Small Deviations Research Articles

Comment on “Modeling groundwater flow with random hydraulic conductivity using radial basis function partition of unity method” by Shile et al. (2024)

The goal of this article is to explain some striking discrepancies between the Monte Carlo inferences for flow in heterogeneous aquifers presented in (Shile et al., 2024) and reliable and verifiable results previously published. Comparisons with statistical inferences done within the same numerical setup and using the same benchmark codes demonstrate that quantifiable aspects, such as a too small departure from the linear theory and the decrease of the standard deviations with the increase of the aquifer heterogeneity, cannot be produced with the tools used by the authors.

Critical physics-informed fatigue life prediction of laser 3D printed AlSi10Mg alloys with mass internal defects

The significant scatter in high cycle fatigue life of additively manufactured metallic components presents an increasing challenge to structural integrity. This fatigue life variation is radically attributed to the differences in physical features of critical defects that lead to crack initiation. To address this issue, this paper proposes an integrated framework for identifying critical defects and predicting fatigue life using physics-informed machine learning, with a focus on the impact of 3D defect features. By employing X-ray tomography, high cycle fatigue tests, and fractography analyses on post-mortem specimens, a dataset associated with mass internal defects is first built up to correlate the spatial geometric features of critical defects with fatigue life. A kernel support vector machine is then used to formulate a critical defect identification model, aimed at identifying critical defects among numerous defects by evaluating their geometric attributes. Finally, a fatigue life prediction model is developed using a physics-informed neural network, which incorporates the influence of defect geometry on fatigue life as physical constraints in the loss function. The integrated framework demonstrates that fatigue life predictions from identified critical defects in each specimen exhibit small deviations, with the average prediction falling within twice the error bands. This study is expected to provide a valuable reference for fatigue assessment of additively manufactured components through sequential critical defect identification and fatigue life prediction.

The analysis of Hermite factor of BKZ algorithm on small lattices

Lattice cryptography is one of the promising directions in modern cryptography research. Digital signatures and key encapsulation mechanisms on lattices have already been used in practice. In the future, such quantum-resistant transformations on lattices replace all standards that are not resistant to attacks on quantum computers. This makes the analysis of their security extremely relevant. Analysis of the security of cryptographic transformations on lattices is often reduced to the estimation of the minimum block size in the lattice reduction algorithm. For the expansion of small vectors, a reduction algorithm can be obtained for a given block size, the GSA model is often used, which uses the so-called Hermitian factor to predict the size of the vectors that the lattice reduction algorithm can obtain given the parameters. Asymptotic formulas have been developed to evaluate it in practice, but the question of their accuracy on cryptographic lattices has not been fully investigated. The work obtained estimates of the accuracy of the existing asymptotic estimates of the Hermite factor for lattices of sizes 120, 145, 170 for the classical BKZ algorithm. Research was conducted using the fpylll library. It was shown that the existing estimators are equivalent from a practical point of view and have a sufficiently small root mean square deviation from the true values. A formula was obtained that binds the root-mean-square error of approximation of the Hermit factor to the cryptographic parameters of lattices. The obtained results are useful for refining the security assessments of existing cryptographic transformations.

Vibroscope method for determination of cross-sectional area of glass and carbon fibres – Theory and further development

Accurate determination of cross-sectional area of glass and carbon fibres by the vibroscope method is examined. Complete derivations of the central frequency solutions are presented, to make these derivations accessible in modern scientific literature. The effect of non-zero bending stiffness is included. The influence of shape of fibre cross-sectional area is analysed. Only small deviations in cross-sectional areas are found due to fibre shape, allowing for the use of the vibroscope method for fibres with non-circular cross-sectional areas. Two correction factors are introduced for the effect of volume change and area change of a tensioned fibre, allowing determination of the cross-sectional area of the non-tensioned fibre. A model plot of the vibroscope equation is presented, showing the numerical effect of the corrections on the fibre cross-sectional area depending on the applied tension force. The relations shown by the model plot have implications for the experimental settings of the vibroscope method.

Non-differential misclassification of outcome under (near)-perfect specificity: a simulation study.

Mismeasurement of a dichotomous outcome yields an unbiased risk ratio estimate when there are no false positive cases (perfect specificity) and when sensitivity is non-differential with respect to exposure status. In studies where these conditions are expected, quantitative bias analysis may be considered unnecessary. We conducted a simulation study to explore the robustness of this special case to small departures from perfect specificity and stochastic departures from non-differential sensitivity. We observed substantial bias of the risk ratio with specificity values as high at 99.8%. The magnitude of bias increased directly with the true underlying risk ratio and was markedly stronger at lower baseline risk. Stochastic departure from non-differential sensitivity also resulted in substantial bias in most simulated scenarios; downward bias prevailed when sensitivity was higher among unexposed compared with exposed, and upward bias prevailed when sensitivity was higher among exposed compared with unexposed. Our results show that seemingly innocuous departures from perfect specificity (e.g., 0.2%) and from non-differential sensitivity can yield substantial bias of the risk ratio under outcome misclassification. We present a web tool permitting easy exploration of this bias mechanism under user-specifiable study scenarios.

Using markerless motion capture and musculoskeletal models: An evaluation of joint kinematics.

This study presents a comprehensive comparison between a marker-based motion capture system (MMC) and a video-based motion capture system (VMC) in the context of kinematic analysis using musculoskeletal models. Focusing on joint angles, the study aimed to evaluate the accuracy of VMC as a viable alternative for biomechanical research. Eighteen healthy subjects performed isolated movements with 17 joint degrees of freedom, and their kinematic data were collected using both an MMC and a VMC setup. The kinematic data were entered into the AnyBody Modelling System, which enables the calculation of joint angles. The mean absolute error (MAE) was calculated to quantify the deviations between the two systems. The results showed good agreement between VMC and MMC at several joint angles. In particular, the shoulder, hip and knee joints showed small deviations in kinematics with MAE values of 4.8∘, 6.8∘ and 3.5∘, respectively. However, the study revealed problems in tracking hand and elbow movements, resulting in higher MAE values of 13.7∘ and 27.7∘. Deviations were also higher for head and thoracic movements. Overall, VMC showed promising results for lower body and shoulder kinematics. However, the tracking of the wrist and pelvis still needs to be refined. The research results provide a basis for further investigations that promote the fusion of VMC and musculoskeletal models.

A novel method for gas-solid contact visualization and efficiency quantification in dry fixed-bed desulfurization

A novel method for the visualization of gas–solid contact states and the quantitative evaluation of contact efficiency in the dry fixed-bed desulfurization process is proposed in this study. This method utilizes the chromogenic properties of phenolphthalein (PP) on the surfaces of various sodium salt products during the sodium bicarbonate dry desulfurization process, enabling visualization of gas–solid contact status. Samples of desulfurization products are photographed, and ImageJ software is employed for image processing to calculate color residual rates, thereby quantifying gas–solid contact efficiency. The specific operating conditions that produced the best visualization effect of gas–solid contact states were determined through experimentation, including: an appropriate PP solid content of ≤ 0.336 % for ultrafine NaHCO3 with D90 = 6.14 μm; a steam volume ratio of approximately 13.94 % to 24.46 %, a temperature inside the reactor of 110 °C–175 °C. Moreover, the fading effect of the indicative sodium-based absorbent was consistent across SO2 concentrations from 850 mg/m3 to 5100 mg/m3, with higher concentrations reducing the time needed for visualizing gas–solid contact and quantifying efficiency. The gas–solid contact efficiency (Egs = 87.85 %) calculated by the method showed a small deviation of only 0.55 % from the efficiency (E’gs = 88.4 %) calculated based on sulfur capacity, validating the method’s reliability. The study’s outcomes present a novel method for analyzing the gas–solid contact state, which can serve future efforts in the design optimization of dry fixed-bed desulfurization reactors.

MINIMIZING TEMPERATURE DEVIATIONS IN RUBBER MIXING PROCESS BY USING ARTIFICIAL NEURAL NETWORKS

ABSTRACT Rubber mixing is a complex manufacturing process that poses challenges for process control due to the high number of control variables, including mixing parameter settings, rheological behavior, compound viscosity, and batch-dependent material variations. Already small deviations from the control variables can influence the compound properties, leading to increased scrap rates. To address these challenges, this paper introduces an artificial intelligence–based approach to enhance process control in rubber mixing by predicting mixing temperatures from input variables. The proposed method uses feedforward neural networks (FFNs) to enable early identification of batch-specific temperature deviations, thereby enabling systematic improvements with each new application. The FFN was trained on a diverse dataset encompassing various rubber recipes and batches. Post-training, the FFN demonstrated remarkable accuracy, achieving a mean absolute percentage error of 1.00% on the training dataset and 1.44% on the validation dataset, thereby showcasing its efficacy in predicting temperature fluctuations within the mixing process. Consequently, the FFN can determine the relevant input variables necessary to achieve specific mixing temperatures, providing a foundation for an automated control system in rubber mixing process. This paper outlines the system architecture of the FFN tailored for rubber mixing and provides a comprehensive overview of the experimental results.

Long-term stability of squeezed light in a fiber-based system using automated alignment.

Providing a cloud service for optical quantum computing requires stabilizing the optical system for extended periods. It is advantageous to construct a fiber-based system, which does not require spatial alignment. However, fiber-based systems are instead subject to fiber-specific instabilities. For instance, there are phase drifts due to ambient temperature changes and external disturbances and polarization fluctuations due to the finite polarization extinction ratio of fiber components. Here, we report the success of measuring squeezed light with a fiber system for 24h. To do this, we introduce stabilization mechanics to suppress fluctuations in the fiber system and an integrated controller to automatically align the entire system. The squeezed light at a wavelength of 1545.3nm is measured every 2min, where automated alignments are inserted every 30min. The squeezing levels with an average of -4.42 dB are recorded with an extremely small standard deviation of 0.08 dB over 24h. With the technologies developed here, we can build complicated optical setups with the fiber-based system and operate them automatically for extended periods, which is promising for cloud service of quantum computation.

Different Methods for Measurements and Estimation of Pulse Wave Velocity are not Interchangeable

BackgroundCarotid-femoral pulse wave velocity (c–f PWV) is a gold standard for the arterial stiffness measurement and important biomarker for the assessment of the cardiovascular (CV) risk. Recent studies have focused on 24-h measurements of arterial stiffness and estimated PWV (ePWV). The aim of this study is to analyze agreement of office c–f PWV measurements (SphygmoCor) with 24-h oscillometric measurements (Mobil-O-Graph and Arteriograph), and with ePWV.ResultsThis study included 154 patients with primary hypertension (average age 38.75 ± 12.65). Arterial stiffness has been measured in the office with SphygmoCor and 24 h with two oscillometric methods (Mobil-O-Graph and Arteriograph). ePWV was calculated using validated equation. PWV values obtained in office (SphygmoCor) showed higher average values compared to both 24-h oscillometric measurements of PWV and ePWV. The mean values of 24-h PWV measured by Arteriograph were higher compared to values obtained with Mobil-O-Graph. The measurement of PWV over 24 h using the Arteriograph is the most accurate among the methods that were compared with the office PWV measurements (accuracy of 0.989). However, the most precise method was the Mobil-O-Graph (0.631), and the highest degree of agreement also was shown with the Mobil-O-Graph (concordance coefficient correlation (CCC) = 0.447). The smallest deviation (TDI) and the highest probability of overlapping (CP) were observed with ePWV (TDI = 45.524, CP = 0.322, respectively).ConclusionIn our group of young treated mild hypertensive patients with low CV risk, we found weak agreements between cfPWV and 24-h PWV. These methods are not interchangeable.

Lagrangian formulation of the Tsallis entropy

We investigate the gravitational origin of the Tsallis entropy, characterized by the nonadditive index δ. Utilizing Wald's formalism within the framework of f(R) modified theories of gravity, we evaluate the entropy on the black hole horizon for constant curvature solutions to the spherically symmetric vacuum field equations. In so doing, we demonstrate that the Tsallis entropy can be effectively derived from a generalization of the Lagrangian L∝R1+ϵ, where ϵ=δ−1 quantifies small deviations from general relativity. In conclusion, we examine the physical implications of our findings in light of cosmological observations and elaborate on the possibility of solving the thermodynamic instability of Schwarzschild black holes.

The Study of Olivine Inclusions in Diamonds from Liaoning, China and the Evaluation of Related Thermometers

Olivine is the most abundant mineral in mantle peridotite and a typical inclusion in diamonds, providing essential evidence for the characterization of the diamondiferous lithospheric mantle. Three olivine inclusions in diamonds (OlDia) from Liaoning in the North China Craton (NCC) were exposed for in situ measurements, and the compositional data of 62 other OlDia from Liaoning were collected based on previous reports. The enrichment of TiO2 (>0.1 wt.%) with high Cr# (>50; Cr# = 100Cr/(Cr + Al) by atom) was revealed, despite the predominance of depleted TiO2 contents and high Mg# (92.8–93.2; Mg# =100Mg/(Mg + Fe) by atom) for OlDia. Silica fluid accompanying olivine still trapped in the host diamond was recognized using Raman spectroscopy. Three thermometers were applied to the OlDia, based on the data from Laser Ablation Inductively Coupled Plasma Mass Spectrometry (LA-ICP-MS) and Electron Probe Micro-Analysis (EPMA), and a temperature range (TLA and TEPMA) of 1080–1380 °C was yielded. With respect to the TLA, Al-in-olivine thermometers were preferred, although there was a smaller deviation between TEPMA and TLA when using the Cr-in-olivine thermometer. The results of these thermometers show a high correlation with TEPMA, enabling their application based on EPMA data. Projections onto 39–42 mW/m2 model geotherms underline a diamondiferous base of the lithospheric mantle beneath the NCC. The lithospheric mantle is characterized by refractory and depleted sections, where enrichment metasomatism may have occurred at the lower roots (161–178 km).

Quantitative Approach to Quality Review of Prenatal Ultrasound Examinations: Fetal Biometry.

Background/Objectives: To evaluate the quality of an ultrasound practice, both large-scale and focused audits are recommended by professional organizations, but such audits can be time-consuming, inefficient, and expensive. Our objective was to develop a time-efficient, quantitative, objective, large-scale method to evaluate fetal biometry measurements for an entire practice, combined with a process for focused image review for personnel whose measurements are outliers. Methods: Ultrasound exam data for a full year are exported from commercial ultrasound reporting software to a statistical package. Fetal biometry measurements are converted to z-scores to standardize across gestational ages. For a large-scale audit, sonographer mean z-scores are compared using analysis of variance (ANOVA) with Scheffe multiple comparisons test. A focused image review is performed on a random sample of exams for sonographers whose mean z-scores differ significantly from the practice mean. A similar large-scale audit is performed, comparing physician mean z-scores. Results: Using fetal abdominal circumference measurements as an example, significant differences between sonographer mean z-scores are readily identified by the ANOVA and Scheffe test. A method is described for the blinded image audit of sonographers with outlier mean z-scores. Examples are also given for the identification and interpretation of several types of systematic errors that are unlikely to be detectable by image review, including z-scores with large or small standard deviations and physicians with outlier mean z-scores. Conclusions: The large-scale quantitative analysis provides an overview of the biometry measurements of all the sonographers and physicians in a practice, so that image audits can be focused on those whose measurements are outliers. The analysis takes little time to perform after initial development and avoids the time, complexity, and expense of auditing providers whose measurements fall within the expected range. We encourage commercial software developers to include tools in their ultrasound reporting software to facilitate such quantitative reviews.

PENGENDALI PINTAR DALAM PENGONTROLAN LAMPU DAN KIPAS MENGGUNAKAN BLUETOOTH

The evolution of mobile technology has revolutionized it from a mere communication tool to a versatile platform capable of handling images, videos, documents, and controlling other devices such as TVs. The Android OS gives developers the flexibility to create applications that meet the diverse needs of users. This shift has made smartphones indispensable, supporting tasks from browsing to entertainment and productivity. The popularity of Android ensures seamless integration with existing hardware for efficient application performance. This research aims to design a smart home device control system, focusing on lights and fans via Android on an Arduino Nano microcontroller. Android's affordability and development through third-party applications make it ideal for smart home systems. Integrating the Arduino Nano and the EMS Blue Shield Bluetooth module improves convenience and energy efficiency. Its limitations include control of basic functions (lights, fan speed) and Android smartphones with Bluetooth. This study aims to design a practical control system and understand the device operation and Android communication. The test results of data transmission response time (latency) show that the average response time of the system for five days is 122.3 ms, with small variations and standard deviations between 2.81 ms and 3.92 ms. The range of response time ranged from 118 ms to 130 ms.

PLS-based hellinger distance method for fault detection in chemical engineering systems

Fault detection is vital in chemical engineering systems to maintain operational efficiency, product quality, and safety through timely identification and correction of deviations from expected behavior. Although partial least squares (PLS) has proven effective in monitoring due to its ability to handle highly correlated variables, traditional detection metrics of PLS may fail to identify small abnormal changes as they rely solely on recent observations. This paper integrates PLS modeling framework with Hellinger Distance (HD)-based fault detection index to overcome the limitations of conventional detection metrics. The utilization of HD is motivated by its sensitivity to quantifying any dissimilarity between distributions, which makes it well-suited for detecting small deviations in process behavior. The HD-based index will be computed between the residuals obtained from the model in the offline stage and the online stage. The HD metric involves careful inspection and comparison of the residuals, which enables it to capture the sensitive details in the data, thus, enhancing the detection of faults. For increased flexibility, kernel density estimation is employed to establish the reference threshold of the PLS-HD approach. The performance of this approach will be evaluated using data from simulated Continuous Stirred-Tank Heater (CSTH) and Continuous Stirred-Tank Reactor (CSTR) processes, by considering various fault types such as bias, freezing, and sensor drift faults. The results demonstrate the superior performance of the proposed PLS-HD approach compared to conventional PLS monitoring methods.

A data fusion method for maritime traffic surveillance: The fusion of AIS data and VHF speech information

The more comprehensive information supply for Vessel Traffic Service (VTS), the greater capacity for maritime traffic surveillance. To supply ship intention information contained in very high frequency (VHF) speech for VTS, we propose an automatic identification system (AIS) data and VHF speech information fusion method. In the first part of this method, the feature information of VHF speech is extracted by Bert-BiLSTM-CRF-based entity extraction method, likes location, ship name, and ship intention information, etc. In the second part, we design a spatio-temporal range to filter AIS data, the temporal range is determined by receive time of VHF speech, and the spatial range is determined by the location information extracted from VHF speech. In the third part, by measuring the ship name similarity between AIS data and VHF speech, the barriers to fusion are successfully overcome. The similarity is calculated by combining with Chinese pinyin character similarity and Arabic number similarity and Chinese pinyin characters are encoded by pronunciation characters, calculated by the dynamic time warping (DTW) distance. Through experiments, the method can effectively provide comprehensive information for maritime traffic surveillance, and even when crews misreport ship name within a small deviation, our method still possesses a great fusion capability.

Cyclic Electrogravimetry Reveals Details of Copper Electrodeposition in the Presence of Additives

Copper electroplating was studied based on cyclic voltammetry combined with a new type of acoustic microgravimetry. The instrument operates similarly to a quartz crystal microbalance with dissipation monitoring (EQCM-D), meaning that it reports shifts in resonance frequency, Δf, and half bandwidth, ΔΓ, on several overtones. Compared to the existing instruments, the time resolution was improved by a factor of 10 down to 10 ms using multifrequency lockin amplification. The frequency noise after accumulation was reduced below 10 mHz ≙ 0.12 ng/cm2 ≙ 0.14 pm (assuming ρ = 8.96 g/cm3) by modulating the electrode potential and averaging of Δf and ΔΓ. Mostly, Δf and ΔΓ are in line with the Sauerbrey prediction (Δf/n ≈const. and ΔΓ/n < -Δf/nwith n the overtone order). Small unsystematic deviations between overtones due to compressional wave effects are seen but no evidence for strong roughness or viscoelasticity. Further, the Faraday efficiency is almost unity, meaning that Δf is close to the expectations derived from the electrical current. The improved sensitivity enables to determine the time derivative of the frequency shift, which is equal to an apparent mass transfer rate that can be compared to the current directly. Again, small deviations are seen for bulk deposition and stripping. These go back to weak roughness effects most pronounced in the initial phase of bulk deposition and, also, to the presence of a Cu(I) intermediate during dissolution. When adding benzotriazole (BTA) or thiourea (TU) as plating additives, the gravimetric and the voltammetric response changes. For BTA, the deviations between mass transfer rate and current vanish indicative of decreased roughness. For TU additional features appear, related to a potential-dependent adsorption of TU and to increased underpotential deposition (UPD). In the presence of TU, the electrode-electrolyte interface displays viscoelasticity, evident by the bandwidth increases during deposition.[1] Caption: Currents, time derivatives of the frequency shift, and bandwidth shift obtained during copper electrodeposition without additives (A), in the presence of 10 µM benzotriazole (B), and in the presence of 10 µM thiourea (C). Reprinted with permission from Reference [1].

Square Wave Electrogravimetry Monitors Transient Submonolayer Adsorption of Redox-Active Molecules with a Precision of Less Than 1% of a Monolayer

Square wave voltammetry on electrolytes containing the reversible redox pairs flavin adenine dinucleotide (FAD) and methyl viologen (MV) was complemented by a new form of acoustic microgravimetry. The analytes FAD and MV have promising applications in bacterial fuel cells and redox flow batteries. The instrument operates similarly to a quartz crystal microbalance with dissipation monitoring (EQCM-D). It reports shifts in resonance frequency and half bandwidth on several overtones. Compared to the existing instruments, the time resolution was improved by a factor of 40 down to 2.5 ms by multifrequency lockin amplification, which is important for the analysis of the transients in electrochemistry. The frequency noise after accumulation was reduced below 10 mHz ≙ 0.12 ng/cm2 ≙ 1.2 pm (assuming ρ = 1 g/cm3) by employing modulation and averaging. Square wave modulation of the electrode potential is superior to linear ramps (cyclic voltammetry) because it reduces the contribution of non-Faraday currents and, also, improves sensitivity. The shifts of frequency,Δf, and half bandwidth, ΔΓ, are in line with the Sauerbrey prediction (Δf/n ≈const. and ΔΓ/n < -Δf/nwith n the overtone order). Small deviations (Figure B and D) presumably are caused by the layer’s softness. The apparent shear modulus, G app, of this layer is in the GPa range. The frequency difference, Δf/n|CT (Figure E), amounts to an apparent mass transfer rate. Plots of Δf/n|CT versus potential sometimes show curves similar to the electric current as observed for e. g. MV. For FAD, the results obtained depended on pH and the apparent mass transfer rates are much different from the current (Figure C and E). This difference is most likely caused by adsorbed molecules that are intermediates of the underlying two-electron process. The explanation is further corroborated by the response time of the QCM signals being much larger than the RC time of double layer recharging as determined with EIS. An interpretation in terms of adsorption/desorption is more plausible than an interpretation in terms of changed viscosity in the diffuse double layer.[1] Caption: Currents and frequency shifts obtained on a solution containing FAD. Df/n|av evidences the preferred adsorption of the intermediate state (FADH).

A novel compact and shadow resistance‐to‐frequency and resistance‐to‐time converter

AbstractThis paper presents a novel compact and shadow resistance‐to‐frequency converter and resistance‐to‐time converter. The design incorporates three current feedback operational amplifiers (CFOA) and can be implemented in CMOS technology. The design's functionality has been proven through simulation and experimental verification. The simulation and experimental findings show that the proposed design works well with small deviation between simulation and experimental results.

Modeling aerosol transmission spectra from n(λ) and k(λ) infrared optical constants measurements of organic liquids and solids

The effects of light scattering and refraction play significantly different roles for aerosols than for bulk materials, making it challenging to identify aerosolized chemicals using traditional spectral methods or spectral reference libraries. Due to a potentially infinite number of particle morphologies, sizes, and compositions, constructing a database of laboratory-measured aerosol spectra is not a practical solution. Here, as an alternative approach, the measured n/k optical vectors of two example organic materials (diethyl phthalate and D-mannitol) are used in combination with particle absorption / scattering theory (Mie theory and FDTD) and the Beer-Lambert law to generate a series of synthetic infrared transmission / scattered light spectra. The synthetic spectra show significant differences versus simple slab transmission spectra, even for small changes in particle size (e.g., 5 vs. 10 µm) for both single particles and ensembles, potentially serving as useful reference data for aerosol sensing. For spherical single particles with diameters of 1 to 10 µm, FDTD simulations predict changes in the magnitudes of spectral shifts and the shapes of the peaks vs. particle size with only small deviations from Mie theory predictions, yet reliably capture the direction of the shifts. Typical spectral peak shifts in the longwave infrared correspond to Δλ ∼0.20 µm (∼34 cm-1) when compared to corresponding slab transmission spectra. Additionally, synthetic spectra generated from the n/k values derived using two different methods (KBr pellet transmission and single-angle reflectance) are compared using the Mie theory model.