Structural Uncertainty Research Articles

Partitioning Uncertainty in Model Predictions from Compartmental Modeling of Global Carbon Cycle

Our comprehension of the real world remains perpetually incomplete, compelling us to rely on models to decipher intricate real-world phenomena. However, these models, at their pinnacle, serve merely as close approximations of the systems they seek to emulate, inherently laden with uncertainty. Therefore, investigating the disparities between observed system behaviors and model-derived predictions is of paramount importance. Although achieving absolute quantification of uncertainty in the model-building process remains challenging, there are avenues for both mitigating and highlighting areas of uncertainty. Central to this study are three key sources of uncertainty, each exerting significant influence: (i) structural uncertainty arising from inadequacies in mathematical formulations within the conceptual models; (ii) scenario uncertainty stemming from our limited foresight or inability to forecast future conditions; and (iii) input factor uncertainty resulting from vaguely defined or estimated input factors. Through uncertainty analysis, this research endeavors to understand these uncertainty domains within compartmental models, which are instrumental in depicting the complexities of the global carbon cycle. The results indicate that parameter uncertainty has the most significant impact on model outputs, followed by structural and scenario uncertainties. Evident deviations between the observed atmospheric CO2 content and simulated data underscore the substantial contribution of certain uncertainties to the overall estimated uncertainty. The conclusions emphasize the need for comprehensive uncertainty quantification to enhance model reliability and the importance of addressing these uncertainties to improve predictions related to global carbon dynamics and inform policy decisions. This paper employs partitioning techniques to discern the contributions of the aforementioned primary sources of uncertainty to the overarching prediction uncertainty.

Structural Uncertainty Due to Fault Timing: A Multimodel Case Study from the Perth Basin.

Faults can fundamentally change a groundwater flow regime and represent a major source of uncertainty in groundwater studies. Much research has been devoted to uncertainty around their location and their barrier-conduit behavior. However, fault timing is one aspect of fault uncertainty that appears to be somewhat overlooked. Many faulted models feature consistent layer offsets, thereby presuming that block faulting has occurred recently and almost instantaneously. Additionally, barrier and/or conduit behavior is often shown to extend vertically through all layers when a fault may in fact terminate well below-ground surface. In this study, we create three plausible geological interpretations for a transect in the Perth Basin. Adjacent boreholes show stratigraphic offsets and thickening which indicate faulting; however, fault timing is unknown. Flow modeling demonstrates that the model with the most recent faulting shows profoundly different flow patterns due to aquifer juxtaposition. Additionally, multiple realizations with stochastically generated parameter sets for layer, fault core, and fault damage zone conductivity show that fault timing influences flow more than layer or fault zone conductivity. Finally, fault conduit behavior that penetrates aquitards has significant implications for transport, while fault barrier behavior has surprisingly little. This research advocates for adequate data collection where faults may cause breaches in aquitards due to layer offsets or conduit behavior in the damage zone. It also promotes the use of multiple geological models to address structural uncertainty, and highlights some of the hurdles in doing so such as computational expense and the availability of seamless geological-flow modeling workflows.

Research on Quantification of Structural Natural Frequency Uncertainty and Finite Element Model Updating Based on Gaussian Processes

During bridge service, material degradation and aging occur, affecting bridge functionality. Bridge health monitoring, crucial for detecting structural damage, includes finite element model modification as a key aspect. Current finite element-based model updating techniques are computationally intensive and lack practicality. Additionally, changes in loading and material property deterioration lead to parameter uncertainty in engineering structures. To enhance computational efficiency and accommodate parameter uncertainty, this study proposes a Gaussian process model-based approach for predicting structural natural frequencies and correcting finite element models. Taking a simply supported beam structure as an example, the elastic modulus and mass density of the structure are sampled by the Sobol sequence. Then, we map the collected samples to the corresponding physical space, substitute them into the finite element model, and calculate the first three natural frequencies of the model. A Gaussian surrogate model was established for the natural frequency of the structure. By analyzing the first three natural frequencies of the simply supported beam, the elastic modulus and mass density of the structure are corrected. The error between the corrected values of elastic modulus and mass density and the calculated values of the finite element model is very small. This study demonstrates that Gaussian process models can improve calculation efficiency, fulfilling the dual objectives of predicting structural natural frequencies and adjusting model parameters.

Development of a multi-layer canopy model for E3SM Land Model with support for heterogeneous computing

The vertical structure of vegetation canopies creates micro-climates. However, the land components of most Earth System Models, including the Energy Exascale Earth System Model (E3SM), typically neglect vertical canopy structure by using a single layer big-leaf representation to simulate water, CO2, and energy exchanges between the land and the atmosphere. In this study, we developed a Multi-Layer Canopy Model for the E3SM Land Model to resolve the micro-climate created by vegetation canopies. The model developed in this study re-implements the CLM-ml_v1 to support heterogeneous computing architectures consisting of CPUs and GPUs and includes three additional optimization-based stomatal conductance models. The use of Portable, Extensible Toolkit for Scientific Computation provides a speedup of 25–50 times on a GPU relative to a CPU. The numerical implementation of the model was verified against CLM-ml_v1 for a month-long simulation using data from the Ameriflux US-University of Michigan Biological Station site. Model structural uncertainty was explored by performing control simulations for five stomatal conductance models that exclude and include the control of plant hydrodynamics (PHD) on photosynthesis. The bias in simulated sensible and latent heat fluxes was lower when PHD was accounted for in the model. Additionally, six idealized simulations were performed to study the impact of three environmental variables (i.e. air temperature, atmospheric CO2, and soil moisture) on canopy processes (i.e. net CO2 assimilation, leaf temperature, and leaf water potential). Increasing air temperature reduced net CO2 assimilation and increased air temperature. Net CO2 assimilation increased at higher atmospheric CO2, while decreasing soil moisture resulted in lower leaf water potential.

Cost-effectiveness analysis of the pediatric 20-valent pneumococcal conjugate vaccine compared with lower-valent alternatives in Argentina

ObjectivesThe 13-valent pneumococcal conjugate vaccine (PCV13) has been recommended for infants in Argentina’s national immunization program (NIP) in a 2 + 1 schedule since 2012. Licensure of the 15-valent vaccine (PCV15) is anticipated soon, and the 20-valent vaccine (PCV20) recently received regulatory approval. This cost-effectiveness analysis examined the public health and economic implications of transitioning from PCV13 to either PCV15 or PCV20 in Argentina’s pediatric NIP. MethodsA decision-analytic Markov model was used with a 10-year time horizon and a 3.0% annual discount rate for costs and benefits. Vaccine effectiveness estimates were derived from Argentinian surveillance data, PCV13 clinical effectiveness and impact studies, and PCV7 efficacy studies. Population, epidemiologic, and economic inputs were obtained from literature and Argentinian-specific data. The study adopted a healthcare system perspective; sensitivity and scenario analyses were conducted to assess input parameters and structural uncertainty. ResultsCompared with PCV13, PCV20 was estimated to avert an additional 7,378, 42,884, and 172,389 cases of invasive pneumococcal disease (IPD), all-cause pneumonia, and all-cause otitis media (OM), respectively, as well as 3,308 deaths, resulting in savings of United States Dollars (USD) 50,973,962 in direct medical costs. Compared with PCV15, PCV20 was also estimated to have greater benefit, averting an additional 6,140, 35,258, and 142,366 cases of IPD, pneumonia, and OM, respectively, as well as 2,624 deaths, resulting in savings of USD 37,697,868 in direct medical costs. PCV20 was associated with a higher quality-adjusted life year gain and a lower cost (i.e., dominance) versus both PCV13 and PCV15. Results remained robust in sensitivity analyses and scenario assessments. ConclusionOver a 10-year horizon, vaccination with PCV20 was expected to be the dominant, cost-saving strategy versus PCV13 and PCV15 in children in Argentina. Policymakers should consider the PCV20 vaccination strategy to achieve the greatest clinical and economic benefit compared with lower-valent options.

Probabilistic analysis of seepage and temperature fields in geothermal extraction process based on discrete fracture network (DFN) model

Enhanced geothermal system is currently the most efficient technology of exploiting geothermal energy from high-temperature rock reservior in deep earth. However, due to the uncertainty of geological structural discontinuities, such as natural or artificial fractures, great challenges are encountered in conducting the precise evaluation of heat extraction within enhanced geothermal system. In this paper, a probability analysis is carried out to incorporate the uncertainty of the fracture network into the analysis of the spatial-time evolution on the seepage and temperature fields, based on a discrete fracture network based modeling scheme developed by the authors. The developed finite element model of the fractured reservior exhibits two-phase structure consisting of rock matrix and fractures, which are practically discretized into triangular elements and zero-thickness elements, respectively. The approach demonstrates a favorable comparison with the results obtained from the thereotical and other numerical solution. Monte Carlo simulation technique is then employed to probabilistically analyze the evolution of coupled thermal–hydraulic behavior, which involves 1000 different realizations considering the uncertainty of fracture structure. The results illustrate that the coefficient of variation of the seepage field decreases from 0 to 0.29 at 1 a to 0.06 to 0.15 at 50 a, averaging at 0.07, and the peak coefficient of variation of the temperature field decreases from 0.61 to 0.52, averaging at 0.27. The uncertainty of the temperature field is varying against time and prominent around the proximity to the advancing cold front, upper and lower boundaries, primarily associated with variations in fractures and constraint of boundary conditions. The existence of highly permeable fractures leads to a pronounced heterogeneity in the seepage and temperature fields within enhanced geothermal system. Furthermore, the importance of taking the uncertainty of the fracture structure into account for geothermal reservoir evaluation is highlighted, to enhance the reliability of numerical modeling for geothermal process prediction.

A hybrid model coupling process-driven and data-driven models for improved real-time flood forecasting

Accurate and reliable incoming flood forecasting is an important prerequisite for flood warning, flood risk analysis and reservoir flood control operation. This paper proposes a hybrid model for real-time flood forecasting that couples process-driven hydrological models (HMs) with data-driven models (DDMs). The generic hybrid model framework adds DDMs as the post-processing procedure for residual correction to the original results of HMs, and considers multiple uncertainties in input data, parameter and model structure simultaneously. The performance of the hybrid model is evaluated comprehensively in terms of deterministic forecast accuracy, interval forecast reliability, and the reliability and sharpness of probabilistic forecast. Taking the multireservoir system at the east Pi River as a study case, the results indicate that: (1) Compared to the benchmark model (ensemble XAJ model), the hybrid model with additional residual analysis show a significant improvement. The average continuous ranked probability score (CRPS) metric values calculated by the Stacking-Hybrid model improved by 71.5 %, 67.0 % and 38.1 % in the three data samples. Furthermore, the adaptability of the Stacking-Hybrid model for residual correction during short-duration intense rainfall events has been validated, with the relative error of the peak discharge improved to within ± 10 %. (2) The Stacking-Hybrid model, which also takes into account structure uncertainty, is able to better exploit the combined advantages and improve the stability of the model performance compared to those that only apply a single DDM. (3) When the number of iterations within the BOA reaches 300, the parameter optimization process is capable to search for the hyperparameters that bring out the best performance of the DDMs. (4) When the ensemble size reaches 200, the uncertainty of HM parameters can be fully defined, and the consumed computational resources can be controlled within an acceptable bound while ensuring stable model performance. Overall, the hybrid model that takes into account multiple sources of uncertainty generates both interval and probabilistic forecast in addition to deterministic forecast, which can provide richer risk information for subsequent flood warning and reservoir operation, making the flood prevention decisions more reliable and scientific.

Buffeting reliability of high-rise bridge tower in mountain area based on CNN-BiLSTM

In recent years, the wind-induced vibration of structures has received a great deal of scholarly attention due to the increasing scale of large structures. In this study, an algorithm that combines a stochastic pseudo excitation method (SPEM), a convolutional neural network (CNN) and a bidirectional long short-term memory network (BiLSTM), named as SPEM-CNN-BiLSTM (SCBL), is proposed. The SCBL is a surrogate model consisting of three different computational modules, in which the SPEM can provide training samples for CNN-BiLSTM (CBL) network architecture, a convolutional layer extracts features of stochastic parameters and a BiLSTM handles time histories of bridge response. The accuracy of the SCBL prediction results is ensured by the set error threshold. The model also accounts for structural uncertainty in the inputs and is adapted during the training step to be more suitable for reliability analysis. According to the output qualified prediction data, the dynamic reliability based on the 99 % threshold is calculated by obtaining its probability density function, and the wind-induced vibration responses of uncertain bridge towers are studied. Firstly, the wind environment of the bridge tower was analyzed, and the average wind speed of 20 m/s among the bridge area was obtained by field measurements, and Computational Fluid Dynamics (CFD). Secondly, the proposed artificial neural network algorithm is applied to bridge jitter reliability analysis and compared with the traditionally recognized methods: the Monte Carlo method (MCM) and the stochastic pseudo excitation method (SPEM). The results of SCBL calculations are closer to the results of MCM than those of other methods. Additionally, the computational efficiency of the method is improved by 40 times over MCM and 2 times over SPEM. Finally, the data generated by the SCBL method will be used for reliability analysis. Uncertainties in structure, wind speed, and yaw angle all contribute to the uncertainty and dispersion of the stochastic response prediction. Among them, the uncertainty in wind speed has the greatest impact on the reliability.

Probabilistic design and optimization of thermal protection system with variable thickness based on non-uniform aerodynamic heating

Thermal Protection System (TPS) is a critical component of space vehicles to protect them from damage by extreme aerothermal heating conditions. The uncertainty of the aerothermal heating conditions, including approaching velocities, atmospheric density, pressure, etc., significantly affects the aerothermal heating imposed on the TPS, vastly changing the initial design conditions. In this study, we developed a new uncertainty quantitative (UQ) analysis method to comprehensively consider all the uncertainty of TPS materials, structures, and aerothermal heating conditions. To address the challenges of a massive amount of input and determined optimization parameters, we first induced the response surface method and Monte Carlo algorithm to produce a large number of analysis samples for Probabilistic Design. Then, the key affecting factors, not all the input design parameters, were chosen for optimization with sequential optimization and reliability assessment (SORA) strategy by a sensitivity analysis. With such improvements, the optimization for UQ analysis becomes practical. We used this new UQ method to analyze the effects of uncertainty of the aerothermal heating conditions on the thermal protection layer. A variable thickness design is proposed to adapt the non-uniform aerothermal heating conditions for the TPS. The results show that significant light-weighting can be achieved without the reliability penalty. The optimized structure also reduces internal temperature gradients and facilitates a more uniform temperature field distribution for the TPS. This study provides a new UQ engineering design approach for the system with many designed parameters.

Differential evolutionary optimization fuzzy entropy for gland segmentation based on breast mammography imaging

ObjectiveThe integration of fuzzy entropy into image segmentation techniques has proven effective in addressing issues related to ambiguous boundaries and uncertainties in complex image structures. This study aims to improve breast mammography image segmentation by optimizing minimum fuzzy entropy. The primary challenges identified are the presence of glandular burrs and irregular edges, as well as premature convergence and local optima in entropy optimization. MethodsWe propose an enhanced differential evolution algorithm combined with fuzzy entropy to address these challenges. This algorithm specifically targets glandular burrs, irregular edges, premature convergence, and local optimal entropy issues. The algorithm's performance was evaluated using breast mammography images representing four types of glands and benchmarked against five state-of-the-art algorithms. ResultsExperimental results demonstrate that the proposed algorithm significantly improves segmentation accuracy compared to the other advanced algorithms. It effectively resolves issues related to glandular burrs, irregular edges, premature convergence, and local optimal entropy, leading to superior segmentation outcomes. ConclusionThe proposed algorithm, which combines an improved differential evolution approach with fuzzy entropy, delivers the best segmentation results for breast gland segmentation. It successfully overcomes the challenges of glandular burrs, irregular edges, premature convergence, and local optimal entropy, thus enhancing breast mammography image segmentation.

Simulation testing performance of ensemble models when catch data are underreported

Abstract Ensemble model use in stock assessment is increasing, yet guidance on construction and an evaluation of performance relative to single models is lacking. Ensemble models can characterize structural uncertainty and avoid the conundrum of selecting a “best” assessment model when alternative models explain observed data equally well. Through simulation, we explore the importance of identifying candidate models for both assessment and short-term forecasts and the consequences of different ensemble weighting methods on estimated quantities. Ensemble performance exceeded a single best model only when the set of candidate models spanned the true model configuration. Accuracy and precision depended on the model weighting scheme, and varied between two case studies investigating the impact of catch accuracy. Information theoretic weighting methods performed well in the case study with accurate catch, while equal weighting performed best when catch was underreported. In both cases, equal weighting produced multimodality. Ensuring that an ensemble spans the true state of nature will be challenging, but we observed that a change in sign of Mohn’s rho across candidate models coincided with the true OM being bounded. Further development of protocols to select an objective and balanced set of candidate models, and diagnostics to assess adequacy of candidates are recommended.

Adaptive cyber-tolerant finite-time frequency control framework for renewable-integrated power system under deception and periodic denial-of-service attacks

This work concentrates on designing and applying an adaptive cyber-tolerant finite-time frequency control framework for smart power systems under state-dependent sensor deception and periodic denial-of-service (DoS) attacks. An adaptive radial-basis function neural network (RBFNN)-based disturbance observer (DO) is designed to estimate undeniable plant disturbances, which includes structural uncertainties and unmodelled dynamics. Then, the DO-based resilient secondary control law based on the adaptive nonlinear sliding mode strategy for the cyber-physical power system (CPPS) is derived to guarantee global uniform asymptotic stability of the parametric error and the selected nonlinear sliding manifold. Furthermore, an in-depth analysis of uniformly ultimately boundedness (UUB) of the estimation error of RBFNN has been demonstrated. Numerical simulation and qualitative assessment have revealed the proficiency of the applied feedback control framework for the undertaken CPPS and a high-degree of cyber-tolerance against malicious attacks.

Accessing Horizon Picking Uncertainty using Seismic Complex Trace Attributes

Many uncertainty sources are linked to the reservoir modeling processes, significantly affecting on all phases of the exploration, development, and production phases of an oil & gas field. Structural uncertainty due to velocity models are commonly considered by taking a range of equiprobable domain conversion velocity models and evaluating the related impact on GRV distributions. In contrast, the seismic interpretation inaccuracy is commonly neglected, because the difficulty in quantifying it. This means that seismic mapping is frequently treated as having no variation or having the intrinsically imprecisions assigned arbitrarily. In this work, we propose an objective approach to evaluate the horizon picking uncertainties, which was based on the complex seismic trace attributes extraction considering a previously mapped reference reflector. In real seismic data, phase distortions may arise from a vast bunch of reasons, such as dispersion, attenuation, bandwidth limitations. Thus, the instantaneous phase attribute can be an indicator of uncertainties associated with seismic reflectors interpretation.

Quantifying structural errors in cloud condensation nuclei activity from reduced representation of aerosol size distributions

Aerosol effects on clouds and radiation are a large source of uncertainty in our understanding of human impacts on the climate system. Uncertainty in aerosol effects results from uncertainty in parameter values, known as parametric uncertainty, and from uncertainty from the model’s structure, known as structural uncertainty. While previous studies have assessed the impact of parametric uncertainty on modeled forcing, structural errors from the numerical representation of particle distributions and their dynamics have not been well quantified. Here we present a framework for quantifying error in aerosol size distributions and cloud condensation nuclei activity, which we apply to the widely used 4-mode version of the Modal Aerosol Module (MAM4). Box model predictions from the MAM4 are evaluated against the Particle Monte Carlo Model for Simulating Aerosol Interactions and Chemistry (PartMC-MOSAIC), a benchmark model that tracks the evolution of individual particles. We show that size distributions simulated by MAM4 diverge from those simulated by PartMC-MOSAIC after only a few hours of aging by condensation and coagulation in polluted conditions, which leads to large errors in modeled cloud condensation nuclei concentrations. We find that differences between MAM4 and PartMC-MOSAIC are largest under polluted conditions, where the size distribution evolves rapidly though aging. These findings indicate that structural error in modeled aerosol properties is a key factor contributing to uncertainty in aerosol forcing.

Application of VIC-WUR model for assessing the spatiotemporal distribution of water availability in anthropogenically-impacted basins

Climate change, rapid increase in population, and urbanization have given rise to over-exploitation and shortage of freshwater resources. Acquiring accurate representations of fresh water availability is therefore crucial to sustainable development. Based on the underlying hydrological processes and storage types, fresh water can be divided into blue and green water components. Hence, quantification of the spatio-temporal distribution of blue and green water requires estimating the components of terrestrial water cycle. In this study, a framework is proposed to evaluate the water scarcity using the blue and green water concept. In this framework, the Wageningen Institute and Research (WUR) version of the Variable Infiltration Capacity Model (VIC) is employed to simulate terrestrial water cycle. Compared to VIC model, VIC-WUR model employs additional modules to account for sectoral water demands, return flows, and groundwater withdrawals, however, very limited number of its applications have been reported so far. The Divandareh-Bijar (DBJ) basin in west of Iran is selected because it has experienced severe anthropogenic alterations in the past three decades. To address precipitation and parameter uncertainty, the VIC-WUR model is separately calibrated for three precipitation datasets. As a part of this framework, the calibrated model is used to simulate blue and green water components and their corresponding scarcity metrics for the first time. According to the results, blue and green water resources in the DBJ are relatively scarce. The results also highlight the importance of considering anthropogenic impacts on the spatiotemporal dynamics of green and blue water resources. Additionally, quantification of the uncertainty in blue and green water components can help produce more reliable estimations for intelligent management of water resources. The ANalysis Of VAriance (ANOVA) method is therefore used to quantify the contribution of three major factors, including precipitation inputs, model parameters, and the interaction of these two, on the uncertainty of calculated water scarcity metrics. Structural uncertainty is implicitly addressed through the use of the modified version of the VIC model. The results indicate seasonality of these contributions for the two metrics under investigation and the differences in relative contribution of different sources to the overall uncertainty. The proposed framework could be employed to identify water stress in various spatiotemporal scales across the globe.

Informing Structural Assumptions for Three State Oncology Cost-Effectiveness Models through Model Efficiency and Fit.

The characteristics and relative strengths and weaknesses of partitioned survival models (PSMs) and state transition models (STMs) for three state oncology cost-effectiveness models have previously been studied. Despite clear and longstanding economic modeling guidelines, more than one structure is rarely presented, and the choice of structure appears correlated more with audience or precedent than disease, decision problem, or available data. One reason may be a lack of guidance and tools available to readily compare measures of internal validity such as the model fit and efficiency of different structures, or sensitivity of results to those choices. To address this gap, methods are presented to evaluate the fit and efficiency of three structures, with an accompanying R software package, psm3mkv. The methods are illustrated by analyzing interim and final analysis datasets of the KEYNOTE-826 randomized controlled trial. At both interim and final analyses, the STM Clock Reset structure provided the best and most efficient fit. Structural uncertainties had been reduced from interim to final analysis. Beyond measures of internal validity, guidelines highlight the importance of reflecting all available data, avoiding model selection purely on the basis of goodness of fit and strongly considering external validity. The method and software allow modelers to more easily evaluate and report model fit and efficiency, examine implicit assumptions, and reveal sensitivities to structural choices.

Active vibration control for flexible towers based on displacement observation and reduced-order controller in modal space: Theory and experiment

Active vibration control is not only suitable but also urgently needed in order to mitigate excessive vibration for dynamic systems such as wind turbine towers. However, there is a challenge of directly observing displacement and developing an efficient reduced-order control strategy. With this in view, a reduced-order controller based on displacement observation is developed for the vibration mitigation of flexible high towers, where the problems of low signal-to-noise ratio (SNR) and intricate acceleration-based control algorithms are eliminated completely. The displacement can be measured by laser or modern videometrics technology. A reduced-order model with an active mass damper (AMD) at the top of the tower is created using modal truncation approach based on modal participation factor (MPF), which successfully preserves the dominant modes of the original structure, and reduces the influence of high-frequency uncertainties. Considering structure uncertainties caused by environmental factors and aging process, an unscented Kalman filter (UKF) is introduced to identify the modal stiffness of the reduced-order model. The present study, using a 5 MW onshore wind turbine as an example, investigates active vibration control under wind and seismic loads and compares it with traditional tuned mass damper (TMD). From a dynamic perspective, the simplified model of wind turbine tower takes the form of a multi-degree-of-freedom series model. Consequently, a six-story steel frame platform has been constructed to experimentally validate the efficacy of the reduced-order controller. According to numerical simulation and laboratory testing, the control effect of the reduced-order controller with a few displacement states as feedback can be utilized as an active control strategy for high-rise flexible towers.

Development of Triphenylmethane Dyes for In Vivo Fluorescence Imaging of Aβ Oligomers.

Detection of amyloid β (Aβ) oligomers, regarded as the most toxic aggregated forms of Aβ, can contribute to the diagnosis and treatment of Alzheimer's disease (AD). Thus, the development of imaging probes for in vivo visualization of Aβ oligomers is crucial. However, the structural uncertainty regarding Aβ oligomers makes it difficult to design imaging probes with high sensitivity to Aβ oligomers against highly aggregated Aβ fibrils. In this study, we developed Aβ oligomer-selective fluorescent probes based on triphenylmethane dyes through screening of commercially available compounds followed by structure-activity relationship (SAR) studies on cyclic or acyclic 4-dialkylamino groups. We synthesized 11 triarylmethane-based Aβ oligomer probe (TAMAOP) derivatives. In vitro evaluation of fluorescence properties, TAMAOP-9, which had bulky 4-diisobutylamino groups introduced into three benzenes of a twisted triphenylmethane backbone, showed marked fluorescence enhancement in the presence of Aβ oligomers and demonstrated high selectivity for Aβ oligomers against Aβ fibrils. In docking studies using the Aβ trimer model, TAMAOP-9 bound to the hydrophobic surface and interacted with the side chain of Phe20. In vitro section staining revealed that TAMAOP-9 could visualize Aβ oligomers in the brains of AD model mice. An in vivo fluorescence imaging study using TAMAOP-9 showed significantly higher fluorescence signals from the brains of AD model mice than those of age-matched wild-type mice, confirmed by ex vivo section observation. These results suggest that TAMAOP-9 is a promising Aβ oligomer-targeting fluorescent probe applicable to in vivo imaging.

Single-Loop Sampling for Estimating Failure-Probability Upper-Bound Function

Under random-interval mixed uncertainties of structures, failure-probability upper-bound function (FPUBF), which varies with the distribution parameters of random inputs, can not only provide the influence of distribution parameters on the failure-probability upper bound (FPUB), but also contribute to decoupling a reliability-based design optimization model. Although FPUBF can be estimated by repeatedly evaluating FPUBs at different distribution parameter realizations, it suffers from unaffordable computational cost resulting from this double-loop framework. To address this issue, this paper proposes a single-loop sampling strategy (SL) to estimate FPUBF at arbitrary realizations in the interested distribution parameter region. Instead of the huge computational cost of a double-loop framework, the SL estimates the entire FPUBF only by one simulation analysis. Moreover, importance sampling (IS) variance reduction technique is introduced, and a single-loop IS probability density function (PDF), or SL-IS-PDF, is constructed to more efficiently estimate FPUBF by reducing the required size of the candidate sample pool. For approximating the optimal SL-IS-PDF and identifying the states of candidate samples efficiently, the double-loop adaptive Kriging model of performance function is introduced to further reduce the number of performance function evaluations. A numerical example and two composite structure examples are employed to verify the accuracy, efficiency, and feasibility of the proposed methods.

Soft Hyperstructures and Their Applications

The real world is full of uncertainties, which we require appropriate mathematical structures to model and handle them. One such structure is the soft set, which can be combined with various algebraic and topological structures. The paper discusses how soft sets and hyperstructures can be combined to create new soft structures that can handle uncertainty and imprecision in algebraic structures. Soft sets are mappings from parameters to subsets of a universal set, and they can model fuzzy concepts. Hyperstructures are generalizations of classical algebraic structures, where the composition of two elements is a set instead of a single element. They can capture complex and diverse phenomena that cannot be modeled by single-valued operations. The paper gives examples of soft structures, such as soft polygroups, soft topological polygroups, soft topological soft polygroups and their applications in mathematics and science. The paper aims to show the usefulness and versatility of soft structures in dealing with uncertainty and imprecision in algebraic structures. We will define the concept of soft topological soft polygroups and examine its characteristics.