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A new method is presented for an application of the Gaussian mixture model (GMM) to a multi-objective robust design optimization (RDO) of planar steel frame structures under aleatory (stochastic) uncertainty in material properties, external loads, and discrete design variables. Uncertainty in the discrete design variables is modeled in the wide range between the smallest and largest values in the catalog of the cross-sectional areas. A weighted sum of Gaussians is statistically trained based on the sampled training data to capture an underlying joint probability distribution function (PDF) of random input variables and the corresponding structural response. A simple regression function for predicting the structural response can be found by extracting the information from a conditional PDF, which is directly derived from the captured joint PDF. A multi-objective RDO problem is formulated with three objective functions, namely, the total mass of the structure, and the mean and variance values of the maximum inter-story drift under some constraints on design strength and serviceability requirements. The optimization problem is solved using a multi-objective genetic algorithm utilizing the trained GMM for calculating the statistical values of objective and constraint functions to obtain Pareto-optimal solutions. Since the three objective functions are highly conflicting, the best trade-off solution is desired and found from the obtained Pareto-optimal solutions by performing fuzzy-based compromise programming. The robustness and feasibility of the proposed method for finding the RDO of planar steel frame structures with discrete variables are demonstrated through two design examples.

A Correction to this paper has been published: https://doi.org/10.1007/s00158-020-02789-9

This paper presents an efficient optimization procedure for solving the reliability-based design optimization (RBDO) problem of structures under aleatory uncertainty in material properties and external loads. To reduce the number of structural analysis calls during the optimization process, mixture models of Gaussian processes (MGPs) are constructed for prediction of structural responses. The MGP is used to expand the application of the Gaussian process model (GPM) to large training sets for well covering the input variable space, significantly reducing the training time, and improving the overall accuracy of the regression models. A large training set of the input variables and associated structural responses is first generated and split into independent subsets of similar training samples using the Gaussian mixture model clustering method. The GPM for each subset is then developed to produce a set of independent GPMs that together define the MGP as their weighted average. The weight vector computed for a specified input variable contains the probability that the input variable belongs to the projection of each subset onto the input variable space. To calculate the failure probabilities and their inverse values required during the process of solving the RBDO problem, a novel saddlepoint approximation is proposed based on the first three cumulants of random variables. The original RBDO problem is replaced by a sequential deterministic optimization (SDO) problem in which the MGPs serve as surrogates for the limit-state functions in probabilistic constraints of the RBDO problem. The SDO problem is strategically solved for exploring a promising region that may contain the optimal solution, improving the accuracy of the MGPs in that region, and producing a reliable solution. Two design examples of a truss and a steel frame demonstrate the efficiency of the proposed optimization procedure.

In this study, responses of rice under drought stress correlating with changes in chemical compositions were examined. Among 20 studied rice cultivars, Q8 was the most tolerant, whereas Q2 was the most susceptible to drought. Total phenols, total flavonoids, and antioxidant activities, and their accumulation in water deficit conditions were proportional to drought resistance levels of rice. In detail, total phenols and total flavonoids in Q8 (65.3 mg gallic acid equivalent (GAE) and 37.8 mg rutin equivalent (RE) were significantly higher than Q2 (33.9 mg GAE/g and 27.4 mg RE/g, respectively) in both control and drought stress groups. Similarly, the antioxidant activities including DPPH radical scavenging, β-carotene bleaching, and lipid peroxidation inhibition in Q8 were also higher than in Q2, and markedly increased in drought stress. In general, contents of individual phenolic acids in Q8 were higher than Q2, and they were significantly increased in drought stress to much greater extents than in Q2. However, p-hydroxybenzoic acid was found uniquely in Q8 cultivars. In addition, only vanillic acid was found in water deficit stress in both drought resistant and susceptible rice, suggesting that this phenolic acid, together with p-hydroxybenzoic acid, may play a key role in drought-tolerance mechanisms of rice. The use of vanillic acid and p-hyroxybenzoic acid, and their derivatives, may be useful to protect rice production against water shortage stress.

This study estimates monthly variation of surface water volume of Thac Mo hydroelectric reservoir (located in South Vietnam), during the 2016–2021 period. Variation of surface water volume is estimated based on variation of surface water extent, derived from Sentinel-1 observations, and variation of surface water level, derived from Jason-3 altimetry data. Except for drought years in 2019 and 2020, surface water extent of Thac Mo reservoir varies in the range 50–100 km2, while its water level varies in the range 202–217 m. Correlation between these two components is high (R = 0.948), as well as correlation between surface water maps derived from Sentinel-1 and free-cloud Sentinel-2 observations (R = 0.98), and correlation between surface water level derived from Jason-3 altimetry data and from in situ measurement (R = 0.99; RMSE = 0.86 m). We showed that water volume of Thac Mo reservoir varies between −0.3 and 0.4 km3 month−1, and it is in a very good agreement with in situ measurement (R = 0.95; RMSE = 0.0682 km3 month−1). This study highlights the advantages in using different types of satellite observations and data for monitoring variation of lakes’ water storage, which is very important for regional hydrological models. Similar research can be applied to monitor lakes in remote areas where in situ measurements are not available, or cannot be accessed freely.

BackgroundEarly detection and localization of myocardial infarction (MI) can reduce the severity of cardiac damage through timely treatment interventions. In recent years, deep learning techniques have shown promise for detecting MI in echocardiographic images. Existing attempts typically formulate this task as classification and rely on a single segmentation model to estimate myocardial segment displacements. However, there has been no examination of how segmentation accuracy affects MI classification performance or the potential benefits of using ensemble learning approaches. Our study investigates this relationship and introduces a robust method that combines features from multiple segmentation models to improve MI classification performance by leveraging ensemble learning.Materials and MethodsOur method combines myocardial segment displacement features from multiple segmentation models, which are then input into a typical classifier to estimate the risk of MI. We validated the proposed approach on two datasets: the public HMC-QU dataset (109 echocardiograms) for training and validation, and an E-Hospital dataset (60 echocardiograms) from a local clinical site in Vietnam for independent testing. Model performance was evaluated based on accuracy, sensitivity, and specificity.ResultsThe proposed approach demonstrated excellent performance in detecting MI. It achieved an F1 score of 0.942, corresponding to an accuracy of 91.4%, a sensitivity of 94.1%, and a specificity of 88.3%. The results showed that the proposed approach outperformed the state-of-the-art feature-based method, which had a precision of 85.2%, a specificity of 70.1%, a sensitivity of 85.9%, an accuracy of 85.5%, and an accuracy of 80.2% on the HMC-QU dataset. On the external validation set, the proposed model still performed well, with an F1 score of 0.8, an accuracy of 76.7%, a sensitivity of 77.8%, and a specificity of 75.0%.ConclusionsOur study demonstrated the ability to accurately predict MI in echocardiograms by combining information from several segmentation models. Further research is necessary to determine its potential use in clinical settings as a tool to assist cardiologists and technicians with objective assessments and reduce dependence on operator subjectivity. Our research codes are available on GitHub athttps://github.com/vinuni-vishc/mi-detection-echo.

Despite its importance in seismic response analysis, solving an inverse problem to identify the cyclic elastoplastic parameters for structural steels using conventional optimization algorithms still demands a substantial computational cost of repeatedly carrying out many nonlinear analyses. The parameters are commonly identified based on experimental measures from a single loading history, leading them to be biased and giving inaccurate predictions of structural behavior under other loading histories. To address these issues, we formulate a multi-objective inverse problem that simultaneously minimizes the error functions representing the differences between simulated responses and those measured experimentally from various cyclic tests of a steel specimen or a structural component. We then propose proximal-exploration multi-objective Bayesian optimization (MOBO) for solving the formulated inverse problem, resulting in an approximate Pareto front of parameters while limiting the number of costly simulations. MOBO sorts an initial Pareto front and constructs Gaussian process (GP) models for the error functions from a training dataset. It then relies on the hypervolume of the current solutions, the GP models, and a proximal exploration surrounding the current best compromise parameters to formulate an acquisition function that guides the improvement of the current solutions intelligently. Two identification examples show that the parameters obtained from the multi-objective inverse problem can reduce the bias induced using a single loading history for identification. The robustness of MOBO as well as a good prediction performance of the best compromise solution of identified parameters are demonstrated.

Bayesian optimization (BO) has become a powerful tool for solving simulation-based engineering optimization problems thanks to its ability to integrate physical and mathematical understandings, consider uncertainty, and address the exploitation-exploration dilemma. Thompson sampling (TS) is a preferred solution for BO to handle the exploitation-exploration trade-off. While it prioritizes exploration by generating and minimizing random sample paths from probabilistic models -- a fundamental ingredient of BO -- TS weakly manages exploitation by gathering information about the true objective function after it obtains new observations. In this work, we improve the exploitation of TS by incorporating the \\(\\)-greedy policy, a well-established selection strategy in reinforcement learning. We first delineate two extremes of TS, namely the generic TS and the sample-average TS. The former promotes exploration, while the latter favors exploitation. We then adopt the \\(\\)-greedy policy to randomly switch between these two extremes. Small and large values of \\(\\) govern exploitation and exploration, respectively. By minimizing two benchmark functions and solving an inverse problem of a steel cantilever beam, we empirically show that \\(\\)-greedy TS equipped with an appropriate \\(\\) is more robust than its two extremes, matching or outperforming the better of the generic TS and the sample-average TS.

Protein–ligand interactions are increasingly profiled at high throughput using affinity selection and massively parallel sequencing. However, these assays do not provide the biophysical parameters that most rigorously quantify molecular interactions. Here we describe a flexible machine learning method, called ProBound, that accurately defines sequence recognition in terms of equilibrium binding constants or kinetic rates. This is achieved using a multi-layered maximum-likelihood framework that models both the molecular interactions and the data generation process. We show that ProBound quantifies transcription factor (TF) behavior with models that predict binding affinity over a range exceeding that of previous resources; captures the impact of DNA modifications and conformational flexibility of multi-TF complexes; and infers specificity directly from in vivo data such as ChIP-seq without peak calling. When coupled with an assay called K D -seq, it determines the absolute affinity of protein–ligand interactions. We also apply ProBound to profile the kinetics of kinase–substrate interactions. ProBound opens new avenues for decoding biological networks and rationally engineering protein–ligand interactions. Protein–ligand binding affinity is predicted quantitatively from sequencing data.

In the modern era of big data, academic institutions, business organizations and government agencies have increasingly needed to deal with a substantial amount of heterogeneous data. It becomes a necessity to develop effective methodologies to extract meaningful insights from this type of data. Among the many methods, mixture modeling is one of the most popular tools and has been successfully adapted to many scientific domains in recent decades. One of its appealing features is the ability to perform data clustering in a well-principled manner. The importance of mixture models is evident in the plethora of publication on the application and theory aspects of mixture modeling in the Statistics and general scientific literature. Fields in which mixture models have been applied with success include economy, astronomy, biology, engineering, psychology, ecology, engineering, computer science, neuroscience among many others in the physical, biological and social science. Our specific contributions to the rich literature of mixture models as follows. The first chapter provides an application of mixture modeling to a complex dataset of solar flares on the surface of Sun. Solar flares are sudden explosions of extremely hot plasma on regions where the Sun's magnetic fields erupt from localized areas known as active regions which are of great interest to physicists. We demonstrate how to explicitly model the heterogeneous patterns of active regions using mixture models. This approach has not yet been pursued in the Space Weather literature at least to our knowledge. Since energetic solar flares are extremely rare events compared to low energy flares which occur orders of magnitude more frequently, statistical inference for this type of data needs to address the data imbalance issue. So another contribution of our work is showing how to deal with the imbalance problem using the Expectation Maximization framework. In the second chapter, we extend an existing identifiability result of well-specified finite mixture models to a setting where the underlying mixture density is of two different kernel families. This setting is motivated by the fact that many datasets in scientific domains typically consist of a signal and a background component. In the latter part of the second chapter, we provide theoretical results of mixture models' behaviors under misspecification. The result begins with the setting of a single Student-t or normal distribution. Then we move to the main result specific to the setting where data population is a mixture of two Student-t distributions but statisticians choose to model as a mixture of two normal distributions. The third chapter utilizes simulation studies to continue the story from the second chapter. Simulation studies are computer experiments that involve creating data by pseudo-random sampling from known probability distributions. A key advantage of simulation studies is that some “truth” (about some parameters of interest) is known from the process of generating the data. It allows us to examine statistical properties such as biases in a relatively straightforward fashion. In this chapter, the bias behaviors of mixture locations and mixing weight are studied for scenarios where biased analytical analysis is difficult to obtain.