Modeling habitat distribution of Cornus officinalis with Maxent modeling and fuzzy logics in China

Aims Predicting suitable habitat distribution is an effective way to protect rare or endangered medicinal plants.Cornus officinalis is a perennial tree growing in forest edge and its air-dried pericarp is one of the traditional Chinese medicines(TCM)with significant medicinal values.In recent years,C.officinalis has undergone severe degeneration of its natural habitat owing to growing market demands and unprecedented damage to the forests.Moreover,the degeneration of suitable habitat has threatened the supply of medicinal materials,and even led to the extinction of some engendered medicinal plant species.In this case,there is a great risk to introduce and cultivate medicinal plants if planners determine the suitable cultivation regions based on personal subjective experience alone.Therefore,predicting suitable potential habitat distribution of medicinal plants(e.g.C.officinalis)and revealing the environmental factors determining such distribution patterns are important to habitat conservation and environmental restoration.Methods In this article,we report the results of a study on the habitat distribution of C.officinalis using maximum entropy(Maxent)modeling and fuzzy logics together with loganin content and environmental variables.The localities of 106 C.officinalis in China were collected by our group and other researchers and used as occurrence data.The loganin content of 234 C.officinalis germplasm resources were tested by high-performance liquid chromatography(HPLC)and used as content data.79 environmental variables were selected and processed with multicollinearity test by using Pearson Correlation Coefficient(r)to determine a set of independent variables.The chosen variables were then processed in the fuzzy linear model according to the cell values(maximum,minimum)of localities with estimated loganin content.The SDMtoolbox was used to spatially rarefy occurrence data and prepare bias files.Furthermore,combined Maxent modeling and fuzzy logics were used to predict the suitable habitat of C.officinalis.The modeling result was validated using null-model method.Important Findings As a result,six environmental factors including tmin3,prec3,bio4,alt,bio12 and bio3 were determined as key influential factors that mostly affected both the habitat suitability and active ingredient of C.officinalis.The highly suitable regions of C.officinalis mainly distribute in a‘core distribution zone’of the east-central China.The statistically significant AUC value indicated that combined Maxent modeling and fuzzy logics could be used to predict the suitable habitat distribution of medicinal plants.Furthermore,our results confirm that ecological factors played critical roles in assessing suitable geographical regions as well as active ingredient of plants,highlighting the need for effective habitat rehabilitation and resource conservation.

Prediction of the undrained shear strength of remolded soil with non-linear regression,fuzzy logic,and artificial neural network

This study aims to predict the undrained shear strength of remolded soil samples using non-linear regression analyses,fuzzy logic,and artificial neural network modeling.A total of 1306 undrained shear strength results from 230 different remolded soil test settings reported in 21 publications were collected,utilizing six different measurement devices.Although water content,plastic limit,and liquid limit were used as input parameters for fuzzy logic and artificial neural network modeling,liquidity index or water content ratio was considered as an input parameter for non-linear regression analyses.In non-linear regression analyses,12 different regression equations were derived for the prediction of undrained shear strength of remolded soil.Feed-Forward backpropagation and the TANSIG transfer function were used for artificial neural network modeling,while the Mamdani inference system was preferred with trapezoidal and triangular membership functions for fuzzy logic modeling.The experimental results of 914 tests were used for training of the artificial neural network models,196 for validation and 196 for testing.It was observed that the accuracy of the artificial neural network and fuzzy logic modeling was higher than that of the non-linear regression analyses.Furthermore,a simple and reliable regression equation was proposed for assessments of undrained shear strength values with higher coefficients of determination.

A Survey on Type-3 Fuzzy Logic Systems and Their Control Applications

In this paper,we offer a review of type-3 fuzzy logic systems and their applications in control.The main objective of this work is to observe and analyze in detail the applications in the control area using type-3 fuzzy logic systems.In this case,we review their most important applications in control and other related topics with type-3 fuzzy systems.Intelligent algorithms have been receiving increasing attention in control and for this reason a review in this area is important.This paper reviews the main applications that make use of Intelligent Computing methods.Specifically,type-3 fuzzy logic systems.The aim of this research is to be able to appreciate,in detail,the applications in control systems and to point out the scientific trends in the use of Intelligent Computing techniques.This is done with the construction and visualization of bibliometric networks,developed with VosViewer Software,which it is a free Java-based program,mainly intended to be used for analyzing and visualizing bibliometric networks.With this tool,we can create maps of publications,authors,or journals based on a co-citation network or construct maps of keywords,countries based on a co-occurrence networks,research groups,etc.

Fuzzy Adaptive State Estimation of Distributed Drive Electric Vehicles with Random Missing Measurements and Unknown Process Noise

Accurate estimation of sideslip angle and vehicle velocity is crucial for effective control of distributed drive electric vehicles.However,as these states are not directly measured,Kalman-based approaches utilizing in-vehicle sensors have been developed to estimate them.Unfortunately,existing methods tend to ignore the impact of data loss on estimation performance.Furthermore,the process noise,which changes dynamically due to varying driving conditions,is not adequately considered.In response to these constraints,we propose a novel method called the fuzzy adaptive fault-tolerant extended Kalman filter(FAFTEKF).Initially,a fault-tolerant EKF is devised to handle missing measurements.Additionally,a fuzzy logic system that dynamically updates the process noise matrix,is built to improve estimation accuracy under different driving conditions.Extensive experimental results validate the superiority of the FAFTEKF over the traditional EKF across various scenarios with different degrees of data loss.

Complex Decision Modeling Framework with Fairly Operators and Quaternion Numbers under Intuitionistic Fuzzy Rough Context

The main goal of informal computing is to overcome the limitations of hypersensitivity to defects and uncertainty while maintaining a balance between high accuracy,accessibility,and cost-effectiveness.This paper investigates the potential applications of intuitionistic fuzzy sets(IFS)with rough sets in the context of sparse data.When it comes to capture uncertain information emanating fromboth upper and lower approximations,these intuitionistic fuzzy rough numbers(IFRNs)are superior to intuitionistic fuzzy sets and pythagorean fuzzy sets,respectively.We use rough sets in conjunction with IFSs to develop several fairly aggregation operators and analyze their underlying properties.We present numerous impartial laws that incorporate the idea of proportionate dispersion in order to ensure that the membership and non-membership activities of IFRNs are treated equally within these principles.These operations lead to the development of the intuitionistic fuzzy rough weighted fairly aggregation operator(IFRWFA)and intuitionistic fuzzy rough ordered weighted fairly aggregation operator(IFRFOWA).These operators successfully adjust to membership and non-membership categories with fairness and subtlety.We highlight the unique qualities of these suggested aggregation operators and investigate their use in the multiattribute decision-making field.We use the intuitionistic fuzzy rough environment’s architecture to create a novel strategy in situation involving several decision-makers and non-weighted data.Additionally,we developed a novel technique by combining the IFSs with quaternion numbers.We establish a unique connection between alternatives and qualities by using intuitionistic fuzzy quaternion numbers(IFQNs).With the help of this framework,we can simulate uncertainty in real-world situations and address a number of decision-making problems.Using the examples we have released,we offer a sophisticated and systematically constructed illustrative scenario that is intricately woven with the complexity ofmedical evaluation in order to thoroughly assess the relevance and efficacy of the suggested methodology.

A fuzzy compensation-Koopman model predictive control design for pressure regulation in proten exchange membrane electrolyzer

Proton exchange membrane(PEM)electrolyzer have attracted increasing attention from the industrial and researchers in recent years due to its excellent hydrogen production performance.Developing accurate models to predict their performance is crucial for promoting and accelerating the design and optimization of electrolysis systems.This work developed a Koopman model predictive control(MPC)method incorporating fuzzy compensation for regulating the anode and cathode pressures in a PEM electrolyzer.A PEM electrolyzer is then built to study pressure control and provide experimental data for the identification of the Koopman linear predictor.The identified linear predictors are used to design the Koopman MPC.In addition,the developed fuzzy compensator can effectively solve the Koopman MPC model mismatch problem.The effectiveness of the proposed method is verified through the hydrogen production process in PEM simulation.

IoT Smart Devices Risk Assessment Model Using Fuzzy Logic and PSO

Increasing Internet of Things(IoT)device connectivity makes botnet attacks more dangerous,carrying catastrophic hazards.As IoT botnets evolve,their dynamic and multifaceted nature hampers conventional detection methods.This paper proposes a risk assessment framework based on fuzzy logic and Particle Swarm Optimization(PSO)to address the risks associated with IoT botnets.Fuzzy logic addresses IoT threat uncertainties and ambiguities methodically.Fuzzy component settings are optimized using PSO to improve accuracy.The methodology allows for more complex thinking by transitioning from binary to continuous assessment.Instead of expert inputs,PSO data-driven tunes rules and membership functions.This study presents a complete IoT botnet risk assessment system.The methodology helps security teams allocate resources by categorizing threats as high,medium,or low severity.This study shows how CICIoT2023 can assess cyber risks.Our research has implications beyond detection,as it provides a proactive approach to risk management and promotes the development of more secure IoT environments.

Fuzzy inference system using genetic algorithm and pattern search for predicting roof fall rate in underground coal mines

One of the most dangerous safety hazard in underground coal mines is roof falls during retreat mining.Roof falls may cause life-threatening and non-fatal injuries to miners and impede mining and transportation operations.As a result,a reliable roof fall prediction model is essential to tackle such challenges.Different parameters that substantially impact roof falls are ill-defined and intangible,making this an uncertain and challenging research issue.The National Institute for Occupational Safety and Health assembled a national database of roof performance from 37 coal mines to explore the factors contributing to roof falls.Data acquired for 37 mines is limited due to several restrictions,which increased the likelihood of incompleteness.Fuzzy logic is a technique for coping with ambiguity,incompleteness,and uncertainty.Therefore,In this paper,the fuzzy inference method is presented,which employs a genetic algorithm to create fuzzy rules based on 109 records of roof fall data and pattern search to refine the membership functions of parameters.The performance of the deployed model is evaluated using statistical measures such as the Root-Mean-Square Error,Mean-Absolute-Error,and coefficient of determination(R_(2)).Based on these criteria,the suggested model outperforms the existing models to precisely predict roof fall rates using fewer fuzzy rules.

Frequency Regulation of Alternating Current Microgrid Based on Hierarchical Control Using Fuzzy Logic

An alternating current(AC)microgrid is a system that integrates renewable power,power converters,controllers and loads.Hierarchical control can manage the frequency of the microgrid to prevent imbalance and collapse of the system.The existing frequency control methods use traditional proportion integration(PI)controllers,which cannot adjust PI parameters in real-time to respond to the status changes of the system.Hierarchical control driven by fuzzy logic allows real-time adjustment of the PI parameters and the method used a two-layer control structure.The primary control used droop control to adjust power distribution,and fuzzy logic was used in the voltage loop of the primary control.The secondary control was added to make up for frequency deviation caused by droop control,and fuzzy logic was used in the secondary frequency control to deal with the dynamic change of frequency caused by the disturbances of loads.The proposed method was simulated in Matlab/Simulink.In the primary control,the proposed method reduced the total harmonic distortion(THD)of two cycles of the output voltage from 4.19%to 3.89%;in the secondary control,the proposed method reduced the frequency fluctuation of the system by about 0.03 Hz and 0.04 Hz when the load was increased and decreased,respectively.The results show that the proposed methods have a better effect on frequency maintenance and voltage control of the AC microgrid.

Adaptive Droop Control for Circulating Current Suppression in Microgrid Based on Fuzzy Logic

Circulating currents in a microgrid increase the power loss of the microgrid, reduce the operational efficiency, as well as affect the power quality of the microgrid. The existing literature is seldom concerned with methods to suppress the loop currents using fuzzy logic control. In this paper, a method based on fuzzy control of droop coefficients is proposed to suppress the circulating currents inside the microgrid.The method combines fuzzy control with droop control and can achieve the effect of suppressing the circulating currents by adaptively adjusting the droop coefficients to make the power distribution between each subgrid more balanced. To verify the proposed method, simulation is carried out in Matlab/Simulink environment, and the simulation results show that the proposed method is significantly better than the traditional proportional-integral control method. The circulating currents reduce from about 10 A to several nanoamperes, the bus voltage and frequency drops are significantly improved, and the total harmonic distortion rate of the output voltage reduces from 4.66% to 1.06%. In addition, the method used in this paper can be extended to be applied in multiple inverters connected in parallel, and the simulation results show that the method has a good effect on the suppression of circulating currents among multiple inverters.

Lithium-Ion Battery Pack Based on Fuzzy Logic Control Research on Multi-Layer Equilibrium Circuits

In order to solve the problem of inconsistent energy in the charging and discharging cycles of lithium-ion battery packs,a new multilayer equilibrium topology is designed in this paper.The structure adopts a hierarchical structure design,which includes intra-group equilibrium,primary inter-group equilibrium and secondary inter-group equilibrium.This structure greatly increases the number of equilibrium paths for lithium-ion batteries,thus shortening the time required for equilibrium,and improving the overall efficiency.In terms of control strategy,fuzzy logic control(FLC)is chosen to control the size of the equilibrium current during the equilibrium process.We performed rigorous modeling and simulation of the proposed system by MATLAB and Simulink software.Experiments show that the multilayer equilibrium circuit structure greatly exceeds the traditional single-layer equilibrium circuit in terms of efficacy,specifically,the Li-ion battery equilibrium speed is improved by 12.71%in static equilibrium,14.48%in charge equilibrium,and 11.19%in discharge equilibrium.In addition,compared with the maximum value algorithm,the use of the FLC algorithm reduces the equalization time by about 3.27%and improves the energy transfer efficiency by about 66.49%under the stationary condition,which verifies the feasibility of the equalization scheme.

Computation Tree Logic Model Checking of Multi-Agent Systems Based on Fuzzy Epistemic Interpreted Systems

Model checking is an automated formal verification method to verify whether epistemic multi-agent systems adhere to property specifications.Although there is an extensive literature on qualitative properties such as safety and liveness,there is still a lack of quantitative and uncertain property verifications for these systems.In uncertain environments,agents must make judicious decisions based on subjective epistemic.To verify epistemic and measurable properties in multi-agent systems,this paper extends fuzzy computation tree logic by introducing epistemic modalities and proposing a new Fuzzy Computation Tree Logic of Knowledge(FCTLK).We represent fuzzy multi-agent systems as distributed knowledge bases with fuzzy epistemic interpreted systems.In addition,we provide a transformation algorithm from fuzzy epistemic interpreted systems to fuzzy Kripke structures,as well as transformation rules from FCTLK formulas to Fuzzy Computation Tree Logic(FCTL)formulas.Accordingly,we transform the FCTLK model checking problem into the FCTL model checking.This enables the verification of FCTLK formulas by using the fuzzy model checking algorithm of FCTL without additional computational overheads.Finally,we present correctness proofs and complexity analyses of the proposed algorithms.Additionally,we further illustrate the practical application of our approach through an example of a train control system.

Ingredients-based Methodology and Fuzzy Logic Combined Short-Duration Heavy Rainfall Short-Range Forecasting:An Improved Scheme

Short-duration heavy rainfall(SHR),as delineated by the National Meteorological Center of the China Me-teorological Administration,is characterized by hourly rainfall amounts no less than 20.0 mm.SHR is one of the most common convective weather phenomena that can cause severe damage.Short-range forecasting of SHR is an important part of operational severe weather prediction.In the present study,an improved objective SHR forecasting scheme was developed by adopting the ingredients-based methodology and using the fuzzy logic approach.The 1.0°×1.0°National Centers for Environmental Prediction(NCEP)final analysis data and the ordinary rainfall(0.1-19.9 mm h-1)and SHR observational data from 411 stations were used in the improved scheme.The best lifted index,the total precipitable water,the 925 hPa specific humidity(Q 925),and the 925 hPa divergence(DIV 925)were selected as predictors based on objective analysis.Continuously distributed membership functions of predictors were obtained based on relative frequency analysis.The weights of predictors were also objectively determined.Experiments with a typhoon SHR case and a spring SHR case show that the main possible areas could be captured by the improved scheme.Verification of SHR forecasts within 96 hours with NCEP global forecasts 1.0°×1.0°data initiated at 08:00 Beijing Time during the warm seasons in 2015 show the results were improved from both deterministic and probabilistic perspectives.This study provides an objectively feasible choice for short-range guidance forecasts of SHR.The scheme can be applied to other convective phenomena.

An integrated fuzzy logic and machine learning platform for porosity detection using optical tomography imaging during laser powder bed fusion

Traditional methods such as mechanical testing and x-ray computed tomography(CT), for quality assessment in laser powder-bed fusion(LPBF), a class of additive manufacturing(AM),are resource-intensive and conducted post-production. Recent advancements in in-situ monitoring, particularly using optical tomography(OT) to detect near-infrared light emissions during the process, offer an opportunity for in-situ defect detection. However, interpreting OT datasets remains challenging due to inherent process characteristics and disturbances that may obscure defect identification. This paper introduces a novel machine learning-based approach that integrates a self-organizing map, a fuzzy logic scheme, and a tailored U-Net architecture to enhance defect prediction capabilities during the LPBF process. This model not only predicts common flaws such as lack of fusion and keyhole defects through analysis of in-situ OT data,but also allows quality assurance professionals to apply their expert knowledge through customizable fuzzy rules. This capability facilitates a more nuanced and interpretable model,enhancing the likelihood of accurate defect detection. The efficacy of this system has been validated through experimental analyses across various process parameters, with results validated by subsequent CT scans, exhibiting strong performance with average model scores ranging from 0.375 to 0.819 for lack of fusion defects and from 0.391 to 0.616 for intentional keyhole defects. These findings underscore the model's reliability and adaptability in predicting defects, highlighting its potential as a transformative tool for in-process quality assurance in AM. A notable benefit of this method is its adaptability, allowing the end-user to adjust the probability threshold for defect detection based on desired quality requirements and custom fuzzy rules.

Effective data transmission through energy-efficient clustering and Fuzzy-Based IDS routing approach in WSNs

Wireless sensor networks(WSN)gather information and sense information samples in a certain region and communicate these readings to a base station(BS).Energy efficiency is considered a major design issue in the WSNs,and can be addressed using clustering and routing techniques.Information is sent from the source to the BS via routing procedures.However,these routing protocols must ensure that packets are delivered securely,guaranteeing that neither adversaries nor unauthentic individuals have access to the sent information.Secure data transfer is intended to protect the data from illegal access,damage,or disruption.Thus,in the proposed model,secure data transmission is developed in an energy-effective manner.A low-energy adaptive clustering hierarchy(LEACH)is developed to efficiently transfer the data.For the intrusion detection systems(IDS),Fuzzy logic and artificial neural networks(ANNs)are proposed.Initially,the nodes were randomly placed in the network and initialized to gather information.To ensure fair energy dissipation between the nodes,LEACH randomly chooses cluster heads(CHs)and allocates this role to the various nodes based on a round-robin management mechanism.The intrusion-detection procedure was then utilized to determine whether intruders were present in the network.Within the WSN,a Fuzzy interference rule was utilized to distinguish the malicious nodes from legal nodes.Subsequently,an ANN was employed to distinguish the harmful nodes from suspicious nodes.The effectiveness of the proposed approach was validated using metrics that attained 97%accuracy,97%specificity,and 97%sensitivity of 95%.Thus,it was proved that the LEACH and Fuzzy-based IDS approaches are the best choices for securing data transmission in an energy-efficient manner.

Implementation of Fuzzy Logic Control into an Equivalent Minimization Strategy for Adaptive Energy Management of A Parallel Hybrid Electric Vehicle

As government agencies continue to tighten emissions regulations due to the continued increase in greenhouse gas production, automotive industries are seeking to produce increasingly efficient vehicle technology. Hybrid electric vehicles (HEVs) have been introduced to mitigate problems while improving fuel economy. HEVs have led to the demand of creating more advanced controls software to consider multiple components for propulsive power in a vehicle. A large section in the software development process is the implementation of an optimal energy management strategy meant to improve the overall fuel efficiency of the vehicle. Optimal strategies can be implemented when driving conditions are known a prior. The Equivalent Consumption Minimization Strategy (ECMS) is an optimal control strategy that uses an equivalence factor to equate electrical to mechanical power when performing torque split determination between the internal combustion engine and electric motor for propulsive and regenerative torque. This equivalence factor is determined from offline vehicle simulations using a sensitivity analysis to provide optimal fuel economy results while maintaining predetermined high voltage battery state of charge (SOC) constraints. When the control hierarchy is modified or different driving styles are applied, the analysis must be redone to update the equivalence factor. The goal of this work is to implement a fuzzy logic controller that dynamically updates the equivalence factor to improve fuel economy, maintain a strict charge sustaining window of operation for the high voltage battery, and reduce computational time required during algorithm development. The adaptive algorithm is validated against global optimum fuel economy and charge sustaining results from a sensitivity analysis performed for multiple drive cycles. Results show a maximum fuel economy improvement of 9.82% when using a mild driving style and a 95% success rate when maintaining an ending SOC within 5% of the desired SOC regardless of starting SOC.

A Neuro T-Norm Fuzzy Logic Based System

In this study, we are first examining well-known approach to improve fuzzy reasoning model (FRM) by use of the genetic-based learning mechanism [1]. Later we propose our alternative way to build FRM, which has significant precision advantages and does not require any adjustment/learning. We put together neuro-fuzzy system (NFS) to connect the set of exemplar input feature vectors (FV) with associated output label (target), both represented by their membership functions (MF). Next unknown FV would be classified by getting upper value of current output MF. After that the fuzzy truths for all MF upper values are maximized and the label of the winner is considered as the class of the input FV. We use the knowledge in the exemplar-label pairs directly with no training. It sets up automatically and then classifies all input FV from the same population as the exemplar FVs. We show that our approach statistically is almost twice as accurate, as well-known genetic-based learning mechanism FRM.

Fuzzy-based approach to quantify the downtime of buildings in developing countries

Earthquake is one of the natural disasters that affects the buildings and communities in developing countries.It causes different levels of damages to the buildings,making them uninhabitable for a period of time,called downtime(DT).This paper proposes a Fuzzy Logic hierarchical method to estimate the downtime of residential buildings in developing countries after an earthquake.The use of expert-based systems allows quantifying the indicators involved in the model using descriptive knowledge instead of hard data,accounting also for the un-certainties that may affect the analysis.The applicability of the methodology is illustrated using the information gathered after the 2015 Gorkha,Nepal,earthquake as a case study.On April 25,2015,Nepal was hit by the Mw 7.8 Gorkha earthquake,which damaged and destroyed more than 500.000 residential buildings.Information obtained from a Rapid Visual Damage Assessment(RVDA)is used through a hierarchical scheme to evaluate the building damageability.Sensitivity analysis based on Sobol method is implemented to evaluate the impor-tance of parameters gathered in the RVDA for building damage estimation.The findings of this work may be used to estimate the restoration time of damaged buildings in developing countries and to plan preventive safety measures.

Enhanced Fuzzy Logic Control Model and Sliding Mode Based on Field Oriented Control of Induction Motor

In the context of induction motor control, there are various control strategies used to separately control torque and flux. One common approach is known as Field-Oriented Control (FOC). This technique involves transforming the three-phase currents and voltages into a rotating reference frame, commonly referred to as the “dq” frame. In this frame, the torque/speed and flux components are decoupled, allowing for independent control, by doing so, the motor’s speed can be regulated accurately and maintain a constant flux which is crucial to ensure optimal motor performance and efficiency. The research focused on studying and simulating a field-oriented control system using fuzzy control techniques for an induction motor. The aim was to address the issue of parameter variations, particularly the change in rotor resistance during motor operation, which causes the control system to deviate from the desired direction. This deviation implies to an increase in the magnetic flux value, specifically the flux component on the q-axis. By employing fuzzy logic techniques to regulate flux vector’s components in the dq frame, this problem was successfully resolved, ensuring that the magnetic flux value remains within the nominal limits. To enhance the control system’s performance, response speed, and efficiency of the motor, sliding mode controllers were implemented to regulate the current in the inner loop. The simulation results demonstrated the proficiency of the proposed methodology.

Coordination of Regulation Devices for Damping Power Oscillations in a Dynamic Disturbance Context: A Fuzzy Logic-Based Approach Applied to the Electrical Grid of the Republic of Congo

This article presents a fuzzy logic-based approach to coordinate the control devices of the power system, such as Power System Stabilizers (PSS) and Static Synchronous Compensators (STATCOM), to damp power oscillations caused by dynamic disturbances. At first, we used the Lyapunov method to study the dynamic stability of the power grid in the Republic of Congo. This method allowed us to analyze the eigenvalues of the state variable matrix and highlight the eigenvalues in the complex plane. Secondly, we proposed a fuzzy logic-based controller to account for uncertainties existing near the thresholds. The inputs to this controller are the generator speed and generator rotor angle. We demonstrated the effectiveness and feasibility of this fuzzy control by applying it to the power grid of the Republic of Congo, with three power stabilizers and two STATCOMs. .