Simple Model Research Articles

Predictive modeling of medication adherence in post myocardial infarction patients: a bayesian approach using beta-regression.

Predicting medication adherence in post myocardial infarction (MI) patients has the potential to improve patient outcomes. Most adherence prediction models dichotomize adherence metrics and status. This study aims to develop medication adherence prediction models that avoid dichotomizing adherence metrics and to test whether a simplified model including only 90-days adherence data would perform similarly to a full multivariable model. Post MI adult patients were followed for 1-year post the event. Data from pharmacy records were used to calculate proportion of days covered (PDC). We used Bayesian beta-regression to model PDC as a proportion, avoiding dichotomization. For each medication group, statins, P2Y12 inhibitors and aspirin, two prediction models were developed, a full and a simplified model. 3692 patients were included for model development. The median (Inter quartile range) PDC at 1-year for statins, P2Y12 inhibitors and aspirin was 0.8 (0.33, 1.00), 0.79 (0.23, 0.99) and 0.79 (0.23, 0.99), respectively. All models showed good fit to the data by visual predictive checks. Bayesian R2 for statins, P2Y12 inhibitors and aspirin models were 61.4%,71.2% and 55.2%, respectively. The simplified models showed similar performance compared with full complex models as evaluated by cross validation. We developed Bayesian multilevel models for statins, P2Y12 inhibitors and aspirin in post MI patients that handled 1-year PDC as a proportion using the beta-distribution. In addition, simplified models, with 90-days adherence as single predictor, had similar performance compared with full complex models.

Realistic modelling of contributions by floor slabs in the earthquake safety assessment of buildings

ABSTRACT The conventional structural design of buildings often neglects the significant contributions of the coupling action of the floor slabs, potentially leading to unsafe designs against seismic actions. The interaction between reinforced concrete (RC) frames and shear walls, especially through slabs, plays a crucial role in the structure’s behaviour under seismic loading. In Australian construction, where wall-type systems are prevalent, it is essential to understand the complex interactions between coupled walls and columns facilitated by slabs. This study addresses this issue by proposing an innovative strain-based model, validated through finite element analysis. The proposed model, when compared with existing simplified models, demonstrates superior accuracy and effectiveness. This innovative approach not only enhances our understanding of seismic behaviour but also offers a straightforward solution that can be easily implemented in practice. Key findings reveal that slab interaction increases material strain and inelastic force capacity while reducing displacement capacity, particularly affecting smaller elements like gravity load-carrying columns. This improved understanding can lead to more effective strategies for enhancing the seismic resilience of RC buildings.

An improved simulation based method for selection of cell in cellular network

An improved simulation based method for selection of cell in cellular network

Encyclopædia Inflationaris

The current flow of high-accuracy astrophysical data, among which are the Cosmic Microwave Background (CMB) measurements by the Planck satellite, offers an unprecedented opportunity to constrain the inflationary theory. This is however a challenging project given the size of the inflationary landscape which contains hundreds of different scenarios. Given that there is currently no observational evidence for primordial non-Gaussianities, isocurvature perturbations or any other non-minimal extension of the inflationary paradigm, a reasonable approach is to consider the simplest models first, namely the slow-roll single-field models with minimal kinetic terms. This still leaves us with a very populated landscape, the exploration of which requires new and efficient strategies. It has been customary to tackle this problem by means of approximate model-independent methods while a more ambitious alternative is to study the inflationary scenarios one by one. We have developed the publicly available runtime library ASPIC11https://github.com/cosmicinflation/aspic. to implement this last approach. The ASPIC code provides all routines needed to quickly derive reheating-consistent observable predictions within this class of scenarios. ASPIC has been designed as an evolutive code which presently supports 118 different models. In this paper, for each of the ASPIC models, we present and collect new results in a systematic manner, thereby constituting the first Encyclopædia Inflationaris.

A contact-based analysis of local energetic frustration dynamics identifies key residues enabling RfaH fold-switch.

Fold-switching enables metamorphic proteins to reversibly interconvert between two highly dissimilar native states to regulate their protein functions. While about 100 proteins have been identified to undergo fold-switching, unveiling the key residues behind this mechanism for each protein remains challenging. Reasoning that fold-switching in proteins is driven by dynamic changes in local energetic frustration, we combined fold-switching simulations generated using simplified structure-based models with frustration analysis to identify key residues involved in this process based on the change in the density of minimally frustrated contacts during refolding. Using this approach to analyze the fold-switch of the bacterial transcription factor RfaH, we identified 20 residues that significantly change their frustration during its fold-switch, some of which have been experimentally and computationally reported in previous works. Our approach, which we developed as an additional module for the FrustratometeR package, highlights the role of local frustration dynamics in protein fold-switching and offers a robust tool to enhance our understanding of other proteins with significant conformational shifts.

Validity of simplified Cariogram models versus conventional Cariogram model in caries risk assessment in young adults: Cross-sectional observational study

Validity of simplified Cariogram models versus conventional Cariogram model in caries risk assessment in young adults: Cross-sectional observational study

Nonlinear Optics: Physics, Analysis, and Numerics

When high-intensity electromagnetic waves at optical frequencies interact with solids and/or nanostructures the materials’ response cannot anymore be described via simple linear relations. The resulting science of nonlinear optics has recently witnessed exiting developments that have brought to the fore numerous mathematical challenges that need to be addressed in order to fully exploit the opportunities that result from these developments. The mathematical modeling involves a system of partial differential equations where the Maxwell equations are coupled to evolution equations of the materials and their response to electromagnetic fields. Typically, the full coupled systems are quite complicated or even intractable so that the derivation, the analysis, and the numerical treatment of simplified effective models is often indispensable. In turn, this requires the close cooperation between researchers from theoretical physics and analysis/numerics in order to push forward the field on nonlinear optics.

Data-Driven Relationship for Reduction Factor of Ballasted Railway Bridge Deflections Due to Load Distribution Within Track

Increasing the operating speed of the trains on modern networks necessitates performing dynamic analyses to assess the performance of bridges under passage of trains. The detailed investigation of their responses requires constructing complex computational models capable to take the train–track–bridge interaction effects into account. Such models have successfully been developed; however, employing those elaborated models for practical engineering applications, or to perform studies that require a large number of analyses may become infeasible. Among such situations are conducting probabilistic investigations, screening of entire networks, or sensitivity analyses. These concerns have been addressed by employing simplified models mostly relying on moving load modeling strategy which disregards the train–track–bridge interaction effects. Those neglected contributions can be compensated by implementing additional correction factors. The distribution of loads within track is one of those disregarded effects where a reduction factor is recommended by design guidelines to take its contribution into account. It has been shown that the existing relationship for these reduction factors delivers an acceptable performance for vertical accelerations, while showing a less favorable performance for displacements. Then, a data-driven strategy is adopted in this study to propose easy-to-apply relationships for reduction factors of deflections, due to load distribution within the track. In this context, three different distributive lengths of triangular load footprints have been considered, namely 2.0, 2.5 and 3.0[Formula: see text]m. The procedure employed has trained and tested for more than 1[Formula: see text]200 train configurations, comprising conventional, articulated and regular vehicles, and including several tens of thousand data points for each distributive length. The performance observed in the new models revealed a considerable improvement with respect to the existing relationship.

Unveiling the core constructs: A statistical approach to evaluating user experience with Chatbots in higher education (A case study from a university in Ecuador)

Introduction: Chatbots are increasingly utilized in education, offering real-time, personalized communication. While research has explored technical aspects of chatbots, user experience remains under-investigated. This study examines a model for evaluating user experience and satisfaction with chatbots in higher education. Methodology: A four-factor model (information quality, system quality, chatbot experience, user satisfaction) was proposed based on prior research. An alternative two-factor model emerged through exploratory factor analysis, focusing on “Chatbot Response Quality” and “User Experience and Satisfaction with the Chatbot.” Surveys were distributed to students and faculty at a university in Ecuador to collect data. Confirmatory factor analysis validated both models. Results: The two-factor model explained a significantly greater proportion of the data’s variance (55.2%) compared to the four-factor model (46.4%). Conclusion: This study suggests that a simpler model focusing on chatbot response quality and user experience is more effective for evaluating chatbots in education. Future research can explore methods to optimize these factors and improve the learning experience for students.

The Impact of Model Misspecification on Phylogenetic Network Inference

The development of statistical methods to infer species phylogenies with reticulations (species networks) has led to many discoveries of gene flow between distinct species. These methods typically assume only incomplete lineage sorting and introgression. Given that phylogenetic networks can be arbitrarily complex, these methods might compensate for model misspecification by increasing the number of dimensions beyond the true value. Herein, we explore the effect of potential model misspecification, including the negligence of gene tree estimation error (GTEE) and assumption of a single substitution rate for all genomic loci, on the accuracy of phylogenetic network inference using both simulated and biological data. In particular, we assess the accuracy of estimated phylogenetic networks as well as test statistics for determining whether a network is the correct evolutionary history, as opposed to the simpler model that is a tree. We found that while GTEE negatively impacts the performance of test statistics to determine the “treeness” of the evolutionary history of a data set, running those tests on triplets of taxa and correcting for multiple-testing significantly ameliorates the problem. We also found that accounting for substitution rate heterogeneity improves the reliability of full Bayesian inference methods of phylogenetic networks, whereas summary statistic methods are robust to GTEE and rate heterogeneity, though currently require manual inspection to determine the network complexity.

Development of a New Thermal-Hydraulic Module for FRENETIC, a Code for the Multiphysics Analysis of Liquid Metal–Cooled Reactors

This paper describes the development of a new thermal-hydraulic (TH) module for the Fast REactor NEutronics/Thermal-hydraulICs (FRENETIC) multiphysics code for the full-core simulation of liquid metal–cooled fast reactors, developed at Politecnico di Torino. The code performs steady-state and transient neutronic (NE) and TH coupled calculations while maintaining a relatively low computational cost thanks to the adoption of simplified physical models. The NE module implements the nodal formulation of the multigroup neutron diffusion equations with delayed neutron precursors whereas the TH module treats the reactor hexagonal assemblies as separate channels, which are individually modeled as one-dimensional in the axial direction, accounting for the thermal coupling in the horizontal direction. The new TH module is more robust and portable while providing improved performance with respect to the previous implementation—also thanks to the adopted OpenMP parallelization. Some physical aspects that were previously neglected, such as the thermal inertia of nonfuel rods, have also been included in the model. The development was carried out in accordance with current best practices for code design, implementation, and testing, thus rendering the code easier to be maintained and possibly to be extended in the future. The code usability has also been improved by means of a set of Python classes purposely developed to simplify the input generation and postprocessing phases. This can potentially widen the usage of FRENETIC within the fast reactor community for the simulation of full-core coupled NE-TH transients and/or as a platform to test new solution methods. The paper also includes the application of this new FRENETIC version to a representative configuration of the Advanced Lead-cooled Fast Reactor European Demonstrator (ALFRED) core design. First, the nominal operating conditions of the ALFRED reactor were simulated, proving that the new upgrade of the code is faster and more robust with respect to the previous one. Then, two accidental transients where NE-TH feedback effects are relevant—an unprotected loss of flow and a total instantaneous blockage of a single fuel assembly—were considered.

Biological Cell Response to Electric Field: A Review of Equivalent Circuit Models and Future Challenges.

Biological cells, characterized by complex and dynamic structures, demand precise models for comprehensive understanding, especially when subjected to external factors such as electric fields (EF) for manipulation or treatment. This interaction is integral to technologies like pulsed electric fields (PEF), inducing reversible and irreversible structural variations. Our study explores both simplified and sophisticated equivalent circuit models for biological cells under the influence of an external EF, covering diverse cell structures from single- to double-shell configurations. The paper highlights challenges in circuit modeling, specifically addressing the incorporation of reversible or irreversible pores in the membrane during external EF interactions, emphasizing the need for further research to refine technical aspects in this field. Additionally, we review a comparative analysis of the performance and applicability of the proposed circuit models, providing insights into their strengths and limitations. This contributes to a deeper insight of the complexities associated with modeling biological cells under external EF influences, paving the way for enhanced applications in medical and technological domains in future.&#xD.

European croplands under climate change: Carbon input changes required to increase projected soil organic carbon stocks

Increasing soil organic carbon (SOC) stocks in agricultural systems is a pivotal strategy for promoting soil health and mitigating climate change. Global initiatives have set ambitious targets, aspiring to achieve an annual SOC stock increase of 4 ‰. In the European Union, the recently approved Nature Restoration Law aims to increase SOC stock trends in the top 30 cm of cropland mineral soils. However, current monitoring and reporting practices in some countries rely on simplistic SOC models with default parameters, which may not provide reliable predictions.In this paper, we study the feasibility of a 4 ‰ target in European croplands (i.e., an aspirational target proposed by The international “4 per 1000” Initiative), through estimations of required C input changes. To ensure robust predictions, we propose a novel calibration approach that links model parameters to pedo-climatic variables via statistical relationships from 16 long-term experiments. The effectiveness of the method is evaluated for three SOC models across 4281 sites from the European LUCAS soil survey.Our findings demonstrate that the statistical calibration of the multi-model ensemble improves the accuracy of 2015 and 2018 SOC stock predictions, compared to default parameterization. This improvement was however mainly due to the substantial enhancement of one of the models. According to the weighted multi-model mean, median C input changes to reach a 4 ‰ target for Northern, Central, and Southern Europe stand at 1.85, 1.20, and 0.13 Mg C ha−1 yr−1 under RCP 2.6, and 2.21, 1.26, and −0.10 Mg C ha−1 yr−1 under RCP 6.0, respectively.To achieve the aspirational 4 ‰ target, estimated C input change requirements exceed the predicted changes in net primary productivity under RCP 2.6 and RCP 6.0. This emphasizes the importance of strategic land-use and land-management interventions to enhance SOC stocks.

Interpretable machine learning models for the prediction of all-cause mortality and time to death in hemodialysis patients.

The elevated mortality and hospitalization rates among hemodialysis (HD) patients underscore the necessity for the development of accurate predictive tools. This study developed two models for predicting all-cause mortality and time to death-one using a comprehensive database and another simpler model based on demographic and clinical data without laboratory tests. A retrospective cohort study was conducted from January 2017 to June 2023. Two models were created: Model A with 85 variables and Model B with 22 variables. We assessed the models using random forest (RF), support vector machine, and logistic regression, comparing their performance via the AU-ROC. The RF regression model was used to predict time to death. To identify the most relevant factors for prediction, the Shapley value method was used. Among 359 HD patients, the RF model provided the most reliable prediction. The optimized Model A showed an AU-ROC of 0.86 ± 0.07, a sensitivity of 0.86, and a specificity of 0.75 for predicting all-cause mortality. It also had an R2 of 0.59 for predicting time to death. The optimized Model B had an AU-ROC of 0.80 ± 0.06, a sensitivity of 0.81, and a specificity of 0.70 for predicting all-cause mortality. In addition, it had an R2 of 0.81 for predicting time to death. Two new interpretable clinical tools have been proposed to predict all-cause mortality and time to death in HD patients using machine learning models. The minimal and readily accessible data on which Model B is based makes it a valuable tool for integrating into clinical decision-making processes.

Direct loss‐based seismic design of low‐rise base‐isolated reinforced concrete buildings

AbstractThis paper proposes a procedure to design low‐rise base‐isolated structures achieving a specific target level of earthquake‐induced loss (e.g., dollars, downtime) while complying with a predefined minimum level of structural reliability. The procedure is “direct” since the target loss is specified at the first step of the process, and virtually no design iterations are required. Direct loss‐based design (DLBD) is enabled by a simplified loss assessment module involving: (1) surrogate probabilistic seismic demand models representing the probability distribution of peak horizontal displacements and accelerations on top of the isolation layer conditional on different ground‐motion intensity levels; (2) approximations of the superstructure response; (3) simplified consequence models for isolation system and superstructure based on damage‐to‐loss ratios (economic loss or repair time); (4) simplified consequence models for acceleration‐ and drift‐sensitive non‐structural components, based on storey loss functions of a potential inventory of components. Given some basic geometrical parameters of the superstructure, DLBD provides the isolation system's force‐displacement curve and the required superstructure's strength complying with a selected loss target. The members' structural detailing follows the principles of direct displacement‐based design, sectional analysis, and the general theory of base isolation. The procedure is illustrated by designing six reinforced concrete wall buildings (two‐, three‐, and four‐storeys) base isolated with lead rubber bearings, to achieve predefined targets of expected repair time. Repair time is benchmarked against a more refined method adopting a cloud‐based non‐linear time history analysis, finding a maximum underestimation of 17%, thus confirming the dependability of DLBD. Such error is almost entirely attributable to the simplified estimation of peak floor accelerations, and it could be potentially eliminated by refining such estimation.

On human nanoscale synaptome: Morphology modeling and storage estimation.

One of the key challenges in neuroscience is to generate the human nanoscale connectome which requires comprehensive knowledge of synaptome forming the neural microcircuits. The synaptic architecture determines limits of individual mental capacity and provides the framework for understanding neurologic disorders. Here, I address morphology modeling and storage estimation for the human synaptome at the nanoscale. A synapse is defined as a pair of pairs [(presynaptic_neuron),(presynaptic_axonal_terminal);(postsynaptic_neuron),(postsynaptic_dendritic_terminal)]. Center coordinates, radius, and identifier characterize a dendritic or axonal terminal. A synapse comprises topology with the paired neuron and terminal identifiers, location with terminal coordinates, and geometry with terminal radii. The storage required for the synaptome depends on the number of synapses and storage necessary for a single synapse determined by a synaptic model. I introduce three synaptic models: topologic with topology, point with topology and location, and geometric with topology, location, and geometry. To accommodate for a wide range of variations in the numbers of neurons and synapses reported in the literature, four cases of neurons (30;86;100;138 billion) and three cases of synapses per neuron (1,000;10,000;30,000) are considered with three full and simplified (to reduce storage) synaptic models resulting in total 72 cases of storage estimation. The full(simplified) synaptic model of the entire human brain requires from 0.21(0.14) petabytes (PB) to 28.98(18.63) PB for the topologic model, from 0.57(0.32) PB to 78.66(43.47) PB for the point model, and from 0.69(0.38) PB to 95.22(51.75) PB for the geometric model. The full(simplified) synaptic model of the cortex needs from 86.80(55.80) TB to 2.60(1.67) PB for the topologic model, from 235.60(130.02) TB to 7.07(3.91) PB for the point model, and from 285.20(155.00) TB to 8.56(4.65) PB for the geometric model. The topologic model is sufficient to compute the connectome's topology, but it is still too big to be stored on today's top supercomputers related to neuroscience. Frontier, the world's most powerful supercomputer for 86 billion neurons can handle the nanoscale synaptome in the range of 1,000-10,000 synapses per neuron. To my best knowledge, this is the first big data work attempting to provide storage estimation for the human nanoscale synaptome.

Space-Charge-Limited Current Measurements: A Problematic Technique for Metal Halide Perovskites.

Space-charge-limited current (SCLC) measurements play a crucial role in the electrical characterization of semiconductors, particularly for metal halide perovskites. Accurate reporting and analysis of SCLC are essential for gaining meaningful insights into charge transport and defect density in these systems. Unfortunately, performing SCLC measurements on perovskites is complicated by their mixed electronic-ionic conductivity. This complexity led to SCLC data often being incorrectly analyzed using simplified models unsuitable for these materials and reported without essential information about how the measurements were performed. In light of recently published SCLC data, common challenges in using SCLC measurements on perovskite materials are addressed, and solutions are discussed in this paper. The applicability of the often-used analytical models, the overlooked issues related to the mixed ionic-electronic conductivity of perovskites, and the complexity of creating single-carrier devices are investigated using drift-diffusion simulations. Finally, guidelines for more accurate reporting and improved analysis are provided.

Plastic deformation and damage modeling of AA7075 synthetic 3D microstructure created using generative AI

3D microstructures provide valuable insight into material behavior which is essential in elucidating microstructural phenomena, such as particle morphology and void damage, and consequent macroscopic material response. However, creating 3D microstructures is extremely laborious and expensive, requiring complex microstructural characterization and imaging techniques such as Focussed-Ion Beam based Scanning Electron Microscopy (FIB-SEM) or X-ray Computed Tomography (XCT). To this end, synthetic 3D microstructures were rapidly generated from orthogonal 2D images using SliceGAN, which proved a practical and cost-effective method. In this study, multiple synthetic microstructures of AA7075-O, a complex microstructure of various strengthening precipitates within a softer aluminum matrix, were post-processed, meshed, and modeled for different damage behavior in FEA using advanced constitutive material models. Subsequently, the synthetic and real microstructures were qualitatively and quantitatively analyzed for their elastoplastic deformation and ductile void damage responses.This study illustrates the viability of an integrated AI-FE methodology in studying microstructural micromechanics, demonstrating that synthetic microstructures exhibited a very similar stress-strain response, especially when using a free boundary condition, and comparable stress distribution and void damage, albeit with some discrepancies. Also, it emphasizes the influence of particle morphology on strength and damage, where highly irregular particles play a dual role in increasing strain hardening by restricting matrix flow at the cost of increased ductile damage induced by decohered particles. Lastly, the more advanced FE models, with multiple voiding mechanisms, reduced the discrepancy between real and synthetic microstructures compared to simpler models

Simplified Neural Network-Based Models for Oil Flow Rate Prediction

Available neural network-based models for predicting the oil flow rate (q<sub>o</sub>) in the Niger Delta are not simplified and are developed from limited data sources. The reproducibility of these models is not feasible as the models’ details are not published. This study developed simplified and reproducible three, five, and six-input variables neural-based models for estimating q<sub>o</sub> using 283 datasets from 21 wells across fields in the Niger Delta. The neural-based models were developed using maximum-minimum (max.-min.) normalized and clip-normalized datasets. The performances and the generalizability of the developed models with published datasets were determined using some statistical indices: coefficient of determination (R<sup>2</sup>), mean square error (MSE), root mean square error (RMSE), average relative error (ARE) and average absolute relative error (AARE). The results indicate that the 3-input-based neural models had overall R<sup>2</sup>, MSE, and RMSE values of 0.9689, 9.6185x10<sup>-4 </sup>and 0.0310, respectively, for the max.-min. normalizing method and R<sup>2</sup> of 0.9663, MSE of 5.7986x10<sup>-3</sup> and RMSE of 0.0762 for the clip scaling approach. The 5-input-based models resulted in R<sup>2</sup> of 0.9865, MSE of 5.7790×10<sup>-4</sup> and RMSE of 0.0240 for the max.-min. scaling method and R<sup>2</sup> of 0.9720, MSE of 3.7243x10<sup>-3</sup> and RMSE of 0.0610 for the clip scaling approach. Also, the 6-input-based models had R<sup>2</sup> of 0.9809, MSE of 8.7520x10<sup>-4</sup> and RMSE of 0.0296 for the max.-min. normalizing approach and R<sup>2</sup> of 0.9791, MSE of 3.8859 x 10<sup>-3</sup> and RMSE of 0.0623 for the clip scaling method. Furthermore, the generality performance of the simplified neural-based models resulted in R<sup>2</sup>, RMSE, ARE, and AAPRE of 0.9644, 205.78, 0.0248, and 0.1275, respectively, for the 3-input-based neural model and R<sup>2</sup> of 0.9264, RMSE of 2089.93, ARE of 0.1656 and AARE of 0.2267 for the 6-input-based neural model. The neural-based models predicted q<sub>o</sub> were more comparable to the test datasets than some existing correlations, as the predicted q<sub>o</sub> result was the lowest error indices. Besides, the overall relative importance of the neural-based models’ input variables on q<sub>o</sub> prediction is S>GLR>P<sub>wh</sub>>T/T<sub>sc</sub>>γ<sub>o</sub>>BS&W>γ<sub>g</sub>. The simplified neural-based models performed better than some empirical correlations from the assessment indicators. Therefore, the models should apply as tools for oil flow rate prediction in the Niger Delta fields, as the necessary details to implement the models are made visible.

On a New Cyclic Symmetry Formulation Accounting for Boundaries Undergoing Nonlinear Forces

Abstract Although cyclic symmetry theory was initially developed for linear structures, the introduction of nonlinear forces on internal nodes of the fundamental sector does not affect the methodology. Nevertheless, the method is ill-suited when nonlinear forces are applied at the cyclic boundary. The purpose of this paper is to provide a complement to this theory and to propose a cyclic symmetry formulation for structures undergoing nonlinear forces at their cyclic boundary. A complete nonlinear cyclic formulation for such systems is derived in this work. The advantages of such an approach lies in the reduction of computational costs using the cyclic symmetry properties. The methodology is employed to characterize the dynamics of several mechanical systems. First, it is validated on simplified models of a cyclic system. Two nonlinearities are considered: a one-dimensional friction contact interface and a cubic nonlinearity. Both cases exhibit very different dynamics behaviors, yet, the results obtained with the new strategy are shown to be very accurate. Once the approach is validated, it is employed on a industrial finite element model of turbine bladed disk featuring contact interfaces between the blades' shrouds. The capability of the method to handle large systems is thus demonstrated. For all cases, periodic excitation are applied following either a traveling or standing wave shape for different engines orders.