Specifying redundancy tactics as crosscutting concerns using aspect-oriented modeling

Various redundancy tactics can be modeled at the design stage of safety-critical systems thereby providing a set of fault-tolerance guidelines for subsequent development activities. However, existing approaches usually interweave redundancy tactics into the functional models making them complex and cluttered; the maintenance of such models is time-consuming and error-prone. To address this problem, we provide a modeling approach to separate the redundancy tactics from the base functional models using aspect-oriented modeling. More specifically, the conceptual models of the redundancy tactics and their semantic constraints are first defined for deriving the relevant aspects. Subsequently, a UML profile is proposed to specify the tactic aspects followed by mapping these concepts to the corresponding concepts of aspect-oriented modeling based on pre-defined principles. In accordance with our proposed profile, reuse directives are applied to handle the overlap of structural features between redundancy tactics and other kinds of tactic. Based on our tactic aspects and their configured attributes, a weaving algorithm is proposed to associate the tactic aspects with the base functional models. The proposed approach is compared with a traditional tactic modeling approach using two safety-critical systems, revealing that： 1） our approach significantly reduces the number of extra model elements needed in the tactic design stage; 2） our approach can largely avoid the impact of changing of the base functional model as the model evolves.

Modeling and Analyzing Web Application with Aspect-Oriented Hierarchical Coloured Petri Nets

Aspect-oriented modeling can uncover potential design faults, yet most existing work fails to achieve both separation and composition in a natural and succinct way. This study presents an aspect-oriented modeling and analysis approach with hierarchical Coloured Petri Nets(HCPN). HCPN has sub-models and well-defined semantics combining a set of submodels. These two characteristics of HCPN are nicely integrated into aspect oriented modeling. Submodels are used to model aspects while the combination mechanism contributes to aspects weaving. Furthermore, the woven aspect oriented HCPN model can be simulated and analyzed by the CPN Tools. A systematic web application case study is conducted. The results show the system original properties are satisfied after weaving aspects and all design flaws are revealed. As such, the approach can support web application design and analysis in an aspect-oriented fashion concisely and effectively.

Predictive modeling for postoperative delirium in elderly patients with abdominal malignancies using synthetic minority oversampling technique

BACKGROUND Postoperative delirium,particularly prevalent in elderly patients after abdominal cancer surgery,presents significant challenges in clinical management.AIM To develop a synthetic minority oversampling technique(SMOTE)-based model for predicting postoperative delirium in elderly abdominal cancer patients.METHODS In this retrospective cohort study,we analyzed data from 611 elderly patients who underwent abdominal malignant tumor surgery at our hospital between September 2020 and October 2022.The incidence of postoperative delirium was recorded for 7 d post-surgery.Patients were divided into delirium and non-delirium groups based on the occurrence of postoperative delirium or not.A multivariate logistic regression model was used to identify risk factors and develop a predictive model for postoperative delirium.The SMOTE technique was applied to enhance the model by oversampling the delirium cases.The model’s predictive accuracy was then validated.RESULTS In our study involving 611 elderly patients with abdominal malignant tumors,multivariate logistic regression analysis identified significant risk factors for postoperative delirium.These included the Charlson comorbidity index,American Society of Anesthesiologists classification,history of cerebrovascular disease,surgical duration,perioperative blood transfusion,and postoperative pain score.The incidence rate of postoperative delirium in our study was 22.91%.The original predictive model(P1)exhibited an area under the receiver operating characteristic curve of 0.862.In comparison,the SMOTE-based logistic early warning model(P2),which utilized the SMOTE oversampling algorithm,showed a slightly lower but comparable area under the curve of 0.856,suggesting no significant difference in performance between the two predictive approaches.CONCLUSION This study confirms that the SMOTE-enhanced predictive model for postoperative delirium in elderly abdominal tumor patients shows performance equivalent to that of traditional methods,effectively addressing data imbalance.

Volume-averaged modeling of multiphase solidification with equiaxed crystal sedimentation in a steel ingot

Macrosegregation is a critical factor that limits the mechanical properties of materials.The impact of equiaxed crystal sedimentation on macrosegregation has been extensively studied,as it plays a significant role in determining the distribution of alloying elements and impurities within a material.To improve macrosegregation in steel connecting shafts,a multiphase solidification model that couples melt flow,heat transfer,microstructure evolution,and solute transport was established based on the volume-averaged Eulerian-Eulerian approach.In this model,the effects of liquid phase,equiaxed crystals,columnar dendrites,and columnar-to-equiaxed transition(CET)during solidification and evolution of microstructure can be considered simultaneously.The sedimentation of equiaxed crystals contributes to negative macrosegregation,where regions between columnar dendrites and equiaxed crystals undergo significant A-type positive macrosegregation due to the CET.Additionally,noticeable positive macrosegregation occurs in the area of final solidification in the ingot.The improvement in macrosegregation is beneficial for enhancing the mechanical properties of connecting shafts.To mitigate the thermal convection of molten steel resulting from excessive superheating,reducing the superheating during casting without employing external fields or altering the design of the ingot mold is indeed an effective approach to control macrosegregation.

Aspect-Oriented Modeling and Verification with Finite State Machines

Aspect-oriented programming modularizes crosscutting concerns into aspects with the advice invoked at the specified points of program execution. Aspects can be used in a harmful way that invalidates desired properties and even destroys the conceptual integrity of programs. To assure the quality of an aspect-oriented system, rigorous analysis and design of aspects are highly desirable. In this paper, we present an approach to aspect-oriented modeling and verification with finite state machines. Our approach provides explicit notations （e.g., pointcut, advice and aspect） for capturing crosscutting concerns and incremental modification requirements with respect to class state models. For verification purposes, we compose the aspect models and class models in an aspect-oriented model through a weaving mechanism. Then we transform the woven models and the class models not affected by the aspects into FSP （Finite State Processes）, which are to be checked by the LTSA （Labeled Transition System Analyzer） model checker against the desired system properties. We have applied our approach to the modeling and verification of three aspect-oriented systems. To further evaluate the effectiveness of verification, we created a large number of flawed aspect models and verified them against the system requirements. The results show that the verification has revealed all flawed models. This indicates that our approach is effective in quality assurance of aspect-oriented state models. As such, our approach can be used for model-checking state-based specification of aspect-oriented design and can uncover some system design problems before the system is implemented.

Predicting the probability distribution of Martian rocks mechanical property based on microscale rock mechanical experiments and accurate grain-based modeling

The exploration of Mars would heavily rely on Martian rocks mechanics and engineering technology.As the mechanical property of Martian rocks is uncertain,it is of utmost importance to predict the probability distribution of Martian rocks mechanical property for the success of Mars exploration.In this paper,a fast and accurate probability distribution method for predicting the macroscale elastic modulus of Martian rocks was proposed by integrating the microscale rock mechanical experiments(micro-RME),accurate grain-based modeling(AGBM)and upscaling methods based on reliability principles.Firstly,the microstructure of NWA12564 Martian sample and elastic modulus of each mineral were obtained by micro-RME with TESCAN integrated mineral analyzer(TIMA)and nanoindentation.The best probability distribution function of the minerals was determined by Kolmogorov-Smirnov(K-S)test.Secondly,based on best distribution function of each mineral,the Monte Carlo simulations(MCS)and upscaling methods were implemented to obtain the probability distribution of upscaled elastic modulus.Thirdly,the correlation between the upscaled elastic modulus and macroscale elastic modulus obtained by AGBM was established.The accurate probability distribution of the macroscale elastic modulus was obtained by this correlation relationship.The proposed method can predict the probability distribution of Martian rocks mechanical property with any size and shape samples.

Background removal from global auroral images:Data-driven dayglow modeling

Global images of auroras obtained by cameras on spacecraft are a key tool for studying the near-Earth environment.However,the cameras are sensitive not only to auroral emissions produced by precipitating particles,but also to dayglow emissions produced by photoelectrons induced by sunlight.Nightglow emissions and scattered sunlight can contribute to the background signal.To fully utilize such images in space science,background contamination must be removed to isolate the auroral signal.Here we outline a data-driven approach to modeling the background intensity in multiple images by formulating linear inverse problems based on B-splines and spherical harmonics.The approach is robust,flexible,and iteratively deselects outliers,such as auroral emissions.The final model is smooth across the terminator and accounts for slow temporal variations and large-scale asymmetries in the dayglow.We demonstrate the model by using the three far ultraviolet cameras on the Imager for Magnetopause-to-Aurora Global Exploration(IMAGE)mission.The method can be applied to historical missions and is relevant for upcoming missions,such as the Solar wind Magnetosphere Ionosphere Link Explorer(SMILE)mission.

Surrogate modeling for unsaturated infiltration via the physics and equality-constrained artificial neural networks

Machine learning(ML)provides a new surrogate method for investigating groundwater flow dynamics in unsaturated soils.Traditional pure data-driven methods(e.g.deep neural network,DNN)can provide rapid predictions,but they do require sufficient on-site data for accurate training,and lack interpretability to the physical processes within the data.In this paper,we provide a physics and equalityconstrained artificial neural network(PECANN),to derive unsaturated infiltration solutions with a small amount of initial and boundary data.PECANN takes the physics-informed neural network(PINN)as a foundation,encodes the unsaturated infiltration physical laws(i.e.Richards equation,RE)into the loss function,and uses the augmented Lagrangian method to constrain the learning process of the solutions of RE by adding stronger penalty for the initial and boundary conditions.Four unsaturated infiltration cases are designed to test the training performance of PECANN,i.e.one-dimensional(1D)steady-state unsaturated infiltration,1D transient-state infiltration,two-dimensional(2D)transient-state infiltration,and 1D coupled unsaturated infiltration and deformation.The predicted results of PECANN are compared with the finite difference solutions or analytical solutions.The results indicate that PECANN can accurately capture the variations of pressure head during the unsaturated infiltration,and present higher precision and robustness than DNN and PINN.It is also revealed that PECANN can achieve the same accuracy as the finite difference method with fewer initial and boundary training data.Additionally,we investigate the effect of the hyperparameters of PECANN on solving RE problem.PECANN provides an effective tool for simulating unsaturated infiltration.

A methodology for damage evaluation of underground tunnels subjected to static loading using numerical modeling

We have proposed a methodology to assess the robustness of underground tunnels against potential failure.This involves developing vulnerability functions for various qualities of rock mass and static loading intensities.To account for these variations,we utilized a Monte Carlo Simulation(MCS)technique coupled with the finite difference code FLAC^(3D),to conduct two thousand seven hundred numerical simulations of a horseshoe tunnel located within a rock mass with different geological strength index system(GSIs)and subjected to different states of static loading.To quantify the severity of damage within the rock mass,we selected one stress-based(brittle shear ratio(BSR))and one strain-based failure criterion(plastic damage index(PDI)).Based on these criteria,we then developed fragility curves.Additionally,we used mathematical approximation techniques to produce vulnerability functions that relate the probabilities of various damage states to loading intensities for different quality classes of blocky rock mass.The results indicated that the fragility curves we obtained could accurately depict the evolution of the inner and outer shell damage around the tunnel.Therefore,we have provided engineers with a tool that can predict levels of damages associated with different failure mechanisms based on variations in rock mass quality and in situ stress state.Our method is a numerically developed,multi-variate approach that can aid engineers in making informed decisions about the robustness of underground tunnels.

Artificial intelligence-driven radiomics study in cancer:the role of feature engineering and modeling

Modern medicine is reliant on various medical imaging technologies for non-invasively observing patients’anatomy.However,the interpretation of medical images can be highly subjective and dependent on the expertise of clinicians.Moreover,some potentially useful quantitative information in medical images,especially that which is not visible to the naked eye,is often ignored during clinical practice.In contrast,radiomics performs high-throughput feature extraction from medical images,which enables quantitative analysis of medical images and prediction of various clinical endpoints.Studies have reported that radiomics exhibits promising performance in diagnosis and predicting treatment responses and prognosis,demonstrating its potential to be a non-invasive auxiliary tool for personalized medicine.However,radiomics remains in a developmental phase as numerous technical challenges have yet to be solved,especially in feature engineering and statistical modeling.In this review,we introduce the current utility of radiomics by summarizing research on its application in the diagnosis,prognosis,and prediction of treatment responses in patients with cancer.We focus on machine learning approaches,for feature extraction and selection during feature engineering and for imbalanced datasets and multi-modality fusion during statistical modeling.Furthermore,we introduce the stability,reproducibility,and interpretability of features,and the generalizability and interpretability of models.Finally,we offer possible solutions to current challenges in radiomics research.

Progressive fragmentation of granular assemblies within rockslides: Insights from discrete-continuous numerical modeling

Rock fragmentation plays a critical role in rock avalanches,yet conventional approaches such as classical granular flow models or the bonded particle model have limitations in accurately characterizing the progressive disintegration and kinematics of multi-deformable rock blocks during rockslides.The present study proposes a discrete-continuous numerical model,based on a cohesive zone model,to explicitly incorporate the progressive fragmentation and intricate interparticle interactions inherent in rockslides.Breakable rock granular assemblies are released along an inclined plane and flow onto a horizontal plane.The numerical scenarios are established to incorporate variations in slope angle,initial height,friction coefficient,and particle number.The evolutions of fragmentation,kinematic,runout and depositional characteristics are quantitatively analyzed and compared with experimental and field data.A positive linear relationship between the equivalent friction coefficient and the apparent friction coefficient is identified.In general,the granular mass predominantly exhibits characteristics of a dense granular flow,with the Savage number exhibiting a decreasing trend as the volume of mass increases.The process of particle breakage gradually occurs in a bottom-up manner,leading to a significant increase in the angular velocities of the rock blocks with increasing depth.The simulation results reproduce the field observations of inverse grading and source stratigraphy preservation in the deposit.We propose a disintegration index that incorporates factors such as drop height,rock mass volume,and rock strength.Our findings demonstrate a consistent linear relationship between this index and the fragmentation degree in all tested scenarios.

Discontinuity development patterns and the challenges for 3D discrete fracture network modeling on complicated exposed rock surfaces

Natural slopes usually display complicated exposed rock surfaces that are characterized by complex and substantial terrain undulation and ubiquitous undesirable phenomena such as vegetation cover and rockfalls.This study presents a systematic outcrop research of fracture pattern variations in a complicated rock slope,and the qualitative and quantitative study of the complex phenomena impact on threedimensional(3D)discrete fracture network(DFN)modeling.As the studies of the outcrop fracture pattern have been so far focused on local variations,thus,we put forward a statistical analysis of global variations.The entire outcrop is partitioned into several subzones,and the subzone-scale variability of fracture geometric properties is analyzed(including the orientation,the density,and the trace length).The results reveal significant variations in fracture characteristics(such as the concentrative degree,the average orientation,the density,and the trace length)among different subzones.Moreover,the density of fracture sets,which is approximately parallel to the slope surface,exhibits a notably higher value compared to other fracture sets across all subzones.To improve the accuracy of the DFN modeling,the effects of three common phenomena resulting from vegetation and rockfalls are qualitatively analyzed and the corresponding quantitative data processing solutions are proposed.Subsequently,the 3D fracture geometric parameters are determined for different areas of the high-steep rock slope in terms of the subzone dimensions.The results show significant variations in the same set of 3D fracture parameters across different regions with density differing by up to tenfold and mean trace length exhibiting differences of 3e4 times.The study results present precise geological structural information,improve modeling accuracy,and provide practical solutions for addressing complex outcrop issues.

The relationship between compartment models and their stochastic counterparts:A comparative study with examples of the COVID-19 epidemic modeling

Deterministic compartment models(CMs)and stochastic models,including stochastic CMs and agent-based models,are widely utilized in epidemic modeling.However,the relationship between CMs and their corresponding stochastic models is not well understood.The present study aimed to address this gap by conducting a comparative study using the susceptible,exposed,infectious,and recovered(SEIR)model and its extended CMs from the coronavirus disease 2019 modeling literature.We demonstrated the equivalence of the numerical solution of CMs using the Euler scheme and their stochastic counterparts through theoretical analysis and simulations.Based on this equivalence,we proposed an efficient model calibration method that could replicate the exact solution of CMs in the corresponding stochastic models through parameter adjustment.The advancement in calibration techniques enhanced the accuracy of stochastic modeling in capturing the dynamics of epidemics.However,it should be noted that discrete-time stochastic models cannot perfectly reproduce the exact solution of continuous-time CMs.Additionally,we proposed a new stochastic compartment and agent mixed model as an alternative to agent-based models for large-scale population simulations with a limited number of agents.This model offered a balance between computational efficiency and accuracy.The results of this research contributed to the comparison and unification of deterministic CMs and stochastic models in epidemic modeling.Furthermore,the results had implications for the development of hybrid models that integrated the strengths of both frameworks.Overall,the present study has provided valuable epidemic modeling techniques and their practical applications for understanding and controlling the spread of infectious diseases.

Hybrid modeling for carbon monoxide gas-phase catalytic coupling to synthesize dimethyl oxalate process

Ethylene glycol(EG)plays a pivotal role as a primary raw material in the polyester industry,and the syngas-to-EG route has become a significant technical route in production.The carbon monoxide(CO)gas-phase catalytic coupling to synthesize dimethyl oxalate(DMO)is a crucial process in the syngas-to-EG route,whereby the composition of the reactor outlet exerts influence on the ultimate quality of the EG product and the energy consumption during the subsequent separation process.However,measuring product quality in real time or establishing accurate dynamic mechanism models is challenging.To effectively model the DMO synthesis process,this study proposes a hybrid modeling strategy that integrates process mechanisms and data-driven approaches.The CO gas-phase catalytic coupling mechanism model is developed based on intrinsic kinetics and material balance,while a long short-term memory(LSTM)neural network is employed to predict the macroscopic reaction rate by leveraging temporal relationships derived from archived measurements.The proposed model is trained semi-supervised to accommodate limited-label data scenarios,leveraging historical data.By integrating these predictions with the mechanism model,the hybrid modeling approach provides reliable and interpretable forecasts of mass fractions.Empirical investigations unequivocally validate the superiority of the proposed hybrid modeling approach over conventional data-driven models(DDMs)and other hybrid modeling techniques.

Exploring Capillary Fringe Flow:Quasilinear Modeling with Kirchhoff Transforms and Gardner Model

Recent studies have underscored the significance of the capillary fringe in hydrological and biochemical processes.Moreover,its role in shallow waters is expected to be considerable.Traditionally,the study of groundwater flow has centered on unsaturated-saturated zones,often overlooking the impact of the capillary fringe.In this study,we introduce a steady-state two-dimensional model that integrates the capillary fringe into a 2-D numerical solution.Our novel approach employs the potential form of the Richards equation,facilitating the determination of boundaries,pressures,and velocities across different ground surface zones.We utilized a two-dimensional Freefem++finite element model to compute the stationary solution.The validation of the model was conducted using experimental data.We employed the OFAT(One_Factor-At-Time)method to identify the most sensitive soil parameters and understand how changes in these parameters may affect the behavior and water dynamics of the capillary fringe.The results emphasize the role of hydraulic conductivity as a key parameter influencing capillary fringe shape and dynamics.Velocity values within the capillary fringe suggest the prevalence of horizontal flow.By variation of the water table level and the incoming flow q0,we have shown the correlation between water table elevation and the upper limit of the capillary fringe.

A Hierarchical Modeling Framework for Electrochemical Behaviors in Lithium-Ion Batteries with Detailed Structures

The accurate representation of lithium plating and aging phenomena has posed a persistent challenge within the battery research community.Empirical evidence underscores the pivotal role of cell structure in influencing aging behaviors and lithium plating within lithium-ion batteries(LIBs).Available lithium-ion plating models often falter in detailed description when integrating the structural intricacies.To address this challenge,this study proposes an innovative hierarchical model that intricately incorporates the layered rolling structure in cells.Notably,our model demonstrates a remarkable capacity to predict the non-uniform distribution of current density and overpotential along the rolling direction of LIBs.Subsequently,we delve into an insightful exploration of the structural factors that influence lithium plating behavior,leveraging the foundation laid by our established model.Furthermore,we easily update the hierarchical model by considering aging factors.This aging model effectively anticipates capacity fatigue and lithium plating tendencies across individual layers of LIBs,all while maintaining computational efficiency.In light of our findings,this model yields novel perspectives on capacity fatigue dynamics and local lithium plating behaviors,offering a substantial advancement compared to existing models.This research paves the way for more efficient and tailored LIB design and operation,with broad implications for energy storage technologies.

Total ionizing dose effect modeling method for CMOS digital-integrated circuit

Simulating the total ionizing dose(TID)of an electrical system using transistor-level models can be difficult and expensive,particularly for digital-integrated circuits(ICs).In this study,a method for modeling TID effects in complementary metaloxide semiconductor(CMOS)digital ICs based on the input/output buffer information specification(IBIS)was proposed.The digital IC was first divided into three parts based on its internal structure:the input buffer,output buffer,and functional area.Each of these three parts was separately modeled.Using the IBIS model,the transistor V-I characteristic curves of the buffers were processed,and the physical parameters were extracted and modeled using VHDL-AMS.In the functional area,logic functions were modeled in VHDL according to the data sheet.A golden digital IC model was developed by combining the input buffer,output buffer,and functional area models.Furthermore,the golden ratio was reconstructed based on TID experimental data,enabling the assessment of TID effects on the threshold voltage,carrier mobility,and time series of the digital IC.TID experiments were conducted using a CMOS non-inverting multiplexer,NC7SZ157,and the results were compared with the simulation results,which showed that the relative errors were less than 2%at each dose point.This confirms the practicality and accuracy of the proposed modeling method.The TID effect model for digital ICs developed using this modeling technique includes both the logical function of the IC and changes in electrical properties and functional degradation impacted by TID,which has potential applications in the design of radiation-hardening tolerance in digital ICs.

Modularized and Parametric Modeling Technology for Finite Element Simulations of Underground Engineering under Complicated Geological Conditions

The surrounding geological conditions and supporting structures of underground engineering are often updated during construction,and these updates require repeated numerical modeling.To improve the numerical modeling efficiency of underground engineering,a modularized and parametric modeling cloud server is developed by using Python codes.The basic framework of the cloud server is as follows:input the modeling parameters into the web platform,implement Rhino software and FLAC3D software to model and run simulations in the cloud server,and return the simulation results to the web platform.The modeling program can automatically generate instructions that can run the modeling process in Rhino based on the input modeling parameters.The main modules of the modeling program include modeling the 3D geological structures,the underground engineering structures,and the supporting structures as well as meshing the geometric models.In particular,various cross-sections of underground caverns are crafted as parametricmodules in themodeling program.Themodularized and parametric modeling program is used for a finite element simulation of the underground powerhouse of the Shuangjiangkou Hydropower Station.This complicatedmodel is rapidly generated for the simulation,and the simulation results are reasonable.Thus,this modularized and parametric modeling program is applicable for three-dimensional finite element simulations and analyses.

Modeling Analysis of Factors Influencing Wind-Borne Seed Dispersal: A Case Study on Dandelion

A weed is a plant that thrives in areas of human disturbance, such as gardens, fields, pastures, waysides, and waste places where it is not intentionally cultivated. Dispersal affects community dynamics and vegetation response to global change. The process of seed disposal is influenced by wind, which plays a crucial role in determining the distance and probability of seed dispersal. Existing models of seed dispersal consider wind direction but fail to incorporate wind intensity. In this paper, a novel seed disposal model was proposed in this paper, incorporating wind intensity based on relevant references. According to various climatic conditions, including temperate, arid, and tropical regions, three specific regions were selected to establish a wind dispersal model that accurately reflects the density function distribution of dispersal distance. Additionally, dandelions growth is influenced by a multitude of factors, encompassing temperature, humidity, climate, and various environmental variables that necessitate meticulous consideration. Based on Factor Analysis model, which completely considers temperature, precipitation, solar radiation, wind, and land carrying capacity, a conclusion is presented, indicating that the growth of seeds is primarily influenced by plant attributes and climate conditions, with the former exerting a relatively stronger impact. Subsequently, the remaining two plants were chosen based on seed weight, yielding consistent conclusion.

Effects of Andrade and Burgers rheologies on glacial isostatic adjustment modeling in Antarctica

Variations in ice mass deform the Earth and modify its gravity field,a process known as Glacial Isostatic Adjustment(GIA).GIA in Antarctica remains poorly constrained due to the cumulative effect of past and present ice-mass changes,the unknown history of the past ice-mass change,and the uncertainties on the mechanical properties of the Earth.This paper investigates the effect of using Andrade and Burgers viscoelastic rheologies,rather than the commonly used Maxwell rheology,to model GIA-induced deformation in Antarctica.The Love number and Green's function formalism are used to compute the radial surface displacements and the gravity changes induced by the past and present ice-mass changes.We consider an Earth model whose elastic properties and radial structure are averaged from the Preliminary Reference Earth Model and two viscosity profiles to account for the recently published results on the present ice-mass changes.Using the three rheological laws affects the temporal response of the Earth differently,leading to smaller discrepancies than those induced by the two viscosity structures.The differences are the largest between Maxwell and Burgers rheologies during the 100-1000 years following the beginning of the surface-mass change.Results show that using the Andrade and Burgers rheologies allows the Earth to respond on decennial to centennial time scales,up to 10 m more than Maxwell.Considering only the recent ice-mass changes,the deformation rates derived from Burgers and Andrade rheologies are several times larger than those estimated by Maxwell rheology.