Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics

Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions.However,material identification is a challenging task,especially when the characteristic of the material is highly nonlinear in nature,as is common in biological tissue.In this work,we identify unknown material properties in continuum solid mechanics via physics-informed neural networks(PINNs).To improve the accuracy and efficiency of PINNs,we develop efficient strategies to nonuniformly sample observational data.We also investigate different approaches to enforce Dirichlet-type boundary conditions(BCs)as soft or hard constraints.Finally,we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space.The estimated material parameters achieve relative errors of less than 1%.As such,this work is relevant to diverse applications,including optimizing structural integrity and developing novel materials.

Fuzzy data envelopment analysis approach based on sample decision making units

The conventional data envelopment analysis （DEA） measures the relative efficiencies of a set of decision making units with exact values of inputs and outputs. In real-world prob- lems, however, inputs and outputs typically have some levels of fuzziness. To analyze a decision making unit （DMU） with fuzzy input/output data, previous studies provided the fuzzy DEA model and proposed an associated evaluating approach. Nonetheless, numerous deficiencies must still be improved, including the α- cut approaches, types of fuzzy numbers, and ranking techniques. Moreover, a fuzzy sample DMU still cannot be evaluated for the Fuzzy DEA model. Therefore, this paper proposes a fuzzy DEA model based on sample decision making unit （FSDEA）. Five eval- uation approaches and the related algorithm and ranking methods are provided to test the fuzzy sample DMU of the FSDEA model. A numerical experiment is used to demonstrate and compare the results with those obtained using alternative approaches.

Data processing of small samples based on grey distance information approach

Data processing of small samples is an important and valuable research problem in the electronic equipment test. Because it is difficult and complex to determine the probability distribution of small samples, it is difficult to use the traditional probability theory to process the samples and assess the degree of uncertainty. Using the grey relational theory and the norm theory, the grey distance information approach, which is based on the grey distance information quantity of a sample and the average grey distance information quantity of the samples, is proposed in this article. The definitions of the grey distance information quantity of a sample and the average grey distance information quantity of the samples, with their characteristics and algorithms, are introduced. The correlative problems, including the algorithm of estimated value, the standard deviation, and the acceptance and rejection criteria of the samples and estimated results, are also proposed. Moreover, the information whitening ratio is introduced to select the weight algorithm and to compare the different samples. Several examples are given to demonstrate the application of the proposed approach. The examples show that the proposed approach, which has no demand for the probability distribution of small samples, is feasible and effective.

Big Data Analytics:Deep Content-Based Prediction with Sampling Perspective

The world of information technology is more than ever being flooded with huge amounts of data,nearly 2.5 quintillion bytes every day.This large stream of data is called big data,and the amount is increasing each day.This research uses a technique called sampling,which selects a representative subset of the data points,manipulates and analyzes this subset to identify patterns and trends in the larger dataset being examined,and finally,creates models.Sampling uses a small proportion of the original data for analysis and model training,so that it is relatively faster while maintaining data integrity and achieving accurate results.Two deep neural networks,AlexNet and DenseNet,were used in this research to test two sampling techniques,namely sampling with replacement and reservoir sampling.The dataset used for this research was divided into three classes:acceptable,flagged as easy,and flagged as hard.The base models were trained with the whole dataset,whereas the other models were trained on 50%of the original dataset.There were four combinations of model and sampling technique.The F-measure for the AlexNet model was 0.807 while that for the DenseNet model was 0.808.Combination 1 was the AlexNet model and sampling with replacement,achieving an average F-measure of 0.8852.Combination 3 was the AlexNet model and reservoir sampling.It had an average F-measure of 0.8545.Combination 2 was the DenseNet model and sampling with replacement,achieving an average F-measure of 0.8017.Finally,combination 4 was the DenseNet model and reservoir sampling.It had an average F-measure of 0.8111.Overall,we conclude that both models trained on a sampled dataset gave equal or better results compared to the base models,which used the whole dataset.

A New Automated Method and Sample Data Flow for Analysis of Volatile Nitrosamines in Human Urine

Volatile nitrosamines (VNAs) are a group of compounds classified as probable (group 2A) and possible (group 2B) carcinogens in humans. Along with certain foods and contaminated drinking water, VNAs are detected at high levels in tobacco products and in both mainstream and side-stream smoke. Our laboratory monitors six urinary VNAs—N-nitrosodimethylamine (NDMA), N-nitrosomethylethylamine (NMEA), N-nitrosodiethylamine (NDEA), N-nitrosopiperidine (NPIP), N-nitrosopyrrolidine (NPYR), and N-nitrosomorpholine (NMOR)—using isotope dilution GC-MS/ MS (QQQ) for large population studies such as the National Health and Nutrition Examination Survey (NHANES). In this paper, we report for the first time a new automated sample preparation method to more efficiently quantitate these VNAs. Automation is done using Hamilton STARTM and Caliper StaccatoTM workstations. This new automated method reduces sample preparation time from 4 hours to 2.5 hours while maintaining precision (inter-run CV < 10%) and accuracy (85% - 111%). More importantly this method increases sample throughput while maintaining a low limit of detection (<10 pg/mL) for all analytes. A streamlined sample data flow was created in parallel to the automated method, in which samples can be tracked from receiving to final LIMs output with minimal human intervention, further minimizing human error in the sample preparation process. This new automated method and the sample data flow are currently applied in bio-monitoring of VNAs in the US non-institutionalized population NHANES 2013-2014 cycle.

A New Approach to Robust Stability Analysis of Sampled-data Control Systems

The lifting technique is now the most popular tool for dealing with sampled-data controlsystems. However, for the robust stability problem the system norm is not preserved by the liftingas expected. And the result is generally conservative under the small gain condition. The reason forthe norm di?erence by the lifting is that the state transition operator in the lifted system is zero inthis case. A new approach to the robust stability analysis is proposed. It is to use an equivalentdiscrete-time uncertainty to replace the continuous-time uncertainty. Then the general discretizedmethod can be used for the robust stability problem, and it is not conservative. Examples are givenin the paper.

Data-Driven Decision-Making for Bank Target Marketing Using Supervised Learning Classifiers on Imbalanced Big Data

Integrating machine learning and data mining is crucial for processing big data and extracting valuable insights to enhance decision-making.However,imbalanced target variables within big data present technical challenges that hinder the performance of supervised learning classifiers on key evaluation metrics,limiting their overall effectiveness.This study presents a comprehensive review of both common and recently developed Supervised Learning Classifiers(SLCs)and evaluates their performance in data-driven decision-making.The evaluation uses various metrics,with a particular focus on the Harmonic Mean Score(F-1 score)on an imbalanced real-world bank target marketing dataset.The findings indicate that grid-search random forest and random-search random forest excel in Precision and area under the curve,while Extreme Gradient Boosting(XGBoost)outperforms other traditional classifiers in terms of F-1 score.Employing oversampling methods to address the imbalanced data shows significant performance improvement in XGBoost,delivering superior results across all metrics,particularly when using the SMOTE variant known as the BorderlineSMOTE2 technique.The study concludes several key factors for effectively addressing the challenges of supervised learning with imbalanced datasets.These factors include the importance of selecting appropriate datasets for training and testing,choosing the right classifiers,employing effective techniques for processing and handling imbalanced datasets,and identifying suitable metrics for performance evaluation.Additionally,factors also entail the utilisation of effective exploratory data analysis in conjunction with visualisation techniques to yield insights conducive to data-driven decision-making.

H_∞ Design for Sampled-Data Systems via Lifting Technique: Conditions and Limitation

The initial motivation of the lifting technique is to solve the H∞control problems. However, the conventional weighted H∞design does not meet the conditions required by lifting, so the result often leads to a misjudgement of the design. Two conditions required by using the lifting technique are presented based on the basic formulae of the lifting. It is pointed out that only the H∞disturbance attenuation problem with no weighting functions can meet these conditions, hence, the application of the lifting technique is quite limited.

EDSUCh:A robust ensemble data summarization method for effective medical diagnosis

Identifying rare patterns for medical diagnosis is a challenging task due to heterogeneity and the volume of data.Data summarization can create a concise version of the original data that can be used for effective diagnosis.In this paper,we propose an ensemble summarization method that combines clustering and sampling to create a summary of the original data to ensure the inclusion of rare patterns.To the best of our knowledge,there has been no such technique available to augment the performance of anomaly detection techniques and simultaneously increase the efficiency of medical diagnosis.The performance of popular anomaly detection algorithms increases significantly in terms of accuracy and computational complexity when the summaries are used.Therefore,the medical diagnosis becomes more effective,and our experimental results reflect that the combination of the proposed summarization scheme and all underlying algorithms used in this paper outperforms the most popular anomaly detection techniques.

Fast Rate Fault Detection Filter for Multirate Sampled-data Systems

This paper focuses on the fast rate fault detection filter (FDF) problem for a class of multirate sampled-data (MSD) systems. A lifting technique is used to convert such an MSD system into a linear time-invariant discrete-time one and an unknown input observer (UIO) is considered as FDF to generate residual. The design of FDF is formulated as an H∞ optimization problem and a solvable condition as well as an optimal solution are derived. The causality of the residual generator can be guaranteed so that the fast rate residual can be implemented via inverse lifting. A numerical example is included to demonstrate the feasibility of the obtained results.

RAD-seq data reveals robust phylogeny and morphological evolutionary history of Rhododendron

Rhododendron is famous for its high ornamental value.However,the genus is taxonomically difficult and the relationships within Rhododendron remain unresolved.In addition,the origin of key morphological characters with high horticulture value need to be explored.Both problems largely hinder utilization of germplasm resources.Most studies attempted to disentangle the phylogeny of Rhododendron,but only used a few genomic markers and lacked large-scale sampling,resulting in low clade support and contradictory phylogenetic signals.Here,we used restriction-site associated DNA sequencing(RAD-seq)data and morphological traits for 144 species of Rhododendron,representing all subgenera and most sections and subsections of this species-rich genus,to decipher its intricate evolutionary history and reconstruct ancestral state.Our results revealed high resolutions at subgenera and section levels of Rhododendron based on RAD-seq data.Both optimal phylogenetic tree and split tree recovered five lineages among Rhododendron.Subg.Therorhodion(cladeⅠ)formed the basal lineage.Subg.Tsutsusi and Azaleastrum formed cladeⅡand had sister relationships.CladeⅢincluded all scaly rhododendron species.Subg.Pentanthera(cladeⅣ)formed a sister group to Subg.Hymenanthes(cladeⅤ).The results of ancestral state reconstruction showed that Rhododendron ancestor was a deciduous woody plant with terminal inflorescence,ten stamens,leaf blade without scales and broadly funnelform corolla with pink or purple color.This study shows significant distinguishability to resolve the evolutionary history of Rhododendron based on high clade support of phylogenetic tree constructed by RAD-seq data.It also provides an example to resolve discordant signals in phylogenetic trees and demonstrates the application feasibility of RAD-seq with large amounts of missing data in deciphering intricate evolutionary relationships.Additionally,the reconstructed ancestral state of six important characters provides insights into the innovation of key characters in Rhododendron.

Sampled-data Observer Design for a Class of Stochastic Nonlinear Systems Based on the Approximate Discrete-time Models

In this paper,we studied the approximate sampleddata observer design for a class of stochastic nonlinear systems.Euler-Maruyama approximation was investigated in this paper because it is the basis of other higher precision numerical methods,and it preserves important structures of the nonlinear systems.Also,the form of Euler-Maruyama model is simple and easy to be calculated.The results provide a reference for sampled-data observer design method for such stochastic nonlinear systems,and may be useful to many practical control applications,such as tracking control in mechanical systems.And the effectiveness of the approach is demonstrated by a simulation example.

FAIR Geoscientific Samples and Data Need International Collaboration

1 Introduction The primary goal of the Deep-time Digital Earth project is to develop an open collaboration and data sharing platform that enables the transition of deep-time geoscientific research to a Big Data driven paradigm.Such an open platform will require the ability to effectively and efficiently access and integrate a wide variety of digital Earth data.

CONTROL CHAOS IN TRANSITION SYSTEM USING SAMPLED-DATA FEEDBACK

The method for controlling chaotic transition system was investigated using sampled- data . The output of chaotic transition system was sampled at a given sampling rate , then the sampled output was used by a feedbacks subsystem to construct a control signal for controlling chaotic transition system to the origin . Numerical simulations are presented to show the effectiveness and feasibility of the developed controller.

Power Analysis and Sample Size Determination for Crossover Trials with Application to Bioequivalence Assessment of Topical Ophthalmic Drugs Using Serial Sampling Pharmacokinetic Data

Objective To develop methods for determining a suitable sample size for bioequivalence assessment of generic topical ophthalmic drugs using crossover design with serial sampling schemes.Methods The power functions of the Fieller-type confidence interval and the asymptotic confidence interval in crossover designs with serial-sampling data are here derived.Simulation studies were conducted to evaluate the derived power functions.Results Simulation studies show that two power functions can provide precise power estimates when normality assumptions are satisfied and yield conservative estimates of power in cases when data are log-normally distributed.The intra-correlation showed a positive correlation with the power of the bioequivalence test.When the expected ratio of the AUCs was less than or equal to 1, the power of the Fieller-type confidence interval was larger than the asymptotic confidence interval.If the expected ratio of the AUCs was larger than 1, the asymptotic confidence interval had greater power.Sample size can be calculated through numerical iteration with the derived power functions.Conclusion The Fieller-type power function and the asymptotic power function can be used to determine sample sizes of crossover trials for bioequivalence assessment of topical ophthalmic drugs.

H_∞ CONTROL FOR SAMPLED-DATA SYSTEMS

This paper presented a tutorial exposition of H ∞ sampled data control, emphasizing the H ∞ discretization which converts the H ∞ sampled data system to an equivalent finite dimensional H ∞ discrete time system. The discretization process involves two steps. First, the original problem is changed into an equivalent infinite dimensional discrete time problem by lifting techniques. Then, further simplification is taken to reduce the problem to an equivalent finite dimensional discrete problem which can be solved by the existing techniques such as state space approach or two riccati method.

Consensus for second-order multi-agent systems with position sampled data

In this paper, the consensus problem with position sampled data for second-order multi-agent systems is investigated.The interaction topology among the agents is depicted by a directed graph. The full-order and reduced-order observers with position sampled data are proposed, by which two kinds of sampled data-based consensus protocols are constructed. With the provided sampled protocols, the consensus convergence analysis of a continuous-time multi-agent system is equivalently transformed into that of a discrete-time system. Then, by using matrix theory and a sampled control analysis method, some sufficient and necessary consensus conditions based on the coupling parameters, spectrum of the Laplacian matrix and sampling period are obtained. While the sampling period tends to zero, our established necessary and sufficient conditions are degenerated to the continuous-time protocol case, which are consistent with the existing result for the continuous-time case. Finally, the effectiveness of our established results is illustrated by a simple simulation example.

Novel Stability Criteria for Sampled-Data Systems With Variable Sampling Periods

This paper is concerned with a novel Lyapunovlike functional approach to the stability of sampled-data systems with variable sampling periods. The Lyapunov-like functional has four striking characters compared to usual ones. First, it is time-dependent. Second, it may be discontinuous. Third, not every term of it is required to be positive definite. Fourth, the Lyapunov functional includes not only the state and the sampled state but also the integral of the state. By using a recently reported inequality to estimate the derivative of this Lyapunov functional, a sampled-interval-dependent stability criterion with reduced conservatism is obtained. The stability criterion is further extended to sampled-data systems with polytopic uncertainties. Finally, three examples are given to illustrate the reduced conservatism of the stability criteria.