors of [1] have shown that when preparing an asphalt mixture, it is very important to take into account changes in the properties of bitumen, which is the main component that characterizes the behavior of asphalt concrete. In the preparation of warm asphalt mixtures, it is advisable to use energy-saving additives, the introduction of which provides relatively new chemical effects that improve the workability, mobility and energy saving of mixtures made at lower temperatures than traditional hot mixtures. At the same time, due to the large number of different types of additives, there is no accurate quantitative data on the dependence of asphalt concrete properties on the content of additives at different amounts of bitumen for different types of asphalt mixtures.

Classification of Fall Out Boy Eras

This paper explored the use of machine learning techniques to differentiate between two different musical eras of the same rock band, including the technique of Logistic Regression. Logistic regression (LR) is a widely used statistical modeling method for binary classification in supervised machine learning. It is often used to predict whether a given event belongs to one of two categories. The process helps data scientists understand which variables are good predictors of class membership. Applications of logistic regression include loan classification in the financial industry and predicting susceptibility to disease in the medical field. In this particular project, a dataset was constructed using data from Spotify and Genius consisting of songs and lyrics written by the band Fall Out Boy. A logistic regression model was developed from scratch to classify the songs and lyrics into one of two eras of the band: before their 2009 hiatus and afterward. The study aimed to determine if a computer could differentiate between the two eras. The model was also tested against other binary classification algorithms, including Random Forest and Support Vector Machines.

Analysis of the situations and influencing factors of public anxiety in China: based on Baidu index data.

Anxiety disorders have emerged as one of the most prevalent mental health problems and health concerns. However, previous research has paid limited attention to measuring public anxiety from a broader perspective. Furthermore, while we know many factors that influence anxiety disorders, we still have an incomplete understanding of how these factors affect public anxiety. We aimed to quantify public anxiety from the perspective of Internet searches, and to analyze its spatiotemporal changing characteristics and influencing factors. This study collected Baidu Index from 2014 to 2022 in 31 provinces in mainland China to measure the degree of public anxiety based on the Baidu Index from 2014 to 2022. The spatial autocorrelation analysis method was used to study the changing trends and spatial distribution characteristics of public anxiety. The influencing factors of public anxiety were studied using spatial statistical modeling methods. Empirical analysis shows that the level of public anxiety in my country has continued to rise in recent years, with significant spatial clustering characteristics, especially in the eastern and central-southern regions. In addition, we constructed ordinary least squares (OLS) and geographically weighted regression (GWR) spatial statistical models to examine the relationship between social, economic, and environmental factors and public anxiety levels. We found that the GWR model that considers spatial correlation and dependence is significantly better than the OLS model in terms of fitting accuracy. Factors such as the number of college graduates, Internet traffic, and urbanization rate are significantly positively correlated with the level of public anxiety. Our research results draw attention to public anxiety among policymakers, highlighting the necessity for a more extensive examination of anxiety issues, especially among university graduates, by the public and relevant authorities.

Recent advances on mechanisms of network generation: Community, exchangeability, and scale‐free properties

AbstractThe mechanisms of network generation have undergone extensive analysis and found broad applications in various real‐world scenarios. Among the fruitful literature on network models, numerous studies seek to explore and interpret fundamental graph structure properties, including the clustering effect, exchangeability, and scale‐free properties. In this paper, we present a comprehensive review of the statistical modeling methods for the mechanisms of network generation. We specifically focus on three representative classes of models, namely the stochastic block models, the exchangeable network models, and the preferential attachment models. For each model type, our approach begins by reviewing existing methods and model setups, followed by an exploration of the core modeling principles behind them. We also summarize relevant statistical inference techniques and provide a unified understanding of theoretical analyses. Furthermore, we emphasize several challenges and open problems that could shed light on future research. We conclude this review with the identification of some possible directions for future study.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms Algorithms and Computational Methods > Networks and Security

Research into the Impact of Phase Shifter Failures on the Characteristics of Slotted Waveguide Array Antenna

Introduction. Currently, the impact of phase shifter (PS) failures on the characteristics of phased antenna arrays, slotted waveguide array antenna (SWAA) in particular, represents a significant problem. A review of publications shows that insufficient attention has been paid to PS failures.Aim. To investigate the characteristics of a SWAA in the event of PS failures, when their phase takes a value equal to zero instead of the required value.Materials and methods. The methods of statistical modeling methods were used to study the impact of failures on SWA characteristics. Calculations were carried using the Mathcad 15 software package.Results. An algorithm for statistical modeling of the impact of PS failures on SWAA characteristics is proposed. A relationship that connects the radiation pattern with the volume of the statistical sample and the number of failed PSs is given. The malfunctions of emitters from 5 to 35 out of 50 elements were studied. Changes in the following characteristics were obtained: standard deviation – from 0.064 to 0.18, radiation pattern width – from 8 to 18 %, the level of side lobes – from 13 to 59 %, radiation power – from 0.9 to 0.3.Conclusion. The results obtained can be used in radio-electronic systems with antenna arrays at the stage of their development. Future work will address PS failures with phases being established randomly and with random values, as well as the case of PS failures where power does not pass into the emitter. Another important direction concerns compensation of distortions resulting from failures of antenna elements.